Exact research checkpoint — Actual divisor sums and Möbius tables

Actual complete proof evidence: 315 original-HA and independently compiled Lean-checked nodes. Download literal proof bundle; 1841261 bytes; SHA-256 96740bcedad194ebed5066ae03fa20cd922e702ae925b2c85f4ed45649aa0307.

Exact inventory roles: 37 new owned theorems, 24 prior non-admitted research prerequisites, 0 current cross-track prerequisites and 253 inherited Alpha theorems. Support rows are not recounted as new. Alpha v30 remains 3222; Stable remains 432. This page claims complete bundle checks, not ordinary-certificate replay for every theorem. Machine-readable report.

Mathematical boundary: These are constructed divisor-sum and Möbius-table prerequisites, not full Möbius inversion. A divisor mask has S n entries indexed 0 through n, with entry zero forced to zero regardless of F(0). Mobius itself remains positive-domain only. Prime-toggle divisor cancellation and G007 inversion remain open.

Frozen authoring sources

peano-lab/py/peano_lab/library/arithmetic_table_extension_candidate.py · d39d08f7178b526daad51aaf4a75c325f567424bb8ae74906c030f4d72e9e294
peano-lab/py/peano_lab/library/mobius_table_candidate.py · 7631337dd93f4a65e6f74ce9a5129d6701a496aa49969764c0945f4248676fc4
peano-lab/py/peano_lab/library/divisor_mask_candidate.py · 740efabb5cbf6e0c804e901dae423e319c52c86f605ebe2a4ad0bffb033d9543

Exact campaign RFC

New results and actual inherited prerequisites

arithmetic_signed_table_component_prefix_preserved

new owned theorem · read exact theorem evidence

Bundle node 277; exact statement SHA-256 20105d3f53a2e24b0f5aeed262d69f234689717809c937b550936ac03b7a9c94

Exact first-order statement

forall F G pb pc nb nc qb qc mb mc l. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> ((G) = (((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) * S ((((qb) + (qc)) * S ((qb) + (qc)) + ((qc) + (qc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))) + ((((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc))) + (((mb) + (mc)) * S ((mb) + (mc)) + ((mc) + (mc)))))) -> (forall pfp_i_pvs_preserve_positive pfp_a_pvs_preserve_positive. (exists pfp_gap_pvs_preserve_positivebound. pfp_gap_pvs_preserve_positivebound + S (pfp_i_pvs_preserve_positive) = (l)) -> (((exists ff_h_pfp_pvs_preserve_positiveold. ff_h_pfp_pvs_preserve_positiveold + S (pfp_a_pvs_preserve_positive) = S ((S (pfp_i_pvs_preserve_positive)) * pc)) /\ exists ff_q_pfp_pvs_preserve_positiveold. pb = ff_q_pfp_pvs_preserve_positiveold * S ((S (pfp_i_pvs_preserve_positive)) * pc) + (pfp_a_pvs_preserve_positive))) -> (((exists ff_h_pfp_pvs_preserve_positivenew. ff_h_pfp_pvs_preserve_positivenew + S (pfp_a_pvs_preserve_positive) = S ((S (pfp_i_pvs_preserve_positive)) * qc)) /\ exists ff_q_pfp_pvs_preserve_positivenew. qb = ff_q_pfp_pvs_preserve_positivenew * S ((S (pfp_i_pvs_preserve_positive)) * qc) + (pfp_a_pvs_preserve_positive)))) -> (forall pfp_i_pvs_preserve_negative pfp_a_pvs_preserve_negative. (exists pfp_gap_pvs_preserve_negativebound. pfp_gap_pvs_preserve_negativebound + S (pfp_i_pvs_preserve_negative) = (l)) -> (((exists ff_h_pfp_pvs_preserve_negativeold. ff_h_pfp_pvs_preserve_negativeold + S (pfp_a_pvs_preserve_negative) = S ((S (pfp_i_pvs_preserve_negative)) * nc)) /\ exists ff_q_pfp_pvs_preserve_negativeold. nb = ff_q_pfp_pvs_preserve_negativeold * S ((S (pfp_i_pvs_preserve_negative)) * nc) + (pfp_a_pvs_preserve_negative))) -> (((exists ff_h_pfp_pvs_preserve_negativenew. ff_h_pfp_pvs_preserve_negativenew + S (pfp_a_pvs_preserve_negative) = S ((S (pfp_i_pvs_preserve_negative)) * mc)) /\ exists ff_q_pfp_pvs_preserve_negativenew. mb = ff_q_pfp_pvs_preserve_negativenew * S ((S (pfp_i_pvs_preserve_negative)) * mc) + (pfp_a_pvs_preserve_negative)))) -> (forall dst_index_preserve_result dst_first_preserve_result dst_second_preserve_result. (exists pvs_gap_preserve_resultbound. pvs_gap_preserve_resultbound + S (dst_index_preserve_result) = (l)) -> (exists dst_positive_code_preserve_resultfirst dst_positive_scale_preserve_resultfirst dst_negative_code_preserve_resultfirst dst_negative_scale_preserve_resultfirst dst_positive_preserve_resultfirst dst_negative_preserve_resultfirst. (((F) = (((((dst_positive_code_preserve_resultfirst) + (dst_positive_scale_preserve_resultfirst)) * S ((dst_positive_code_preserve_resultfirst) + (dst_positive_scale_preserve_resultfirst)) + ((dst_positive_scale_preserve_resultfirst) + (dst_positive_scale_preserve_resultfirst))) + (((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) * S ((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) + ((dst_negative_scale_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)))) * S ((((dst_positive_code_preserve_resultfirst) + (dst_positive_scale_preserve_resultfirst)) * S ((dst_positive_code_preserve_resultfirst) + (dst_positive_scale_preserve_resultfirst)) + ((dst_positive_scale_preserve_resultfirst) + (dst_positive_scale_preserve_resultfirst))) + (((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) * S ((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) + ((dst_negative_scale_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)))) + ((((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) * S ((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) + ((dst_negative_scale_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst))) + (((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) * S ((dst_negative_code_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)) + ((dst_negative_scale_preserve_resultfirst) + (dst_negative_scale_preserve_resultfirst)))))) /\ (((((exists ff_h_pvs_preserve_resultfirstpositive. ff_h_pvs_preserve_resultfirstpositive + S (dst_positive_preserve_resultfirst) = S ((S (dst_index_preserve_result)) * dst_positive_scale_preserve_resultfirst)) /\ exists ff_q_pvs_preserve_resultfirstpositive. dst_positive_code_preserve_resultfirst = ff_q_pvs_preserve_resultfirstpositive * S ((S (dst_index_preserve_result)) * dst_positive_scale_preserve_resultfirst) + (dst_positive_preserve_resultfirst))) /\ (((((exists ff_h_pvs_preserve_resultfirstnegative. ff_h_pvs_preserve_resultfirstnegative + S (dst_negative_preserve_resultfirst) = S ((S (dst_index_preserve_result)) * dst_negative_scale_preserve_resultfirst)) /\ exists ff_q_pvs_preserve_resultfirstnegative. dst_negative_code_preserve_resultfirst = ff_q_pvs_preserve_resultfirstnegative * S ((S (dst_index_preserve_result)) * dst_negative_scale_preserve_resultfirst) + (dst_negative_preserve_resultfirst))) /\ (exists ge_balance_positive_preserve_resultfirstvalue ge_balance_negative_preserve_resultfirstvalue. (((((dst_first_preserve_result) = 2 * (ge_balance_positive_preserve_resultfirstvalue) /\ (ge_balance_negative_preserve_resultfirstvalue) = 0) \/ exists ge_signed_half_preserve_resultfirstvaluedecode. (((dst_first_preserve_result) = 2 * ge_signed_half_preserve_resultfirstvaluedecode + 1 /\ (ge_balance_positive_preserve_resultfirstvalue) = 0) /\ (ge_balance_negative_preserve_resultfirstvalue) = S ge_signed_half_preserve_resultfirstvaluedecode))) /\ ((dst_positive_preserve_resultfirst) + ge_balance_negative_preserve_resultfirstvalue = (dst_negative_preserve_resultfirst) + ge_balance_positive_preserve_resultfirstvalue))))))))) -> (exists dst_positive_code_preserve_resultsecond dst_positive_scale_preserve_resultsecond dst_negative_code_preserve_resultsecond dst_negative_scale_preserve_resultsecond dst_positive_preserve_resultsecond dst_negative_preserve_resultsecond. (((G) = (((((dst_positive_code_preserve_resultsecond) + (dst_positive_scale_preserve_resultsecond)) * S ((dst_positive_code_preserve_resultsecond) + (dst_positive_scale_preserve_resultsecond)) + ((dst_positive_scale_preserve_resultsecond) + (dst_positive_scale_preserve_resultsecond))) + (((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) * S ((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) + ((dst_negative_scale_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)))) * S ((((dst_positive_code_preserve_resultsecond) + (dst_positive_scale_preserve_resultsecond)) * S ((dst_positive_code_preserve_resultsecond) + (dst_positive_scale_preserve_resultsecond)) + ((dst_positive_scale_preserve_resultsecond) + (dst_positive_scale_preserve_resultsecond))) + (((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) * S ((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) + ((dst_negative_scale_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)))) + ((((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) * S ((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) + ((dst_negative_scale_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond))) + (((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) * S ((dst_negative_code_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)) + ((dst_negative_scale_preserve_resultsecond) + (dst_negative_scale_preserve_resultsecond)))))) /\ (((((exists ff_h_pvs_preserve_resultsecondpositive. ff_h_pvs_preserve_resultsecondpositive + S (dst_positive_preserve_resultsecond) = S ((S (dst_index_preserve_result)) * dst_positive_scale_preserve_resultsecond)) /\ exists ff_q_pvs_preserve_resultsecondpositive. dst_positive_code_preserve_resultsecond = ff_q_pvs_preserve_resultsecondpositive * S ((S (dst_index_preserve_result)) * dst_positive_scale_preserve_resultsecond) + (dst_positive_preserve_resultsecond))) /\ (((((exists ff_h_pvs_preserve_resultsecondnegative. ff_h_pvs_preserve_resultsecondnegative + S (dst_negative_preserve_resultsecond) = S ((S (dst_index_preserve_result)) * dst_negative_scale_preserve_resultsecond)) /\ exists ff_q_pvs_preserve_resultsecondnegative. dst_negative_code_preserve_resultsecond = ff_q_pvs_preserve_resultsecondnegative * S ((S (dst_index_preserve_result)) * dst_negative_scale_preserve_resultsecond) + (dst_negative_preserve_resultsecond))) /\ (exists ge_balance_positive_preserve_resultsecondvalue ge_balance_negative_preserve_resultsecondvalue. (((((dst_second_preserve_result) = 2 * (ge_balance_positive_preserve_resultsecondvalue) /\ (ge_balance_negative_preserve_resultsecondvalue) = 0) \/ exists ge_signed_half_preserve_resultsecondvaluedecode. (((dst_second_preserve_result) = 2 * ge_signed_half_preserve_resultsecondvaluedecode + 1 /\ (ge_balance_positive_preserve_resultsecondvalue) = 0) /\ (ge_balance_negative_preserve_resultsecondvalue) = S ge_signed_half_preserve_resultsecondvaluedecode))) /\ ((dst_positive_preserve_resultsecond) + ge_balance_negative_preserve_resultsecondvalue = (dst_negative_preserve_resultsecond) + ge_balance_positive_preserve_resultsecondvalue))))))))) -> dst_first_preserve_result = dst_second_preserve_result)

arithmetic_signed_table_equal_entry_transport

new owned theorem · read exact theorem evidence

Bundle node 278; exact statement SHA-256 4e04ddcaa4c53c823cce502be3989db78fcddfd56beefffea38691a50260bb68

Exact first-order statement

forall N F G l i z. (exists dst_positive_code_transport_valid dst_positive_scale_transport_valid dst_negative_code_transport_valid dst_negative_scale_transport_valid. (((G) = (((((dst_positive_code_transport_valid) + (dst_positive_scale_transport_valid)) * S ((dst_positive_code_transport_valid) + (dst_positive_scale_transport_valid)) + ((dst_positive_scale_transport_valid) + (dst_positive_scale_transport_valid))) + (((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) * S ((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) + ((dst_negative_scale_transport_valid) + (dst_negative_scale_transport_valid)))) * S ((((dst_positive_code_transport_valid) + (dst_positive_scale_transport_valid)) * S ((dst_positive_code_transport_valid) + (dst_positive_scale_transport_valid)) + ((dst_positive_scale_transport_valid) + (dst_positive_scale_transport_valid))) + (((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) * S ((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) + ((dst_negative_scale_transport_valid) + (dst_negative_scale_transport_valid)))) + ((((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) * S ((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) + ((dst_negative_scale_transport_valid) + (dst_negative_scale_transport_valid))) + (((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) * S ((dst_negative_code_transport_valid) + (dst_negative_scale_transport_valid)) + ((dst_negative_scale_transport_valid) + (dst_negative_scale_transport_valid)))))) /\ (forall dst_index_transport_valid. (exists pvs_le_gap_transport_validdomain. pvs_le_gap_transport_validdomain + (dst_index_transport_valid) = (N)) -> exists dst_positive_transport_valid dst_negative_transport_valid dst_value_transport_valid. ((((exists ff_h_pvs_transport_validentrypositive. ff_h_pvs_transport_validentrypositive + S (dst_positive_transport_valid) = S ((S (dst_index_transport_valid)) * dst_positive_scale_transport_valid)) /\ exists ff_q_pvs_transport_validentrypositive. dst_positive_code_transport_valid = ff_q_pvs_transport_validentrypositive * S ((S (dst_index_transport_valid)) * dst_positive_scale_transport_valid) + (dst_positive_transport_valid))) /\ (((((exists ff_h_pvs_transport_validentrynegative. ff_h_pvs_transport_validentrynegative + S (dst_negative_transport_valid) = S ((S (dst_index_transport_valid)) * dst_negative_scale_transport_valid)) /\ exists ff_q_pvs_transport_validentrynegative. dst_negative_code_transport_valid = ff_q_pvs_transport_validentrynegative * S ((S (dst_index_transport_valid)) * dst_negative_scale_transport_valid) + (dst_negative_transport_valid))) /\ (exists ge_balance_positive_transport_validentryvalue ge_balance_negative_transport_validentryvalue. (((((dst_value_transport_valid) = 2 * (ge_balance_positive_transport_validentryvalue) /\ (ge_balance_negative_transport_validentryvalue) = 0) \/ exists ge_signed_half_transport_validentryvaluedecode. (((dst_value_transport_valid) = 2 * ge_signed_half_transport_validentryvaluedecode + 1 /\ (ge_balance_positive_transport_validentryvalue) = 0) /\ (ge_balance_negative_transport_validentryvalue) = S ge_signed_half_transport_validentryvaluedecode))) /\ ((dst_positive_transport_valid) + ge_balance_negative_transport_validentryvalue = (dst_negative_transport_valid) + ge_balance_positive_transport_validentryvalue))))))))) -> (forall dst_index_transport_prefix dst_first_transport_prefix dst_second_transport_prefix. (exists pvs_gap_transport_prefixbound. pvs_gap_transport_prefixbound + S (dst_index_transport_prefix) = (l)) -> (exists dst_positive_code_transport_prefixfirst dst_positive_scale_transport_prefixfirst dst_negative_code_transport_prefixfirst dst_negative_scale_transport_prefixfirst dst_positive_transport_prefixfirst dst_negative_transport_prefixfirst. (((F) = (((((dst_positive_code_transport_prefixfirst) + (dst_positive_scale_transport_prefixfirst)) * S ((dst_positive_code_transport_prefixfirst) + (dst_positive_scale_transport_prefixfirst)) + ((dst_positive_scale_transport_prefixfirst) + (dst_positive_scale_transport_prefixfirst))) + (((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) * S ((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) + ((dst_negative_scale_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)))) * S ((((dst_positive_code_transport_prefixfirst) + (dst_positive_scale_transport_prefixfirst)) * S ((dst_positive_code_transport_prefixfirst) + (dst_positive_scale_transport_prefixfirst)) + ((dst_positive_scale_transport_prefixfirst) + (dst_positive_scale_transport_prefixfirst))) + (((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) * S ((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) + ((dst_negative_scale_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)))) + ((((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) * S ((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) + ((dst_negative_scale_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst))) + (((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) * S ((dst_negative_code_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)) + ((dst_negative_scale_transport_prefixfirst) + (dst_negative_scale_transport_prefixfirst)))))) /\ (((((exists ff_h_pvs_transport_prefixfirstpositive. ff_h_pvs_transport_prefixfirstpositive + S (dst_positive_transport_prefixfirst) = S ((S (dst_index_transport_prefix)) * dst_positive_scale_transport_prefixfirst)) /\ exists ff_q_pvs_transport_prefixfirstpositive. dst_positive_code_transport_prefixfirst = ff_q_pvs_transport_prefixfirstpositive * S ((S (dst_index_transport_prefix)) * dst_positive_scale_transport_prefixfirst) + (dst_positive_transport_prefixfirst))) /\ (((((exists ff_h_pvs_transport_prefixfirstnegative. ff_h_pvs_transport_prefixfirstnegative + S (dst_negative_transport_prefixfirst) = S ((S (dst_index_transport_prefix)) * dst_negative_scale_transport_prefixfirst)) /\ exists ff_q_pvs_transport_prefixfirstnegative. dst_negative_code_transport_prefixfirst = ff_q_pvs_transport_prefixfirstnegative * S ((S (dst_index_transport_prefix)) * dst_negative_scale_transport_prefixfirst) + (dst_negative_transport_prefixfirst))) /\ (exists ge_balance_positive_transport_prefixfirstvalue ge_balance_negative_transport_prefixfirstvalue. (((((dst_first_transport_prefix) = 2 * (ge_balance_positive_transport_prefixfirstvalue) /\ (ge_balance_negative_transport_prefixfirstvalue) = 0) \/ exists ge_signed_half_transport_prefixfirstvaluedecode. (((dst_first_transport_prefix) = 2 * ge_signed_half_transport_prefixfirstvaluedecode + 1 /\ (ge_balance_positive_transport_prefixfirstvalue) = 0) /\ (ge_balance_negative_transport_prefixfirstvalue) = S ge_signed_half_transport_prefixfirstvaluedecode))) /\ ((dst_positive_transport_prefixfirst) + ge_balance_negative_transport_prefixfirstvalue = (dst_negative_transport_prefixfirst) + ge_balance_positive_transport_prefixfirstvalue))))))))) -> (exists dst_positive_code_transport_prefixsecond dst_positive_scale_transport_prefixsecond dst_negative_code_transport_prefixsecond dst_negative_scale_transport_prefixsecond dst_positive_transport_prefixsecond dst_negative_transport_prefixsecond. (((G) = (((((dst_positive_code_transport_prefixsecond) + (dst_positive_scale_transport_prefixsecond)) * S ((dst_positive_code_transport_prefixsecond) + (dst_positive_scale_transport_prefixsecond)) + ((dst_positive_scale_transport_prefixsecond) + (dst_positive_scale_transport_prefixsecond))) + (((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) * S ((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) + ((dst_negative_scale_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)))) * S ((((dst_positive_code_transport_prefixsecond) + (dst_positive_scale_transport_prefixsecond)) * S ((dst_positive_code_transport_prefixsecond) + (dst_positive_scale_transport_prefixsecond)) + ((dst_positive_scale_transport_prefixsecond) + (dst_positive_scale_transport_prefixsecond))) + (((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) * S ((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) + ((dst_negative_scale_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)))) + ((((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) * S ((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) + ((dst_negative_scale_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond))) + (((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) * S ((dst_negative_code_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)) + ((dst_negative_scale_transport_prefixsecond) + (dst_negative_scale_transport_prefixsecond)))))) /\ (((((exists ff_h_pvs_transport_prefixsecondpositive. ff_h_pvs_transport_prefixsecondpositive + S (dst_positive_transport_prefixsecond) = S ((S (dst_index_transport_prefix)) * dst_positive_scale_transport_prefixsecond)) /\ exists ff_q_pvs_transport_prefixsecondpositive. dst_positive_code_transport_prefixsecond = ff_q_pvs_transport_prefixsecondpositive * S ((S (dst_index_transport_prefix)) * dst_positive_scale_transport_prefixsecond) + (dst_positive_transport_prefixsecond))) /\ (((((exists ff_h_pvs_transport_prefixsecondnegative. ff_h_pvs_transport_prefixsecondnegative + S (dst_negative_transport_prefixsecond) = S ((S (dst_index_transport_prefix)) * dst_negative_scale_transport_prefixsecond)) /\ exists ff_q_pvs_transport_prefixsecondnegative. dst_negative_code_transport_prefixsecond = ff_q_pvs_transport_prefixsecondnegative * S ((S (dst_index_transport_prefix)) * dst_negative_scale_transport_prefixsecond) + (dst_negative_transport_prefixsecond))) /\ (exists ge_balance_positive_transport_prefixsecondvalue ge_balance_negative_transport_prefixsecondvalue. (((((dst_second_transport_prefix) = 2 * (ge_balance_positive_transport_prefixsecondvalue) /\ (ge_balance_negative_transport_prefixsecondvalue) = 0) \/ exists ge_signed_half_transport_prefixsecondvaluedecode. (((dst_second_transport_prefix) = 2 * ge_signed_half_transport_prefixsecondvaluedecode + 1 /\ (ge_balance_positive_transport_prefixsecondvalue) = 0) /\ (ge_balance_negative_transport_prefixsecondvalue) = S ge_signed_half_transport_prefixsecondvaluedecode))) /\ ((dst_positive_transport_prefixsecond) + ge_balance_negative_transport_prefixsecondvalue = (dst_negative_transport_prefixsecond) + ge_balance_positive_transport_prefixsecondvalue))))))))) -> dst_first_transport_prefix = dst_second_transport_prefix) -> (exists pvs_le_gap_transport_domain. pvs_le_gap_transport_domain + (i) = (N)) -> (exists pvs_gap_transport_index. pvs_gap_transport_index + S (i) = (l)) -> (exists dst_positive_code_transport_source dst_positive_scale_transport_source dst_negative_code_transport_source dst_negative_scale_transport_source dst_positive_transport_source dst_negative_transport_source. (((F) = (((((dst_positive_code_transport_source) + (dst_positive_scale_transport_source)) * S ((dst_positive_code_transport_source) + (dst_positive_scale_transport_source)) + ((dst_positive_scale_transport_source) + (dst_positive_scale_transport_source))) + (((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) * S ((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) + ((dst_negative_scale_transport_source) + (dst_negative_scale_transport_source)))) * S ((((dst_positive_code_transport_source) + (dst_positive_scale_transport_source)) * S ((dst_positive_code_transport_source) + (dst_positive_scale_transport_source)) + ((dst_positive_scale_transport_source) + (dst_positive_scale_transport_source))) + (((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) * S ((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) + ((dst_negative_scale_transport_source) + (dst_negative_scale_transport_source)))) + ((((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) * S ((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) + ((dst_negative_scale_transport_source) + (dst_negative_scale_transport_source))) + (((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) * S ((dst_negative_code_transport_source) + (dst_negative_scale_transport_source)) + ((dst_negative_scale_transport_source) + (dst_negative_scale_transport_source)))))) /\ (((((exists ff_h_pvs_transport_sourcepositive. ff_h_pvs_transport_sourcepositive + S (dst_positive_transport_source) = S ((S (i)) * dst_positive_scale_transport_source)) /\ exists ff_q_pvs_transport_sourcepositive. dst_positive_code_transport_source = ff_q_pvs_transport_sourcepositive * S ((S (i)) * dst_positive_scale_transport_source) + (dst_positive_transport_source))) /\ (((((exists ff_h_pvs_transport_sourcenegative. ff_h_pvs_transport_sourcenegative + S (dst_negative_transport_source) = S ((S (i)) * dst_negative_scale_transport_source)) /\ exists ff_q_pvs_transport_sourcenegative. dst_negative_code_transport_source = ff_q_pvs_transport_sourcenegative * S ((S (i)) * dst_negative_scale_transport_source) + (dst_negative_transport_source))) /\ (exists ge_balance_positive_transport_sourcevalue ge_balance_negative_transport_sourcevalue. (((((z) = 2 * (ge_balance_positive_transport_sourcevalue) /\ (ge_balance_negative_transport_sourcevalue) = 0) \/ exists ge_signed_half_transport_sourcevaluedecode. (((z) = 2 * ge_signed_half_transport_sourcevaluedecode + 1 /\ (ge_balance_positive_transport_sourcevalue) = 0) /\ (ge_balance_negative_transport_sourcevalue) = S ge_signed_half_transport_sourcevaluedecode))) /\ ((dst_positive_transport_source) + ge_balance_negative_transport_sourcevalue = (dst_negative_transport_source) + ge_balance_positive_transport_sourcevalue))))))))) -> (exists dst_positive_code_transport_target dst_positive_scale_transport_target dst_negative_code_transport_target dst_negative_scale_transport_target dst_positive_transport_target dst_negative_transport_target. (((G) = (((((dst_positive_code_transport_target) + (dst_positive_scale_transport_target)) * S ((dst_positive_code_transport_target) + (dst_positive_scale_transport_target)) + ((dst_positive_scale_transport_target) + (dst_positive_scale_transport_target))) + (((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) * S ((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) + ((dst_negative_scale_transport_target) + (dst_negative_scale_transport_target)))) * S ((((dst_positive_code_transport_target) + (dst_positive_scale_transport_target)) * S ((dst_positive_code_transport_target) + (dst_positive_scale_transport_target)) + ((dst_positive_scale_transport_target) + (dst_positive_scale_transport_target))) + (((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) * S ((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) + ((dst_negative_scale_transport_target) + (dst_negative_scale_transport_target)))) + ((((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) * S ((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) + ((dst_negative_scale_transport_target) + (dst_negative_scale_transport_target))) + (((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) * S ((dst_negative_code_transport_target) + (dst_negative_scale_transport_target)) + ((dst_negative_scale_transport_target) + (dst_negative_scale_transport_target)))))) /\ (((((exists ff_h_pvs_transport_targetpositive. ff_h_pvs_transport_targetpositive + S (dst_positive_transport_target) = S ((S (i)) * dst_positive_scale_transport_target)) /\ exists ff_q_pvs_transport_targetpositive. dst_positive_code_transport_target = ff_q_pvs_transport_targetpositive * S ((S (i)) * dst_positive_scale_transport_target) + (dst_positive_transport_target))) /\ (((((exists ff_h_pvs_transport_targetnegative. ff_h_pvs_transport_targetnegative + S (dst_negative_transport_target) = S ((S (i)) * dst_negative_scale_transport_target)) /\ exists ff_q_pvs_transport_targetnegative. dst_negative_code_transport_target = ff_q_pvs_transport_targetnegative * S ((S (i)) * dst_negative_scale_transport_target) + (dst_negative_transport_target))) /\ (exists ge_balance_positive_transport_targetvalue ge_balance_negative_transport_targetvalue. (((((z) = 2 * (ge_balance_positive_transport_targetvalue) /\ (ge_balance_negative_transport_targetvalue) = 0) \/ exists ge_signed_half_transport_targetvaluedecode. (((z) = 2 * ge_signed_half_transport_targetvaluedecode + 1 /\ (ge_balance_positive_transport_targetvalue) = 0) /\ (ge_balance_negative_transport_targetvalue) = S ge_signed_half_transport_targetvaluedecode))) /\ ((dst_positive_transport_target) + ge_balance_negative_transport_targetvalue = (dst_negative_transport_target) + ge_balance_positive_transport_targetvalue)))))))))

arithmetic_signed_table_extend_at

new owned theorem · read exact theorem evidence

Bundle node 279; exact statement SHA-256 8315f86e7a5f4cd47a5320566ce9aa00d52e4873f5dca8da2f26da8662040eb5

Exact first-order statement

forall N F l z. (exists dst_positive_code_extend_input dst_positive_scale_extend_input dst_negative_code_extend_input dst_negative_scale_extend_input. (((F) = (((((dst_positive_code_extend_input) + (dst_positive_scale_extend_input)) * S ((dst_positive_code_extend_input) + (dst_positive_scale_extend_input)) + ((dst_positive_scale_extend_input) + (dst_positive_scale_extend_input))) + (((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) * S ((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) + ((dst_negative_scale_extend_input) + (dst_negative_scale_extend_input)))) * S ((((dst_positive_code_extend_input) + (dst_positive_scale_extend_input)) * S ((dst_positive_code_extend_input) + (dst_positive_scale_extend_input)) + ((dst_positive_scale_extend_input) + (dst_positive_scale_extend_input))) + (((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) * S ((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) + ((dst_negative_scale_extend_input) + (dst_negative_scale_extend_input)))) + ((((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) * S ((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) + ((dst_negative_scale_extend_input) + (dst_negative_scale_extend_input))) + (((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) * S ((dst_negative_code_extend_input) + (dst_negative_scale_extend_input)) + ((dst_negative_scale_extend_input) + (dst_negative_scale_extend_input)))))) /\ (forall dst_index_extend_input. (exists pvs_le_gap_extend_inputdomain. pvs_le_gap_extend_inputdomain + (dst_index_extend_input) = (N)) -> exists dst_positive_extend_input dst_negative_extend_input dst_value_extend_input. ((((exists ff_h_pvs_extend_inputentrypositive. ff_h_pvs_extend_inputentrypositive + S (dst_positive_extend_input) = S ((S (dst_index_extend_input)) * dst_positive_scale_extend_input)) /\ exists ff_q_pvs_extend_inputentrypositive. dst_positive_code_extend_input = ff_q_pvs_extend_inputentrypositive * S ((S (dst_index_extend_input)) * dst_positive_scale_extend_input) + (dst_positive_extend_input))) /\ (((((exists ff_h_pvs_extend_inputentrynegative. ff_h_pvs_extend_inputentrynegative + S (dst_negative_extend_input) = S ((S (dst_index_extend_input)) * dst_negative_scale_extend_input)) /\ exists ff_q_pvs_extend_inputentrynegative. dst_negative_code_extend_input = ff_q_pvs_extend_inputentrynegative * S ((S (dst_index_extend_input)) * dst_negative_scale_extend_input) + (dst_negative_extend_input))) /\ (exists ge_balance_positive_extend_inputentryvalue ge_balance_negative_extend_inputentryvalue. (((((dst_value_extend_input) = 2 * (ge_balance_positive_extend_inputentryvalue) /\ (ge_balance_negative_extend_inputentryvalue) = 0) \/ exists ge_signed_half_extend_inputentryvaluedecode. (((dst_value_extend_input) = 2 * ge_signed_half_extend_inputentryvaluedecode + 1 /\ (ge_balance_positive_extend_inputentryvalue) = 0) /\ (ge_balance_negative_extend_inputentryvalue) = S ge_signed_half_extend_inputentryvaluedecode))) /\ ((dst_positive_extend_input) + ge_balance_negative_extend_inputentryvalue = (dst_negative_extend_input) + ge_balance_positive_extend_inputentryvalue))))))))) -> exists G. (((exists dst_positive_code_extend_outputtable dst_positive_scale_extend_outputtable dst_negative_code_extend_outputtable dst_negative_scale_extend_outputtable. (((G) = (((((dst_positive_code_extend_outputtable) + (dst_positive_scale_extend_outputtable)) * S ((dst_positive_code_extend_outputtable) + (dst_positive_scale_extend_outputtable)) + ((dst_positive_scale_extend_outputtable) + (dst_positive_scale_extend_outputtable))) + (((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) * S ((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) + ((dst_negative_scale_extend_outputtable) + (dst_negative_scale_extend_outputtable)))) * S ((((dst_positive_code_extend_outputtable) + (dst_positive_scale_extend_outputtable)) * S ((dst_positive_code_extend_outputtable) + (dst_positive_scale_extend_outputtable)) + ((dst_positive_scale_extend_outputtable) + (dst_positive_scale_extend_outputtable))) + (((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) * S ((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) + ((dst_negative_scale_extend_outputtable) + (dst_negative_scale_extend_outputtable)))) + ((((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) * S ((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) + ((dst_negative_scale_extend_outputtable) + (dst_negative_scale_extend_outputtable))) + (((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) * S ((dst_negative_code_extend_outputtable) + (dst_negative_scale_extend_outputtable)) + ((dst_negative_scale_extend_outputtable) + (dst_negative_scale_extend_outputtable)))))) /\ (forall dst_index_extend_outputtable. (exists pvs_le_gap_extend_outputtabledomain. pvs_le_gap_extend_outputtabledomain + (dst_index_extend_outputtable) = (l)) -> exists dst_positive_extend_outputtable dst_negative_extend_outputtable dst_value_extend_outputtable. ((((exists ff_h_pvs_extend_outputtableentrypositive. ff_h_pvs_extend_outputtableentrypositive + S (dst_positive_extend_outputtable) = S ((S (dst_index_extend_outputtable)) * dst_positive_scale_extend_outputtable)) /\ exists ff_q_pvs_extend_outputtableentrypositive. dst_positive_code_extend_outputtable = ff_q_pvs_extend_outputtableentrypositive * S ((S (dst_index_extend_outputtable)) * dst_positive_scale_extend_outputtable) + (dst_positive_extend_outputtable))) /\ (((((exists ff_h_pvs_extend_outputtableentrynegative. ff_h_pvs_extend_outputtableentrynegative + S (dst_negative_extend_outputtable) = S ((S (dst_index_extend_outputtable)) * dst_negative_scale_extend_outputtable)) /\ exists ff_q_pvs_extend_outputtableentrynegative. dst_negative_code_extend_outputtable = ff_q_pvs_extend_outputtableentrynegative * S ((S (dst_index_extend_outputtable)) * dst_negative_scale_extend_outputtable) + (dst_negative_extend_outputtable))) /\ (exists ge_balance_positive_extend_outputtableentryvalue ge_balance_negative_extend_outputtableentryvalue. (((((dst_value_extend_outputtable) = 2 * (ge_balance_positive_extend_outputtableentryvalue) /\ (ge_balance_negative_extend_outputtableentryvalue) = 0) \/ exists ge_signed_half_extend_outputtableentryvaluedecode. (((dst_value_extend_outputtable) = 2 * ge_signed_half_extend_outputtableentryvaluedecode + 1 /\ (ge_balance_positive_extend_outputtableentryvalue) = 0) /\ (ge_balance_negative_extend_outputtableentryvalue) = S ge_signed_half_extend_outputtableentryvaluedecode))) /\ ((dst_positive_extend_outputtable) + ge_balance_negative_extend_outputtableentryvalue = (dst_negative_extend_outputtable) + ge_balance_positive_extend_outputtableentryvalue))))))))) /\ (((forall dst_index_extend_outputprefix dst_first_extend_outputprefix dst_second_extend_outputprefix. (exists pvs_gap_extend_outputprefixbound. pvs_gap_extend_outputprefixbound + S (dst_index_extend_outputprefix) = (l)) -> (exists dst_positive_code_extend_outputprefixfirst dst_positive_scale_extend_outputprefixfirst dst_negative_code_extend_outputprefixfirst dst_negative_scale_extend_outputprefixfirst dst_positive_extend_outputprefixfirst dst_negative_extend_outputprefixfirst. (((F) = (((((dst_positive_code_extend_outputprefixfirst) + (dst_positive_scale_extend_outputprefixfirst)) * S ((dst_positive_code_extend_outputprefixfirst) + (dst_positive_scale_extend_outputprefixfirst)) + ((dst_positive_scale_extend_outputprefixfirst) + (dst_positive_scale_extend_outputprefixfirst))) + (((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) * S ((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) + ((dst_negative_scale_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)))) * S ((((dst_positive_code_extend_outputprefixfirst) + (dst_positive_scale_extend_outputprefixfirst)) * S ((dst_positive_code_extend_outputprefixfirst) + (dst_positive_scale_extend_outputprefixfirst)) + ((dst_positive_scale_extend_outputprefixfirst) + (dst_positive_scale_extend_outputprefixfirst))) + (((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) * S ((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) + ((dst_negative_scale_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)))) + ((((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) * S ((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) + ((dst_negative_scale_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst))) + (((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) * S ((dst_negative_code_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)) + ((dst_negative_scale_extend_outputprefixfirst) + (dst_negative_scale_extend_outputprefixfirst)))))) /\ (((((exists ff_h_pvs_extend_outputprefixfirstpositive. ff_h_pvs_extend_outputprefixfirstpositive + S (dst_positive_extend_outputprefixfirst) = S ((S (dst_index_extend_outputprefix)) * dst_positive_scale_extend_outputprefixfirst)) /\ exists ff_q_pvs_extend_outputprefixfirstpositive. dst_positive_code_extend_outputprefixfirst = ff_q_pvs_extend_outputprefixfirstpositive * S ((S (dst_index_extend_outputprefix)) * dst_positive_scale_extend_outputprefixfirst) + (dst_positive_extend_outputprefixfirst))) /\ (((((exists ff_h_pvs_extend_outputprefixfirstnegative. ff_h_pvs_extend_outputprefixfirstnegative + S (dst_negative_extend_outputprefixfirst) = S ((S (dst_index_extend_outputprefix)) * dst_negative_scale_extend_outputprefixfirst)) /\ exists ff_q_pvs_extend_outputprefixfirstnegative. dst_negative_code_extend_outputprefixfirst = ff_q_pvs_extend_outputprefixfirstnegative * S ((S (dst_index_extend_outputprefix)) * dst_negative_scale_extend_outputprefixfirst) + (dst_negative_extend_outputprefixfirst))) /\ (exists ge_balance_positive_extend_outputprefixfirstvalue ge_balance_negative_extend_outputprefixfirstvalue. (((((dst_first_extend_outputprefix) = 2 * (ge_balance_positive_extend_outputprefixfirstvalue) /\ (ge_balance_negative_extend_outputprefixfirstvalue) = 0) \/ exists ge_signed_half_extend_outputprefixfirstvaluedecode. (((dst_first_extend_outputprefix) = 2 * ge_signed_half_extend_outputprefixfirstvaluedecode + 1 /\ (ge_balance_positive_extend_outputprefixfirstvalue) = 0) /\ (ge_balance_negative_extend_outputprefixfirstvalue) = S ge_signed_half_extend_outputprefixfirstvaluedecode))) /\ ((dst_positive_extend_outputprefixfirst) + ge_balance_negative_extend_outputprefixfirstvalue = (dst_negative_extend_outputprefixfirst) + ge_balance_positive_extend_outputprefixfirstvalue))))))))) -> (exists dst_positive_code_extend_outputprefixsecond dst_positive_scale_extend_outputprefixsecond dst_negative_code_extend_outputprefixsecond dst_negative_scale_extend_outputprefixsecond dst_positive_extend_outputprefixsecond dst_negative_extend_outputprefixsecond. (((G) = (((((dst_positive_code_extend_outputprefixsecond) + (dst_positive_scale_extend_outputprefixsecond)) * S ((dst_positive_code_extend_outputprefixsecond) + (dst_positive_scale_extend_outputprefixsecond)) + ((dst_positive_scale_extend_outputprefixsecond) + (dst_positive_scale_extend_outputprefixsecond))) + (((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) * S ((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) + ((dst_negative_scale_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)))) * S ((((dst_positive_code_extend_outputprefixsecond) + (dst_positive_scale_extend_outputprefixsecond)) * S ((dst_positive_code_extend_outputprefixsecond) + (dst_positive_scale_extend_outputprefixsecond)) + ((dst_positive_scale_extend_outputprefixsecond) + (dst_positive_scale_extend_outputprefixsecond))) + (((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) * S ((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) + ((dst_negative_scale_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)))) + ((((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) * S ((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) + ((dst_negative_scale_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond))) + (((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) * S ((dst_negative_code_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)) + ((dst_negative_scale_extend_outputprefixsecond) + (dst_negative_scale_extend_outputprefixsecond)))))) /\ (((((exists ff_h_pvs_extend_outputprefixsecondpositive. ff_h_pvs_extend_outputprefixsecondpositive + S (dst_positive_extend_outputprefixsecond) = S ((S (dst_index_extend_outputprefix)) * dst_positive_scale_extend_outputprefixsecond)) /\ exists ff_q_pvs_extend_outputprefixsecondpositive. dst_positive_code_extend_outputprefixsecond = ff_q_pvs_extend_outputprefixsecondpositive * S ((S (dst_index_extend_outputprefix)) * dst_positive_scale_extend_outputprefixsecond) + (dst_positive_extend_outputprefixsecond))) /\ (((((exists ff_h_pvs_extend_outputprefixsecondnegative. ff_h_pvs_extend_outputprefixsecondnegative + S (dst_negative_extend_outputprefixsecond) = S ((S (dst_index_extend_outputprefix)) * dst_negative_scale_extend_outputprefixsecond)) /\ exists ff_q_pvs_extend_outputprefixsecondnegative. dst_negative_code_extend_outputprefixsecond = ff_q_pvs_extend_outputprefixsecondnegative * S ((S (dst_index_extend_outputprefix)) * dst_negative_scale_extend_outputprefixsecond) + (dst_negative_extend_outputprefixsecond))) /\ (exists ge_balance_positive_extend_outputprefixsecondvalue ge_balance_negative_extend_outputprefixsecondvalue. (((((dst_second_extend_outputprefix) = 2 * (ge_balance_positive_extend_outputprefixsecondvalue) /\ (ge_balance_negative_extend_outputprefixsecondvalue) = 0) \/ exists ge_signed_half_extend_outputprefixsecondvaluedecode. (((dst_second_extend_outputprefix) = 2 * ge_signed_half_extend_outputprefixsecondvaluedecode + 1 /\ (ge_balance_positive_extend_outputprefixsecondvalue) = 0) /\ (ge_balance_negative_extend_outputprefixsecondvalue) = S ge_signed_half_extend_outputprefixsecondvaluedecode))) /\ ((dst_positive_extend_outputprefixsecond) + ge_balance_negative_extend_outputprefixsecondvalue = (dst_negative_extend_outputprefixsecond) + ge_balance_positive_extend_outputprefixsecondvalue))))))))) -> dst_first_extend_outputprefix = dst_second_extend_outputprefix) /\ (exists dst_positive_code_extend_outputlast dst_positive_scale_extend_outputlast dst_negative_code_extend_outputlast dst_negative_scale_extend_outputlast dst_positive_extend_outputlast dst_negative_extend_outputlast. (((G) = (((((dst_positive_code_extend_outputlast) + (dst_positive_scale_extend_outputlast)) * S ((dst_positive_code_extend_outputlast) + (dst_positive_scale_extend_outputlast)) + ((dst_positive_scale_extend_outputlast) + (dst_positive_scale_extend_outputlast))) + (((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) * S ((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) + ((dst_negative_scale_extend_outputlast) + (dst_negative_scale_extend_outputlast)))) * S ((((dst_positive_code_extend_outputlast) + (dst_positive_scale_extend_outputlast)) * S ((dst_positive_code_extend_outputlast) + (dst_positive_scale_extend_outputlast)) + ((dst_positive_scale_extend_outputlast) + (dst_positive_scale_extend_outputlast))) + (((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) * S ((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) + ((dst_negative_scale_extend_outputlast) + (dst_negative_scale_extend_outputlast)))) + ((((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) * S ((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) + ((dst_negative_scale_extend_outputlast) + (dst_negative_scale_extend_outputlast))) + (((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) * S ((dst_negative_code_extend_outputlast) + (dst_negative_scale_extend_outputlast)) + ((dst_negative_scale_extend_outputlast) + (dst_negative_scale_extend_outputlast)))))) /\ (((((exists ff_h_pvs_extend_outputlastpositive. ff_h_pvs_extend_outputlastpositive + S (dst_positive_extend_outputlast) = S ((S (l)) * dst_positive_scale_extend_outputlast)) /\ exists ff_q_pvs_extend_outputlastpositive. dst_positive_code_extend_outputlast = ff_q_pvs_extend_outputlastpositive * S ((S (l)) * dst_positive_scale_extend_outputlast) + (dst_positive_extend_outputlast))) /\ (((((exists ff_h_pvs_extend_outputlastnegative. ff_h_pvs_extend_outputlastnegative + S (dst_negative_extend_outputlast) = S ((S (l)) * dst_negative_scale_extend_outputlast)) /\ exists ff_q_pvs_extend_outputlastnegative. dst_negative_code_extend_outputlast = ff_q_pvs_extend_outputlastnegative * S ((S (l)) * dst_negative_scale_extend_outputlast) + (dst_negative_extend_outputlast))) /\ (exists ge_balance_positive_extend_outputlastvalue ge_balance_negative_extend_outputlastvalue. (((((z) = 2 * (ge_balance_positive_extend_outputlastvalue) /\ (ge_balance_negative_extend_outputlastvalue) = 0) \/ exists ge_signed_half_extend_outputlastvaluedecode. (((z) = 2 * ge_signed_half_extend_outputlastvaluedecode + 1 /\ (ge_balance_positive_extend_outputlastvalue) = 0) /\ (ge_balance_negative_extend_outputlastvalue) = S ge_signed_half_extend_outputlastvaluedecode))) /\ ((dst_positive_extend_outputlast) + ge_balance_negative_extend_outputlastvalue = (dst_negative_extend_outputlast) + ge_balance_positive_extend_outputlastvalue)))))))))))))

arithmetic_signed_table_append

new owned theorem · read exact theorem evidence

Bundle node 280; exact statement SHA-256 ec6557a7add5837044f6aedc005d234d2b8350490facee08eac8d5e371992d6f

Exact first-order statement

forall N F z. (exists dst_positive_code_append_input dst_positive_scale_append_input dst_negative_code_append_input dst_negative_scale_append_input. (((F) = (((((dst_positive_code_append_input) + (dst_positive_scale_append_input)) * S ((dst_positive_code_append_input) + (dst_positive_scale_append_input)) + ((dst_positive_scale_append_input) + (dst_positive_scale_append_input))) + (((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input)))) * S ((((dst_positive_code_append_input) + (dst_positive_scale_append_input)) * S ((dst_positive_code_append_input) + (dst_positive_scale_append_input)) + ((dst_positive_scale_append_input) + (dst_positive_scale_append_input))) + (((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input)))) + ((((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input))) + (((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input)))))) /\ (forall dst_index_append_input. (exists pvs_le_gap_append_inputdomain. pvs_le_gap_append_inputdomain + (dst_index_append_input) = (N)) -> exists dst_positive_append_input dst_negative_append_input dst_value_append_input. ((((exists ff_h_pvs_append_inputentrypositive. ff_h_pvs_append_inputentrypositive + S (dst_positive_append_input) = S ((S (dst_index_append_input)) * dst_positive_scale_append_input)) /\ exists ff_q_pvs_append_inputentrypositive. dst_positive_code_append_input = ff_q_pvs_append_inputentrypositive * S ((S (dst_index_append_input)) * dst_positive_scale_append_input) + (dst_positive_append_input))) /\ (((((exists ff_h_pvs_append_inputentrynegative. ff_h_pvs_append_inputentrynegative + S (dst_negative_append_input) = S ((S (dst_index_append_input)) * dst_negative_scale_append_input)) /\ exists ff_q_pvs_append_inputentrynegative. dst_negative_code_append_input = ff_q_pvs_append_inputentrynegative * S ((S (dst_index_append_input)) * dst_negative_scale_append_input) + (dst_negative_append_input))) /\ (exists ge_balance_positive_append_inputentryvalue ge_balance_negative_append_inputentryvalue. (((((dst_value_append_input) = 2 * (ge_balance_positive_append_inputentryvalue) /\ (ge_balance_negative_append_inputentryvalue) = 0) \/ exists ge_signed_half_append_inputentryvaluedecode. (((dst_value_append_input) = 2 * ge_signed_half_append_inputentryvaluedecode + 1 /\ (ge_balance_positive_append_inputentryvalue) = 0) /\ (ge_balance_negative_append_inputentryvalue) = S ge_signed_half_append_inputentryvaluedecode))) /\ ((dst_positive_append_input) + ge_balance_negative_append_inputentryvalue = (dst_negative_append_input) + ge_balance_positive_append_inputentryvalue))))))))) -> exists G. (((exists dst_positive_code_append_outputtable dst_positive_scale_append_outputtable dst_negative_code_append_outputtable dst_negative_scale_append_outputtable. (((G) = (((((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) * S ((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) + ((dst_positive_scale_append_outputtable) + (dst_positive_scale_append_outputtable))) + (((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable)))) * S ((((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) * S ((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) + ((dst_positive_scale_append_outputtable) + (dst_positive_scale_append_outputtable))) + (((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable)))) + ((((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable))) + (((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable)))))) /\ (forall dst_index_append_outputtable. (exists pvs_le_gap_append_outputtabledomain. pvs_le_gap_append_outputtabledomain + (dst_index_append_outputtable) = (S N)) -> exists dst_positive_append_outputtable dst_negative_append_outputtable dst_value_append_outputtable. ((((exists ff_h_pvs_append_outputtableentrypositive. ff_h_pvs_append_outputtableentrypositive + S (dst_positive_append_outputtable) = S ((S (dst_index_append_outputtable)) * dst_positive_scale_append_outputtable)) /\ exists ff_q_pvs_append_outputtableentrypositive. dst_positive_code_append_outputtable = ff_q_pvs_append_outputtableentrypositive * S ((S (dst_index_append_outputtable)) * dst_positive_scale_append_outputtable) + (dst_positive_append_outputtable))) /\ (((((exists ff_h_pvs_append_outputtableentrynegative. ff_h_pvs_append_outputtableentrynegative + S (dst_negative_append_outputtable) = S ((S (dst_index_append_outputtable)) * dst_negative_scale_append_outputtable)) /\ exists ff_q_pvs_append_outputtableentrynegative. dst_negative_code_append_outputtable = ff_q_pvs_append_outputtableentrynegative * S ((S (dst_index_append_outputtable)) * dst_negative_scale_append_outputtable) + (dst_negative_append_outputtable))) /\ (exists ge_balance_positive_append_outputtableentryvalue ge_balance_negative_append_outputtableentryvalue. (((((dst_value_append_outputtable) = 2 * (ge_balance_positive_append_outputtableentryvalue) /\ (ge_balance_negative_append_outputtableentryvalue) = 0) \/ exists ge_signed_half_append_outputtableentryvaluedecode. (((dst_value_append_outputtable) = 2 * ge_signed_half_append_outputtableentryvaluedecode + 1 /\ (ge_balance_positive_append_outputtableentryvalue) = 0) /\ (ge_balance_negative_append_outputtableentryvalue) = S ge_signed_half_append_outputtableentryvaluedecode))) /\ ((dst_positive_append_outputtable) + ge_balance_negative_append_outputtableentryvalue = (dst_negative_append_outputtable) + ge_balance_positive_append_outputtableentryvalue))))))))) /\ (((forall dst_index_append_outputprefix dst_first_append_outputprefix dst_second_append_outputprefix. (exists pvs_gap_append_outputprefixbound. pvs_gap_append_outputprefixbound + S (dst_index_append_outputprefix) = (S N)) -> (exists dst_positive_code_append_outputprefixfirst dst_positive_scale_append_outputprefixfirst dst_negative_code_append_outputprefixfirst dst_negative_scale_append_outputprefixfirst dst_positive_append_outputprefixfirst dst_negative_append_outputprefixfirst. (((F) = (((((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) * S ((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) + ((dst_positive_scale_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst))) + (((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)))) * S ((((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) * S ((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) + ((dst_positive_scale_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst))) + (((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)))) + ((((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst))) + (((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)))))) /\ (((((exists ff_h_pvs_append_outputprefixfirstpositive. ff_h_pvs_append_outputprefixfirstpositive + S (dst_positive_append_outputprefixfirst) = S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixfirst)) /\ exists ff_q_pvs_append_outputprefixfirstpositive. dst_positive_code_append_outputprefixfirst = ff_q_pvs_append_outputprefixfirstpositive * S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixfirst) + (dst_positive_append_outputprefixfirst))) /\ (((((exists ff_h_pvs_append_outputprefixfirstnegative. ff_h_pvs_append_outputprefixfirstnegative + S (dst_negative_append_outputprefixfirst) = S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixfirst)) /\ exists ff_q_pvs_append_outputprefixfirstnegative. dst_negative_code_append_outputprefixfirst = ff_q_pvs_append_outputprefixfirstnegative * S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixfirst) + (dst_negative_append_outputprefixfirst))) /\ (exists ge_balance_positive_append_outputprefixfirstvalue ge_balance_negative_append_outputprefixfirstvalue. (((((dst_first_append_outputprefix) = 2 * (ge_balance_positive_append_outputprefixfirstvalue) /\ (ge_balance_negative_append_outputprefixfirstvalue) = 0) \/ exists ge_signed_half_append_outputprefixfirstvaluedecode. (((dst_first_append_outputprefix) = 2 * ge_signed_half_append_outputprefixfirstvaluedecode + 1 /\ (ge_balance_positive_append_outputprefixfirstvalue) = 0) /\ (ge_balance_negative_append_outputprefixfirstvalue) = S ge_signed_half_append_outputprefixfirstvaluedecode))) /\ ((dst_positive_append_outputprefixfirst) + ge_balance_negative_append_outputprefixfirstvalue = (dst_negative_append_outputprefixfirst) + ge_balance_positive_append_outputprefixfirstvalue))))))))) -> (exists dst_positive_code_append_outputprefixsecond dst_positive_scale_append_outputprefixsecond dst_negative_code_append_outputprefixsecond dst_negative_scale_append_outputprefixsecond dst_positive_append_outputprefixsecond dst_negative_append_outputprefixsecond. (((G) = (((((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) * S ((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) + ((dst_positive_scale_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond))) + (((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)))) * S ((((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) * S ((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) + ((dst_positive_scale_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond))) + (((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)))) + ((((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond))) + (((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)))))) /\ (((((exists ff_h_pvs_append_outputprefixsecondpositive. ff_h_pvs_append_outputprefixsecondpositive + S (dst_positive_append_outputprefixsecond) = S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixsecond)) /\ exists ff_q_pvs_append_outputprefixsecondpositive. dst_positive_code_append_outputprefixsecond = ff_q_pvs_append_outputprefixsecondpositive * S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixsecond) + (dst_positive_append_outputprefixsecond))) /\ (((((exists ff_h_pvs_append_outputprefixsecondnegative. ff_h_pvs_append_outputprefixsecondnegative + S (dst_negative_append_outputprefixsecond) = S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixsecond)) /\ exists ff_q_pvs_append_outputprefixsecondnegative. dst_negative_code_append_outputprefixsecond = ff_q_pvs_append_outputprefixsecondnegative * S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixsecond) + (dst_negative_append_outputprefixsecond))) /\ (exists ge_balance_positive_append_outputprefixsecondvalue ge_balance_negative_append_outputprefixsecondvalue. (((((dst_second_append_outputprefix) = 2 * (ge_balance_positive_append_outputprefixsecondvalue) /\ (ge_balance_negative_append_outputprefixsecondvalue) = 0) \/ exists ge_signed_half_append_outputprefixsecondvaluedecode. (((dst_second_append_outputprefix) = 2 * ge_signed_half_append_outputprefixsecondvaluedecode + 1 /\ (ge_balance_positive_append_outputprefixsecondvalue) = 0) /\ (ge_balance_negative_append_outputprefixsecondvalue) = S ge_signed_half_append_outputprefixsecondvaluedecode))) /\ ((dst_positive_append_outputprefixsecond) + ge_balance_negative_append_outputprefixsecondvalue = (dst_negative_append_outputprefixsecond) + ge_balance_positive_append_outputprefixsecondvalue))))))))) -> dst_first_append_outputprefix = dst_second_append_outputprefix) /\ (exists dst_positive_code_append_outputlast dst_positive_scale_append_outputlast dst_negative_code_append_outputlast dst_negative_scale_append_outputlast dst_positive_append_outputlast dst_negative_append_outputlast. (((G) = (((((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) * S ((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) + ((dst_positive_scale_append_outputlast) + (dst_positive_scale_append_outputlast))) + (((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast)))) * S ((((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) * S ((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) + ((dst_positive_scale_append_outputlast) + (dst_positive_scale_append_outputlast))) + (((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast)))) + ((((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast))) + (((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast)))))) /\ (((((exists ff_h_pvs_append_outputlastpositive. ff_h_pvs_append_outputlastpositive + S (dst_positive_append_outputlast) = S ((S (S N)) * dst_positive_scale_append_outputlast)) /\ exists ff_q_pvs_append_outputlastpositive. dst_positive_code_append_outputlast = ff_q_pvs_append_outputlastpositive * S ((S (S N)) * dst_positive_scale_append_outputlast) + (dst_positive_append_outputlast))) /\ (((((exists ff_h_pvs_append_outputlastnegative. ff_h_pvs_append_outputlastnegative + S (dst_negative_append_outputlast) = S ((S (S N)) * dst_negative_scale_append_outputlast)) /\ exists ff_q_pvs_append_outputlastnegative. dst_negative_code_append_outputlast = ff_q_pvs_append_outputlastnegative * S ((S (S N)) * dst_negative_scale_append_outputlast) + (dst_negative_append_outputlast))) /\ (exists ge_balance_positive_append_outputlastvalue ge_balance_negative_append_outputlastvalue. (((((z) = 2 * (ge_balance_positive_append_outputlastvalue) /\ (ge_balance_negative_append_outputlastvalue) = 0) \/ exists ge_signed_half_append_outputlastvaluedecode. (((z) = 2 * ge_signed_half_append_outputlastvaluedecode + 1 /\ (ge_balance_positive_append_outputlastvalue) = 0) /\ (ge_balance_negative_append_outputlastvalue) = S ge_signed_half_append_outputlastvaluedecode))) /\ ((dst_positive_append_outputlast) + ge_balance_negative_append_outputlastvalue = (dst_negative_append_outputlast) + ge_balance_positive_append_outputlastvalue)))))))))))))

arithmetic_signed_table_singleton

new owned theorem · read exact theorem evidence

Bundle node 281; exact statement SHA-256 abcbb4b6594540acf09ee93dbc93131123d57bce6d3599ec2232d9ff0939bc7c

Exact first-order statement

forall z. exists F. (exists dst_positive_code_singleton_valid dst_positive_scale_singleton_valid dst_negative_code_singleton_valid dst_negative_scale_singleton_valid. (((F) = (((((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) * S ((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) + ((dst_positive_scale_singleton_valid) + (dst_positive_scale_singleton_valid))) + (((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid)))) * S ((((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) * S ((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) + ((dst_positive_scale_singleton_valid) + (dst_positive_scale_singleton_valid))) + (((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid)))) + ((((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid))) + (((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid)))))) /\ (forall dst_index_singleton_valid. (exists pvs_le_gap_singleton_validdomain. pvs_le_gap_singleton_validdomain + (dst_index_singleton_valid) = (0)) -> exists dst_positive_singleton_valid dst_negative_singleton_valid dst_value_singleton_valid. ((((exists ff_h_pvs_singleton_validentrypositive. ff_h_pvs_singleton_validentrypositive + S (dst_positive_singleton_valid) = S ((S (dst_index_singleton_valid)) * dst_positive_scale_singleton_valid)) /\ exists ff_q_pvs_singleton_validentrypositive. dst_positive_code_singleton_valid = ff_q_pvs_singleton_validentrypositive * S ((S (dst_index_singleton_valid)) * dst_positive_scale_singleton_valid) + (dst_positive_singleton_valid))) /\ (((((exists ff_h_pvs_singleton_validentrynegative. ff_h_pvs_singleton_validentrynegative + S (dst_negative_singleton_valid) = S ((S (dst_index_singleton_valid)) * dst_negative_scale_singleton_valid)) /\ exists ff_q_pvs_singleton_validentrynegative. dst_negative_code_singleton_valid = ff_q_pvs_singleton_validentrynegative * S ((S (dst_index_singleton_valid)) * dst_negative_scale_singleton_valid) + (dst_negative_singleton_valid))) /\ (exists ge_balance_positive_singleton_validentryvalue ge_balance_negative_singleton_validentryvalue. (((((dst_value_singleton_valid) = 2 * (ge_balance_positive_singleton_validentryvalue) /\ (ge_balance_negative_singleton_validentryvalue) = 0) \/ exists ge_signed_half_singleton_validentryvaluedecode. (((dst_value_singleton_valid) = 2 * ge_signed_half_singleton_validentryvaluedecode + 1 /\ (ge_balance_positive_singleton_validentryvalue) = 0) /\ (ge_balance_negative_singleton_validentryvalue) = S ge_signed_half_singleton_validentryvaluedecode))) /\ ((dst_positive_singleton_valid) + ge_balance_negative_singleton_validentryvalue = (dst_negative_singleton_valid) + ge_balance_positive_singleton_validentryvalue))))))))) /\ (exists dst_positive_code_singleton_value dst_positive_scale_singleton_value dst_negative_code_singleton_value dst_negative_scale_singleton_value dst_positive_singleton_value dst_negative_singleton_value. (((F) = (((((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) * S ((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) + ((dst_positive_scale_singleton_value) + (dst_positive_scale_singleton_value))) + (((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value)))) * S ((((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) * S ((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) + ((dst_positive_scale_singleton_value) + (dst_positive_scale_singleton_value))) + (((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value)))) + ((((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value))) + (((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value)))))) /\ (((((exists ff_h_pvs_singleton_valuepositive. ff_h_pvs_singleton_valuepositive + S (dst_positive_singleton_value) = S ((S (0)) * dst_positive_scale_singleton_value)) /\ exists ff_q_pvs_singleton_valuepositive. dst_positive_code_singleton_value = ff_q_pvs_singleton_valuepositive * S ((S (0)) * dst_positive_scale_singleton_value) + (dst_positive_singleton_value))) /\ (((((exists ff_h_pvs_singleton_valuenegative. ff_h_pvs_singleton_valuenegative + S (dst_negative_singleton_value) = S ((S (0)) * dst_negative_scale_singleton_value)) /\ exists ff_q_pvs_singleton_valuenegative. dst_negative_code_singleton_value = ff_q_pvs_singleton_valuenegative * S ((S (0)) * dst_negative_scale_singleton_value) + (dst_negative_singleton_value))) /\ (exists ge_balance_positive_singleton_valuevalue ge_balance_negative_singleton_valuevalue. (((((z) = 2 * (ge_balance_positive_singleton_valuevalue) /\ (ge_balance_negative_singleton_valuevalue) = 0) \/ exists ge_signed_half_singleton_valuevaluedecode. (((z) = 2 * ge_signed_half_singleton_valuevaluedecode + 1 /\ (ge_balance_positive_singleton_valuevalue) = 0) /\ (ge_balance_negative_singleton_valuevalue) = S ge_signed_half_singleton_valuevaluedecode))) /\ ((dst_positive_singleton_value) + ge_balance_negative_singleton_valuevalue = (dst_negative_singleton_value) + ge_balance_positive_singleton_valuevalue)))))))))

arithmetic_signed_sum_exists

new owned theorem · read exact theorem evidence

Bundle node 282; exact statement SHA-256 7bb45a2e5b2803d34704616cef0c8007b1ea4cfe478e9230cccba80afa9f249c

Exact first-order statement

forall N F l. (exists dst_positive_code_sum_exists_input dst_positive_scale_sum_exists_input dst_negative_code_sum_exists_input dst_negative_scale_sum_exists_input. (((F) = (((((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) * S ((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) + ((dst_positive_scale_sum_exists_input) + (dst_positive_scale_sum_exists_input))) + (((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input)))) * S ((((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) * S ((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) + ((dst_positive_scale_sum_exists_input) + (dst_positive_scale_sum_exists_input))) + (((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input)))) + ((((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input))) + (((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input)))))) /\ (forall dst_index_sum_exists_input. (exists pvs_le_gap_sum_exists_inputdomain. pvs_le_gap_sum_exists_inputdomain + (dst_index_sum_exists_input) = (N)) -> exists dst_positive_sum_exists_input dst_negative_sum_exists_input dst_value_sum_exists_input. ((((exists ff_h_pvs_sum_exists_inputentrypositive. ff_h_pvs_sum_exists_inputentrypositive + S (dst_positive_sum_exists_input) = S ((S (dst_index_sum_exists_input)) * dst_positive_scale_sum_exists_input)) /\ exists ff_q_pvs_sum_exists_inputentrypositive. dst_positive_code_sum_exists_input = ff_q_pvs_sum_exists_inputentrypositive * S ((S (dst_index_sum_exists_input)) * dst_positive_scale_sum_exists_input) + (dst_positive_sum_exists_input))) /\ (((((exists ff_h_pvs_sum_exists_inputentrynegative. ff_h_pvs_sum_exists_inputentrynegative + S (dst_negative_sum_exists_input) = S ((S (dst_index_sum_exists_input)) * dst_negative_scale_sum_exists_input)) /\ exists ff_q_pvs_sum_exists_inputentrynegative. dst_negative_code_sum_exists_input = ff_q_pvs_sum_exists_inputentrynegative * S ((S (dst_index_sum_exists_input)) * dst_negative_scale_sum_exists_input) + (dst_negative_sum_exists_input))) /\ (exists ge_balance_positive_sum_exists_inputentryvalue ge_balance_negative_sum_exists_inputentryvalue. (((((dst_value_sum_exists_input) = 2 * (ge_balance_positive_sum_exists_inputentryvalue) /\ (ge_balance_negative_sum_exists_inputentryvalue) = 0) \/ exists ge_signed_half_sum_exists_inputentryvaluedecode. (((dst_value_sum_exists_input) = 2 * ge_signed_half_sum_exists_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_exists_inputentryvalue) = 0) /\ (ge_balance_negative_sum_exists_inputentryvalue) = S ge_signed_half_sum_exists_inputentryvaluedecode))) /\ ((dst_positive_sum_exists_input) + ge_balance_negative_sum_exists_inputentryvalue = (dst_negative_sum_exists_input) + ge_balance_positive_sum_exists_inputentryvalue))))))))) -> exists z. (exists dst_positive_code_sum_exists_output dst_positive_scale_sum_exists_output dst_negative_code_sum_exists_output dst_negative_scale_sum_exists_output dst_positive_sum_sum_exists_output dst_negative_sum_sum_exists_output. (((F) = (((((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) * S ((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) + ((dst_positive_scale_sum_exists_output) + (dst_positive_scale_sum_exists_output))) + (((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output)))) * S ((((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) * S ((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) + ((dst_positive_scale_sum_exists_output) + (dst_positive_scale_sum_exists_output))) + (((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output)))) + ((((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output))) + (((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output)))))) /\ (((exists fs_u_dst_sum_exists_outputpositive fs_v_dst_sum_exists_outputpositive. ((((exists fs_h_dst_sum_exists_outputpositive_body_start. fs_h_dst_sum_exists_outputpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_start. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_start * S ((S (0)) * fs_v_dst_sum_exists_outputpositive) + (0))) /\ ((((exists fs_h_dst_sum_exists_outputpositive_body_terminal. fs_h_dst_sum_exists_outputpositive_body_terminal + S (dst_positive_sum_sum_exists_output) = S ((S (l)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_terminal. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_outputpositive) + (dst_positive_sum_sum_exists_output))) /\ forall fs_i_dst_sum_exists_outputpositive_body_steps. (exists fs_lt_dst_sum_exists_outputpositive_body_steps_bound. fs_lt_dst_sum_exists_outputpositive_body_steps_bound + S fs_i_dst_sum_exists_outputpositive_body_steps = l) -> exists fs_a_dst_sum_exists_outputpositive_body_steps fs_r_dst_sum_exists_outputpositive_body_steps fs_s_dst_sum_exists_outputpositive_body_steps. ((((exists fs_h_dst_sum_exists_outputpositive_body_steps_summand. fs_h_dst_sum_exists_outputpositive_body_steps_summand + S (fs_a_dst_sum_exists_outputpositive_body_steps) = S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * dst_positive_scale_sum_exists_output)) /\ exists fs_q_dst_sum_exists_outputpositive_body_steps_summand. dst_positive_code_sum_exists_output = fs_q_dst_sum_exists_outputpositive_body_steps_summand * S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * dst_positive_scale_sum_exists_output) + (fs_a_dst_sum_exists_outputpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputpositive_body_steps_partial. fs_h_dst_sum_exists_outputpositive_body_steps_partial + S (fs_r_dst_sum_exists_outputpositive_body_steps) = S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_steps_partial. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_steps_partial * S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive) + (fs_r_dst_sum_exists_outputpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputpositive_body_steps_successor. fs_h_dst_sum_exists_outputpositive_body_steps_successor + S (fs_s_dst_sum_exists_outputpositive_body_steps) = S ((S (S fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_steps_successor. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_steps_successor * S ((S (S fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive) + (fs_s_dst_sum_exists_outputpositive_body_steps))) /\ fs_s_dst_sum_exists_outputpositive_body_steps = fs_r_dst_sum_exists_outputpositive_body_steps + fs_a_dst_sum_exists_outputpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_exists_outputnegative fs_v_dst_sum_exists_outputnegative. ((((exists fs_h_dst_sum_exists_outputnegative_body_start. fs_h_dst_sum_exists_outputnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_start. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_start * S ((S (0)) * fs_v_dst_sum_exists_outputnegative) + (0))) /\ ((((exists fs_h_dst_sum_exists_outputnegative_body_terminal. fs_h_dst_sum_exists_outputnegative_body_terminal + S (dst_negative_sum_sum_exists_output) = S ((S (l)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_terminal. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_outputnegative) + (dst_negative_sum_sum_exists_output))) /\ forall fs_i_dst_sum_exists_outputnegative_body_steps. (exists fs_lt_dst_sum_exists_outputnegative_body_steps_bound. fs_lt_dst_sum_exists_outputnegative_body_steps_bound + S fs_i_dst_sum_exists_outputnegative_body_steps = l) -> exists fs_a_dst_sum_exists_outputnegative_body_steps fs_r_dst_sum_exists_outputnegative_body_steps fs_s_dst_sum_exists_outputnegative_body_steps. ((((exists fs_h_dst_sum_exists_outputnegative_body_steps_summand. fs_h_dst_sum_exists_outputnegative_body_steps_summand + S (fs_a_dst_sum_exists_outputnegative_body_steps) = S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * dst_negative_scale_sum_exists_output)) /\ exists fs_q_dst_sum_exists_outputnegative_body_steps_summand. dst_negative_code_sum_exists_output = fs_q_dst_sum_exists_outputnegative_body_steps_summand * S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * dst_negative_scale_sum_exists_output) + (fs_a_dst_sum_exists_outputnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputnegative_body_steps_partial. fs_h_dst_sum_exists_outputnegative_body_steps_partial + S (fs_r_dst_sum_exists_outputnegative_body_steps) = S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_steps_partial. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_steps_partial * S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative) + (fs_r_dst_sum_exists_outputnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputnegative_body_steps_successor. fs_h_dst_sum_exists_outputnegative_body_steps_successor + S (fs_s_dst_sum_exists_outputnegative_body_steps) = S ((S (S fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_steps_successor. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_steps_successor * S ((S (S fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative) + (fs_s_dst_sum_exists_outputnegative_body_steps))) /\ fs_s_dst_sum_exists_outputnegative_body_steps = fs_r_dst_sum_exists_outputnegative_body_steps + fs_a_dst_sum_exists_outputnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_exists_outputresult ge_balance_negative_sum_exists_outputresult. (((((z) = 2 * (ge_balance_positive_sum_exists_outputresult) /\ (ge_balance_negative_sum_exists_outputresult) = 0) \/ exists ge_signed_half_sum_exists_outputresultdecode. (((z) = 2 * ge_signed_half_sum_exists_outputresultdecode + 1 /\ (ge_balance_positive_sum_exists_outputresult) = 0) /\ (ge_balance_negative_sum_exists_outputresult) = S ge_signed_half_sum_exists_outputresultdecode))) /\ ((dst_positive_sum_sum_exists_output) + ge_balance_negative_sum_exists_outputresult = (dst_negative_sum_sum_exists_output) + ge_balance_positive_sum_exists_outputresult)))))))))

arithmetic_signed_sum_append_transport

new owned theorem · read exact theorem evidence

Bundle node 283; exact statement SHA-256 6310f62889b1603c315c961ac6f8e1409ddce3ba4144e4e997e539ba4fbf5752

Exact first-order statement

forall F G l a b c. (exists dst_positive_code_append_sum_valid dst_positive_scale_append_sum_valid dst_negative_code_append_sum_valid dst_negative_scale_append_sum_valid. (((G) = (((((dst_positive_code_append_sum_valid) + (dst_positive_scale_append_sum_valid)) * S ((dst_positive_code_append_sum_valid) + (dst_positive_scale_append_sum_valid)) + ((dst_positive_scale_append_sum_valid) + (dst_positive_scale_append_sum_valid))) + (((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) * S ((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) + ((dst_negative_scale_append_sum_valid) + (dst_negative_scale_append_sum_valid)))) * S ((((dst_positive_code_append_sum_valid) + (dst_positive_scale_append_sum_valid)) * S ((dst_positive_code_append_sum_valid) + (dst_positive_scale_append_sum_valid)) + ((dst_positive_scale_append_sum_valid) + (dst_positive_scale_append_sum_valid))) + (((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) * S ((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) + ((dst_negative_scale_append_sum_valid) + (dst_negative_scale_append_sum_valid)))) + ((((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) * S ((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) + ((dst_negative_scale_append_sum_valid) + (dst_negative_scale_append_sum_valid))) + (((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) * S ((dst_negative_code_append_sum_valid) + (dst_negative_scale_append_sum_valid)) + ((dst_negative_scale_append_sum_valid) + (dst_negative_scale_append_sum_valid)))))) /\ (forall dst_index_append_sum_valid. (exists pvs_le_gap_append_sum_validdomain. pvs_le_gap_append_sum_validdomain + (dst_index_append_sum_valid) = (l)) -> exists dst_positive_append_sum_valid dst_negative_append_sum_valid dst_value_append_sum_valid. ((((exists ff_h_pvs_append_sum_validentrypositive. ff_h_pvs_append_sum_validentrypositive + S (dst_positive_append_sum_valid) = S ((S (dst_index_append_sum_valid)) * dst_positive_scale_append_sum_valid)) /\ exists ff_q_pvs_append_sum_validentrypositive. dst_positive_code_append_sum_valid = ff_q_pvs_append_sum_validentrypositive * S ((S (dst_index_append_sum_valid)) * dst_positive_scale_append_sum_valid) + (dst_positive_append_sum_valid))) /\ (((((exists ff_h_pvs_append_sum_validentrynegative. ff_h_pvs_append_sum_validentrynegative + S (dst_negative_append_sum_valid) = S ((S (dst_index_append_sum_valid)) * dst_negative_scale_append_sum_valid)) /\ exists ff_q_pvs_append_sum_validentrynegative. dst_negative_code_append_sum_valid = ff_q_pvs_append_sum_validentrynegative * S ((S (dst_index_append_sum_valid)) * dst_negative_scale_append_sum_valid) + (dst_negative_append_sum_valid))) /\ (exists ge_balance_positive_append_sum_validentryvalue ge_balance_negative_append_sum_validentryvalue. (((((dst_value_append_sum_valid) = 2 * (ge_balance_positive_append_sum_validentryvalue) /\ (ge_balance_negative_append_sum_validentryvalue) = 0) \/ exists ge_signed_half_append_sum_validentryvaluedecode. (((dst_value_append_sum_valid) = 2 * ge_signed_half_append_sum_validentryvaluedecode + 1 /\ (ge_balance_positive_append_sum_validentryvalue) = 0) /\ (ge_balance_negative_append_sum_validentryvalue) = S ge_signed_half_append_sum_validentryvaluedecode))) /\ ((dst_positive_append_sum_valid) + ge_balance_negative_append_sum_validentryvalue = (dst_negative_append_sum_valid) + ge_balance_positive_append_sum_validentryvalue))))))))) -> (forall dst_index_append_sum_prefix dst_first_append_sum_prefix dst_second_append_sum_prefix. (exists pvs_gap_append_sum_prefixbound. pvs_gap_append_sum_prefixbound + S (dst_index_append_sum_prefix) = (l)) -> (exists dst_positive_code_append_sum_prefixfirst dst_positive_scale_append_sum_prefixfirst dst_negative_code_append_sum_prefixfirst dst_negative_scale_append_sum_prefixfirst dst_positive_append_sum_prefixfirst dst_negative_append_sum_prefixfirst. (((F) = (((((dst_positive_code_append_sum_prefixfirst) + (dst_positive_scale_append_sum_prefixfirst)) * S ((dst_positive_code_append_sum_prefixfirst) + (dst_positive_scale_append_sum_prefixfirst)) + ((dst_positive_scale_append_sum_prefixfirst) + (dst_positive_scale_append_sum_prefixfirst))) + (((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) * S ((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) + ((dst_negative_scale_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)))) * S ((((dst_positive_code_append_sum_prefixfirst) + (dst_positive_scale_append_sum_prefixfirst)) * S ((dst_positive_code_append_sum_prefixfirst) + (dst_positive_scale_append_sum_prefixfirst)) + ((dst_positive_scale_append_sum_prefixfirst) + (dst_positive_scale_append_sum_prefixfirst))) + (((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) * S ((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) + ((dst_negative_scale_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)))) + ((((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) * S ((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) + ((dst_negative_scale_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst))) + (((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) * S ((dst_negative_code_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)) + ((dst_negative_scale_append_sum_prefixfirst) + (dst_negative_scale_append_sum_prefixfirst)))))) /\ (((((exists ff_h_pvs_append_sum_prefixfirstpositive. ff_h_pvs_append_sum_prefixfirstpositive + S (dst_positive_append_sum_prefixfirst) = S ((S (dst_index_append_sum_prefix)) * dst_positive_scale_append_sum_prefixfirst)) /\ exists ff_q_pvs_append_sum_prefixfirstpositive. dst_positive_code_append_sum_prefixfirst = ff_q_pvs_append_sum_prefixfirstpositive * S ((S (dst_index_append_sum_prefix)) * dst_positive_scale_append_sum_prefixfirst) + (dst_positive_append_sum_prefixfirst))) /\ (((((exists ff_h_pvs_append_sum_prefixfirstnegative. ff_h_pvs_append_sum_prefixfirstnegative + S (dst_negative_append_sum_prefixfirst) = S ((S (dst_index_append_sum_prefix)) * dst_negative_scale_append_sum_prefixfirst)) /\ exists ff_q_pvs_append_sum_prefixfirstnegative. dst_negative_code_append_sum_prefixfirst = ff_q_pvs_append_sum_prefixfirstnegative * S ((S (dst_index_append_sum_prefix)) * dst_negative_scale_append_sum_prefixfirst) + (dst_negative_append_sum_prefixfirst))) /\ (exists ge_balance_positive_append_sum_prefixfirstvalue ge_balance_negative_append_sum_prefixfirstvalue. (((((dst_first_append_sum_prefix) = 2 * (ge_balance_positive_append_sum_prefixfirstvalue) /\ (ge_balance_negative_append_sum_prefixfirstvalue) = 0) \/ exists ge_signed_half_append_sum_prefixfirstvaluedecode. (((dst_first_append_sum_prefix) = 2 * ge_signed_half_append_sum_prefixfirstvaluedecode + 1 /\ (ge_balance_positive_append_sum_prefixfirstvalue) = 0) /\ (ge_balance_negative_append_sum_prefixfirstvalue) = S ge_signed_half_append_sum_prefixfirstvaluedecode))) /\ ((dst_positive_append_sum_prefixfirst) + ge_balance_negative_append_sum_prefixfirstvalue = (dst_negative_append_sum_prefixfirst) + ge_balance_positive_append_sum_prefixfirstvalue))))))))) -> (exists dst_positive_code_append_sum_prefixsecond dst_positive_scale_append_sum_prefixsecond dst_negative_code_append_sum_prefixsecond dst_negative_scale_append_sum_prefixsecond dst_positive_append_sum_prefixsecond dst_negative_append_sum_prefixsecond. (((G) = (((((dst_positive_code_append_sum_prefixsecond) + (dst_positive_scale_append_sum_prefixsecond)) * S ((dst_positive_code_append_sum_prefixsecond) + (dst_positive_scale_append_sum_prefixsecond)) + ((dst_positive_scale_append_sum_prefixsecond) + (dst_positive_scale_append_sum_prefixsecond))) + (((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) * S ((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) + ((dst_negative_scale_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)))) * S ((((dst_positive_code_append_sum_prefixsecond) + (dst_positive_scale_append_sum_prefixsecond)) * S ((dst_positive_code_append_sum_prefixsecond) + (dst_positive_scale_append_sum_prefixsecond)) + ((dst_positive_scale_append_sum_prefixsecond) + (dst_positive_scale_append_sum_prefixsecond))) + (((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) * S ((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) + ((dst_negative_scale_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)))) + ((((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) * S ((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) + ((dst_negative_scale_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond))) + (((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) * S ((dst_negative_code_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)) + ((dst_negative_scale_append_sum_prefixsecond) + (dst_negative_scale_append_sum_prefixsecond)))))) /\ (((((exists ff_h_pvs_append_sum_prefixsecondpositive. ff_h_pvs_append_sum_prefixsecondpositive + S (dst_positive_append_sum_prefixsecond) = S ((S (dst_index_append_sum_prefix)) * dst_positive_scale_append_sum_prefixsecond)) /\ exists ff_q_pvs_append_sum_prefixsecondpositive. dst_positive_code_append_sum_prefixsecond = ff_q_pvs_append_sum_prefixsecondpositive * S ((S (dst_index_append_sum_prefix)) * dst_positive_scale_append_sum_prefixsecond) + (dst_positive_append_sum_prefixsecond))) /\ (((((exists ff_h_pvs_append_sum_prefixsecondnegative. ff_h_pvs_append_sum_prefixsecondnegative + S (dst_negative_append_sum_prefixsecond) = S ((S (dst_index_append_sum_prefix)) * dst_negative_scale_append_sum_prefixsecond)) /\ exists ff_q_pvs_append_sum_prefixsecondnegative. dst_negative_code_append_sum_prefixsecond = ff_q_pvs_append_sum_prefixsecondnegative * S ((S (dst_index_append_sum_prefix)) * dst_negative_scale_append_sum_prefixsecond) + (dst_negative_append_sum_prefixsecond))) /\ (exists ge_balance_positive_append_sum_prefixsecondvalue ge_balance_negative_append_sum_prefixsecondvalue. (((((dst_second_append_sum_prefix) = 2 * (ge_balance_positive_append_sum_prefixsecondvalue) /\ (ge_balance_negative_append_sum_prefixsecondvalue) = 0) \/ exists ge_signed_half_append_sum_prefixsecondvaluedecode. (((dst_second_append_sum_prefix) = 2 * ge_signed_half_append_sum_prefixsecondvaluedecode + 1 /\ (ge_balance_positive_append_sum_prefixsecondvalue) = 0) /\ (ge_balance_negative_append_sum_prefixsecondvalue) = S ge_signed_half_append_sum_prefixsecondvaluedecode))) /\ ((dst_positive_append_sum_prefixsecond) + ge_balance_negative_append_sum_prefixsecondvalue = (dst_negative_append_sum_prefixsecond) + ge_balance_positive_append_sum_prefixsecondvalue))))))))) -> dst_first_append_sum_prefix = dst_second_append_sum_prefix) -> (exists dst_positive_code_append_sum_before dst_positive_scale_append_sum_before dst_negative_code_append_sum_before dst_negative_scale_append_sum_before dst_positive_sum_append_sum_before dst_negative_sum_append_sum_before. (((F) = (((((dst_positive_code_append_sum_before) + (dst_positive_scale_append_sum_before)) * S ((dst_positive_code_append_sum_before) + (dst_positive_scale_append_sum_before)) + ((dst_positive_scale_append_sum_before) + (dst_positive_scale_append_sum_before))) + (((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) * S ((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) + ((dst_negative_scale_append_sum_before) + (dst_negative_scale_append_sum_before)))) * S ((((dst_positive_code_append_sum_before) + (dst_positive_scale_append_sum_before)) * S ((dst_positive_code_append_sum_before) + (dst_positive_scale_append_sum_before)) + ((dst_positive_scale_append_sum_before) + (dst_positive_scale_append_sum_before))) + (((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) * S ((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) + ((dst_negative_scale_append_sum_before) + (dst_negative_scale_append_sum_before)))) + ((((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) * S ((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) + ((dst_negative_scale_append_sum_before) + (dst_negative_scale_append_sum_before))) + (((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) * S ((dst_negative_code_append_sum_before) + (dst_negative_scale_append_sum_before)) + ((dst_negative_scale_append_sum_before) + (dst_negative_scale_append_sum_before)))))) /\ (((exists fs_u_dst_append_sum_beforepositive fs_v_dst_append_sum_beforepositive. ((((exists fs_h_dst_append_sum_beforepositive_body_start. fs_h_dst_append_sum_beforepositive_body_start + S (0) = S ((S (0)) * fs_v_dst_append_sum_beforepositive)) /\ exists fs_q_dst_append_sum_beforepositive_body_start. fs_u_dst_append_sum_beforepositive = fs_q_dst_append_sum_beforepositive_body_start * S ((S (0)) * fs_v_dst_append_sum_beforepositive) + (0))) /\ ((((exists fs_h_dst_append_sum_beforepositive_body_terminal. fs_h_dst_append_sum_beforepositive_body_terminal + S (dst_positive_sum_append_sum_before) = S ((S (l)) * fs_v_dst_append_sum_beforepositive)) /\ exists fs_q_dst_append_sum_beforepositive_body_terminal. fs_u_dst_append_sum_beforepositive = fs_q_dst_append_sum_beforepositive_body_terminal * S ((S (l)) * fs_v_dst_append_sum_beforepositive) + (dst_positive_sum_append_sum_before))) /\ forall fs_i_dst_append_sum_beforepositive_body_steps. (exists fs_lt_dst_append_sum_beforepositive_body_steps_bound. fs_lt_dst_append_sum_beforepositive_body_steps_bound + S fs_i_dst_append_sum_beforepositive_body_steps = l) -> exists fs_a_dst_append_sum_beforepositive_body_steps fs_r_dst_append_sum_beforepositive_body_steps fs_s_dst_append_sum_beforepositive_body_steps. ((((exists fs_h_dst_append_sum_beforepositive_body_steps_summand. fs_h_dst_append_sum_beforepositive_body_steps_summand + S (fs_a_dst_append_sum_beforepositive_body_steps) = S ((S (fs_i_dst_append_sum_beforepositive_body_steps)) * dst_positive_scale_append_sum_before)) /\ exists fs_q_dst_append_sum_beforepositive_body_steps_summand. dst_positive_code_append_sum_before = fs_q_dst_append_sum_beforepositive_body_steps_summand * S ((S (fs_i_dst_append_sum_beforepositive_body_steps)) * dst_positive_scale_append_sum_before) + (fs_a_dst_append_sum_beforepositive_body_steps))) /\ ((((exists fs_h_dst_append_sum_beforepositive_body_steps_partial. fs_h_dst_append_sum_beforepositive_body_steps_partial + S (fs_r_dst_append_sum_beforepositive_body_steps) = S ((S (fs_i_dst_append_sum_beforepositive_body_steps)) * fs_v_dst_append_sum_beforepositive)) /\ exists fs_q_dst_append_sum_beforepositive_body_steps_partial. fs_u_dst_append_sum_beforepositive = fs_q_dst_append_sum_beforepositive_body_steps_partial * S ((S (fs_i_dst_append_sum_beforepositive_body_steps)) * fs_v_dst_append_sum_beforepositive) + (fs_r_dst_append_sum_beforepositive_body_steps))) /\ ((((exists fs_h_dst_append_sum_beforepositive_body_steps_successor. fs_h_dst_append_sum_beforepositive_body_steps_successor + S (fs_s_dst_append_sum_beforepositive_body_steps) = S ((S (S fs_i_dst_append_sum_beforepositive_body_steps)) * fs_v_dst_append_sum_beforepositive)) /\ exists fs_q_dst_append_sum_beforepositive_body_steps_successor. fs_u_dst_append_sum_beforepositive = fs_q_dst_append_sum_beforepositive_body_steps_successor * S ((S (S fs_i_dst_append_sum_beforepositive_body_steps)) * fs_v_dst_append_sum_beforepositive) + (fs_s_dst_append_sum_beforepositive_body_steps))) /\ fs_s_dst_append_sum_beforepositive_body_steps = fs_r_dst_append_sum_beforepositive_body_steps + fs_a_dst_append_sum_beforepositive_body_steps)))))) /\ (((exists fs_u_dst_append_sum_beforenegative fs_v_dst_append_sum_beforenegative. ((((exists fs_h_dst_append_sum_beforenegative_body_start. fs_h_dst_append_sum_beforenegative_body_start + S (0) = S ((S (0)) * fs_v_dst_append_sum_beforenegative)) /\ exists fs_q_dst_append_sum_beforenegative_body_start. fs_u_dst_append_sum_beforenegative = fs_q_dst_append_sum_beforenegative_body_start * S ((S (0)) * fs_v_dst_append_sum_beforenegative) + (0))) /\ ((((exists fs_h_dst_append_sum_beforenegative_body_terminal. fs_h_dst_append_sum_beforenegative_body_terminal + S (dst_negative_sum_append_sum_before) = S ((S (l)) * fs_v_dst_append_sum_beforenegative)) /\ exists fs_q_dst_append_sum_beforenegative_body_terminal. fs_u_dst_append_sum_beforenegative = fs_q_dst_append_sum_beforenegative_body_terminal * S ((S (l)) * fs_v_dst_append_sum_beforenegative) + (dst_negative_sum_append_sum_before))) /\ forall fs_i_dst_append_sum_beforenegative_body_steps. (exists fs_lt_dst_append_sum_beforenegative_body_steps_bound. fs_lt_dst_append_sum_beforenegative_body_steps_bound + S fs_i_dst_append_sum_beforenegative_body_steps = l) -> exists fs_a_dst_append_sum_beforenegative_body_steps fs_r_dst_append_sum_beforenegative_body_steps fs_s_dst_append_sum_beforenegative_body_steps. ((((exists fs_h_dst_append_sum_beforenegative_body_steps_summand. fs_h_dst_append_sum_beforenegative_body_steps_summand + S (fs_a_dst_append_sum_beforenegative_body_steps) = S ((S (fs_i_dst_append_sum_beforenegative_body_steps)) * dst_negative_scale_append_sum_before)) /\ exists fs_q_dst_append_sum_beforenegative_body_steps_summand. dst_negative_code_append_sum_before = fs_q_dst_append_sum_beforenegative_body_steps_summand * S ((S (fs_i_dst_append_sum_beforenegative_body_steps)) * dst_negative_scale_append_sum_before) + (fs_a_dst_append_sum_beforenegative_body_steps))) /\ ((((exists fs_h_dst_append_sum_beforenegative_body_steps_partial. fs_h_dst_append_sum_beforenegative_body_steps_partial + S (fs_r_dst_append_sum_beforenegative_body_steps) = S ((S (fs_i_dst_append_sum_beforenegative_body_steps)) * fs_v_dst_append_sum_beforenegative)) /\ exists fs_q_dst_append_sum_beforenegative_body_steps_partial. fs_u_dst_append_sum_beforenegative = fs_q_dst_append_sum_beforenegative_body_steps_partial * S ((S (fs_i_dst_append_sum_beforenegative_body_steps)) * fs_v_dst_append_sum_beforenegative) + (fs_r_dst_append_sum_beforenegative_body_steps))) /\ ((((exists fs_h_dst_append_sum_beforenegative_body_steps_successor. fs_h_dst_append_sum_beforenegative_body_steps_successor + S (fs_s_dst_append_sum_beforenegative_body_steps) = S ((S (S fs_i_dst_append_sum_beforenegative_body_steps)) * fs_v_dst_append_sum_beforenegative)) /\ exists fs_q_dst_append_sum_beforenegative_body_steps_successor. fs_u_dst_append_sum_beforenegative = fs_q_dst_append_sum_beforenegative_body_steps_successor * S ((S (S fs_i_dst_append_sum_beforenegative_body_steps)) * fs_v_dst_append_sum_beforenegative) + (fs_s_dst_append_sum_beforenegative_body_steps))) /\ fs_s_dst_append_sum_beforenegative_body_steps = fs_r_dst_append_sum_beforenegative_body_steps + fs_a_dst_append_sum_beforenegative_body_steps)))))) /\ (exists ge_balance_positive_append_sum_beforeresult ge_balance_negative_append_sum_beforeresult. (((((a) = 2 * (ge_balance_positive_append_sum_beforeresult) /\ (ge_balance_negative_append_sum_beforeresult) = 0) \/ exists ge_signed_half_append_sum_beforeresultdecode. (((a) = 2 * ge_signed_half_append_sum_beforeresultdecode + 1 /\ (ge_balance_positive_append_sum_beforeresult) = 0) /\ (ge_balance_negative_append_sum_beforeresult) = S ge_signed_half_append_sum_beforeresultdecode))) /\ ((dst_positive_sum_append_sum_before) + ge_balance_negative_append_sum_beforeresult = (dst_negative_sum_append_sum_before) + ge_balance_positive_append_sum_beforeresult))))))))) -> (exists dst_positive_code_append_sum_entry dst_positive_scale_append_sum_entry dst_negative_code_append_sum_entry dst_negative_scale_append_sum_entry dst_positive_append_sum_entry dst_negative_append_sum_entry. (((G) = (((((dst_positive_code_append_sum_entry) + (dst_positive_scale_append_sum_entry)) * S ((dst_positive_code_append_sum_entry) + (dst_positive_scale_append_sum_entry)) + ((dst_positive_scale_append_sum_entry) + (dst_positive_scale_append_sum_entry))) + (((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) * S ((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) + ((dst_negative_scale_append_sum_entry) + (dst_negative_scale_append_sum_entry)))) * S ((((dst_positive_code_append_sum_entry) + (dst_positive_scale_append_sum_entry)) * S ((dst_positive_code_append_sum_entry) + (dst_positive_scale_append_sum_entry)) + ((dst_positive_scale_append_sum_entry) + (dst_positive_scale_append_sum_entry))) + (((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) * S ((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) + ((dst_negative_scale_append_sum_entry) + (dst_negative_scale_append_sum_entry)))) + ((((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) * S ((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) + ((dst_negative_scale_append_sum_entry) + (dst_negative_scale_append_sum_entry))) + (((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) * S ((dst_negative_code_append_sum_entry) + (dst_negative_scale_append_sum_entry)) + ((dst_negative_scale_append_sum_entry) + (dst_negative_scale_append_sum_entry)))))) /\ (((((exists ff_h_pvs_append_sum_entrypositive. ff_h_pvs_append_sum_entrypositive + S (dst_positive_append_sum_entry) = S ((S (l)) * dst_positive_scale_append_sum_entry)) /\ exists ff_q_pvs_append_sum_entrypositive. dst_positive_code_append_sum_entry = ff_q_pvs_append_sum_entrypositive * S ((S (l)) * dst_positive_scale_append_sum_entry) + (dst_positive_append_sum_entry))) /\ (((((exists ff_h_pvs_append_sum_entrynegative. ff_h_pvs_append_sum_entrynegative + S (dst_negative_append_sum_entry) = S ((S (l)) * dst_negative_scale_append_sum_entry)) /\ exists ff_q_pvs_append_sum_entrynegative. dst_negative_code_append_sum_entry = ff_q_pvs_append_sum_entrynegative * S ((S (l)) * dst_negative_scale_append_sum_entry) + (dst_negative_append_sum_entry))) /\ (exists ge_balance_positive_append_sum_entryvalue ge_balance_negative_append_sum_entryvalue. (((((b) = 2 * (ge_balance_positive_append_sum_entryvalue) /\ (ge_balance_negative_append_sum_entryvalue) = 0) \/ exists ge_signed_half_append_sum_entryvaluedecode. (((b) = 2 * ge_signed_half_append_sum_entryvaluedecode + 1 /\ (ge_balance_positive_append_sum_entryvalue) = 0) /\ (ge_balance_negative_append_sum_entryvalue) = S ge_signed_half_append_sum_entryvaluedecode))) /\ ((dst_positive_append_sum_entry) + ge_balance_negative_append_sum_entryvalue = (dst_negative_append_sum_entry) + ge_balance_positive_append_sum_entryvalue))))))))) -> (exists dsa_ap_append_sum_add dsa_an_append_sum_add dsa_bp_append_sum_add dsa_bn_append_sum_add dsa_cp_append_sum_add dsa_cn_append_sum_add. (((((a) = 2 * (dsa_ap_append_sum_add) /\ (dsa_an_append_sum_add) = 0) \/ exists ge_signed_half_append_sum_addleft. (((a) = 2 * ge_signed_half_append_sum_addleft + 1 /\ (dsa_ap_append_sum_add) = 0) /\ (dsa_an_append_sum_add) = S ge_signed_half_append_sum_addleft))) /\ ((((((b) = 2 * (dsa_bp_append_sum_add) /\ (dsa_bn_append_sum_add) = 0) \/ exists ge_signed_half_append_sum_addright. (((b) = 2 * ge_signed_half_append_sum_addright + 1 /\ (dsa_bp_append_sum_add) = 0) /\ (dsa_bn_append_sum_add) = S ge_signed_half_append_sum_addright))) /\ ((((((c) = 2 * (dsa_cp_append_sum_add) /\ (dsa_cn_append_sum_add) = 0) \/ exists ge_signed_half_append_sum_addoutput. (((c) = 2 * ge_signed_half_append_sum_addoutput + 1 /\ (dsa_cp_append_sum_add) = 0) /\ (dsa_cn_append_sum_add) = S ge_signed_half_append_sum_addoutput))) /\ ((dsa_ap_append_sum_add + dsa_bp_append_sum_add) + dsa_cn_append_sum_add = (dsa_an_append_sum_add + dsa_bn_append_sum_add) + dsa_cp_append_sum_add))))))) -> (exists dst_positive_code_append_sum_result dst_positive_scale_append_sum_result dst_negative_code_append_sum_result dst_negative_scale_append_sum_result dst_positive_sum_append_sum_result dst_negative_sum_append_sum_result. (((G) = (((((dst_positive_code_append_sum_result) + (dst_positive_scale_append_sum_result)) * S ((dst_positive_code_append_sum_result) + (dst_positive_scale_append_sum_result)) + ((dst_positive_scale_append_sum_result) + (dst_positive_scale_append_sum_result))) + (((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) * S ((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) + ((dst_negative_scale_append_sum_result) + (dst_negative_scale_append_sum_result)))) * S ((((dst_positive_code_append_sum_result) + (dst_positive_scale_append_sum_result)) * S ((dst_positive_code_append_sum_result) + (dst_positive_scale_append_sum_result)) + ((dst_positive_scale_append_sum_result) + (dst_positive_scale_append_sum_result))) + (((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) * S ((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) + ((dst_negative_scale_append_sum_result) + (dst_negative_scale_append_sum_result)))) + ((((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) * S ((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) + ((dst_negative_scale_append_sum_result) + (dst_negative_scale_append_sum_result))) + (((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) * S ((dst_negative_code_append_sum_result) + (dst_negative_scale_append_sum_result)) + ((dst_negative_scale_append_sum_result) + (dst_negative_scale_append_sum_result)))))) /\ (((exists fs_u_dst_append_sum_resultpositive fs_v_dst_append_sum_resultpositive. ((((exists fs_h_dst_append_sum_resultpositive_body_start. fs_h_dst_append_sum_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_append_sum_resultpositive)) /\ exists fs_q_dst_append_sum_resultpositive_body_start. fs_u_dst_append_sum_resultpositive = fs_q_dst_append_sum_resultpositive_body_start * S ((S (0)) * fs_v_dst_append_sum_resultpositive) + (0))) /\ ((((exists fs_h_dst_append_sum_resultpositive_body_terminal. fs_h_dst_append_sum_resultpositive_body_terminal + S (dst_positive_sum_append_sum_result) = S ((S (S l)) * fs_v_dst_append_sum_resultpositive)) /\ exists fs_q_dst_append_sum_resultpositive_body_terminal. fs_u_dst_append_sum_resultpositive = fs_q_dst_append_sum_resultpositive_body_terminal * S ((S (S l)) * fs_v_dst_append_sum_resultpositive) + (dst_positive_sum_append_sum_result))) /\ forall fs_i_dst_append_sum_resultpositive_body_steps. (exists fs_lt_dst_append_sum_resultpositive_body_steps_bound. fs_lt_dst_append_sum_resultpositive_body_steps_bound + S fs_i_dst_append_sum_resultpositive_body_steps = S l) -> exists fs_a_dst_append_sum_resultpositive_body_steps fs_r_dst_append_sum_resultpositive_body_steps fs_s_dst_append_sum_resultpositive_body_steps. ((((exists fs_h_dst_append_sum_resultpositive_body_steps_summand. fs_h_dst_append_sum_resultpositive_body_steps_summand + S (fs_a_dst_append_sum_resultpositive_body_steps) = S ((S (fs_i_dst_append_sum_resultpositive_body_steps)) * dst_positive_scale_append_sum_result)) /\ exists fs_q_dst_append_sum_resultpositive_body_steps_summand. dst_positive_code_append_sum_result = fs_q_dst_append_sum_resultpositive_body_steps_summand * S ((S (fs_i_dst_append_sum_resultpositive_body_steps)) * dst_positive_scale_append_sum_result) + (fs_a_dst_append_sum_resultpositive_body_steps))) /\ ((((exists fs_h_dst_append_sum_resultpositive_body_steps_partial. fs_h_dst_append_sum_resultpositive_body_steps_partial + S (fs_r_dst_append_sum_resultpositive_body_steps) = S ((S (fs_i_dst_append_sum_resultpositive_body_steps)) * fs_v_dst_append_sum_resultpositive)) /\ exists fs_q_dst_append_sum_resultpositive_body_steps_partial. fs_u_dst_append_sum_resultpositive = fs_q_dst_append_sum_resultpositive_body_steps_partial * S ((S (fs_i_dst_append_sum_resultpositive_body_steps)) * fs_v_dst_append_sum_resultpositive) + (fs_r_dst_append_sum_resultpositive_body_steps))) /\ ((((exists fs_h_dst_append_sum_resultpositive_body_steps_successor. fs_h_dst_append_sum_resultpositive_body_steps_successor + S (fs_s_dst_append_sum_resultpositive_body_steps) = S ((S (S fs_i_dst_append_sum_resultpositive_body_steps)) * fs_v_dst_append_sum_resultpositive)) /\ exists fs_q_dst_append_sum_resultpositive_body_steps_successor. fs_u_dst_append_sum_resultpositive = fs_q_dst_append_sum_resultpositive_body_steps_successor * S ((S (S fs_i_dst_append_sum_resultpositive_body_steps)) * fs_v_dst_append_sum_resultpositive) + (fs_s_dst_append_sum_resultpositive_body_steps))) /\ fs_s_dst_append_sum_resultpositive_body_steps = fs_r_dst_append_sum_resultpositive_body_steps + fs_a_dst_append_sum_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_append_sum_resultnegative fs_v_dst_append_sum_resultnegative. ((((exists fs_h_dst_append_sum_resultnegative_body_start. fs_h_dst_append_sum_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_append_sum_resultnegative)) /\ exists fs_q_dst_append_sum_resultnegative_body_start. fs_u_dst_append_sum_resultnegative = fs_q_dst_append_sum_resultnegative_body_start * S ((S (0)) * fs_v_dst_append_sum_resultnegative) + (0))) /\ ((((exists fs_h_dst_append_sum_resultnegative_body_terminal. fs_h_dst_append_sum_resultnegative_body_terminal + S (dst_negative_sum_append_sum_result) = S ((S (S l)) * fs_v_dst_append_sum_resultnegative)) /\ exists fs_q_dst_append_sum_resultnegative_body_terminal. fs_u_dst_append_sum_resultnegative = fs_q_dst_append_sum_resultnegative_body_terminal * S ((S (S l)) * fs_v_dst_append_sum_resultnegative) + (dst_negative_sum_append_sum_result))) /\ forall fs_i_dst_append_sum_resultnegative_body_steps. (exists fs_lt_dst_append_sum_resultnegative_body_steps_bound. fs_lt_dst_append_sum_resultnegative_body_steps_bound + S fs_i_dst_append_sum_resultnegative_body_steps = S l) -> exists fs_a_dst_append_sum_resultnegative_body_steps fs_r_dst_append_sum_resultnegative_body_steps fs_s_dst_append_sum_resultnegative_body_steps. ((((exists fs_h_dst_append_sum_resultnegative_body_steps_summand. fs_h_dst_append_sum_resultnegative_body_steps_summand + S (fs_a_dst_append_sum_resultnegative_body_steps) = S ((S (fs_i_dst_append_sum_resultnegative_body_steps)) * dst_negative_scale_append_sum_result)) /\ exists fs_q_dst_append_sum_resultnegative_body_steps_summand. dst_negative_code_append_sum_result = fs_q_dst_append_sum_resultnegative_body_steps_summand * S ((S (fs_i_dst_append_sum_resultnegative_body_steps)) * dst_negative_scale_append_sum_result) + (fs_a_dst_append_sum_resultnegative_body_steps))) /\ ((((exists fs_h_dst_append_sum_resultnegative_body_steps_partial. fs_h_dst_append_sum_resultnegative_body_steps_partial + S (fs_r_dst_append_sum_resultnegative_body_steps) = S ((S (fs_i_dst_append_sum_resultnegative_body_steps)) * fs_v_dst_append_sum_resultnegative)) /\ exists fs_q_dst_append_sum_resultnegative_body_steps_partial. fs_u_dst_append_sum_resultnegative = fs_q_dst_append_sum_resultnegative_body_steps_partial * S ((S (fs_i_dst_append_sum_resultnegative_body_steps)) * fs_v_dst_append_sum_resultnegative) + (fs_r_dst_append_sum_resultnegative_body_steps))) /\ ((((exists fs_h_dst_append_sum_resultnegative_body_steps_successor. fs_h_dst_append_sum_resultnegative_body_steps_successor + S (fs_s_dst_append_sum_resultnegative_body_steps) = S ((S (S fs_i_dst_append_sum_resultnegative_body_steps)) * fs_v_dst_append_sum_resultnegative)) /\ exists fs_q_dst_append_sum_resultnegative_body_steps_successor. fs_u_dst_append_sum_resultnegative = fs_q_dst_append_sum_resultnegative_body_steps_successor * S ((S (S fs_i_dst_append_sum_resultnegative_body_steps)) * fs_v_dst_append_sum_resultnegative) + (fs_s_dst_append_sum_resultnegative_body_steps))) /\ fs_s_dst_append_sum_resultnegative_body_steps = fs_r_dst_append_sum_resultnegative_body_steps + fs_a_dst_append_sum_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_append_sum_resultresult ge_balance_negative_append_sum_resultresult. (((((c) = 2 * (ge_balance_positive_append_sum_resultresult) /\ (ge_balance_negative_append_sum_resultresult) = 0) \/ exists ge_signed_half_append_sum_resultresultdecode. (((c) = 2 * ge_signed_half_append_sum_resultresultdecode + 1 /\ (ge_balance_positive_append_sum_resultresult) = 0) /\ (ge_balance_negative_append_sum_resultresult) = S ge_signed_half_append_sum_resultresultdecode))) /\ ((dst_positive_sum_append_sum_result) + ge_balance_negative_append_sum_resultresult = (dst_negative_sum_append_sum_result) + ge_balance_positive_append_sum_resultresult)))))))))

mobius_table_zero_constructor

new owned theorem · read exact theorem evidence

Bundle node 284; exact statement SHA-256 12d74174a422ac083c869223daee6b85796188d493673fcfcdc61dadb2064f70

Exact first-order statement

forall F. (exists dst_positive_code_base_table dst_positive_scale_base_table dst_negative_code_base_table dst_negative_scale_base_table. (((F) = (((((dst_positive_code_base_table) + (dst_positive_scale_base_table)) * S ((dst_positive_code_base_table) + (dst_positive_scale_base_table)) + ((dst_positive_scale_base_table) + (dst_positive_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))) * S ((((dst_positive_code_base_table) + (dst_positive_scale_base_table)) * S ((dst_positive_code_base_table) + (dst_positive_scale_base_table)) + ((dst_positive_scale_base_table) + (dst_positive_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))) + ((((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))))) /\ (forall dst_index_base_table. (exists pvs_le_gap_base_tabledomain. pvs_le_gap_base_tabledomain + (dst_index_base_table) = (0)) -> exists dst_positive_base_table dst_negative_base_table dst_value_base_table. ((((exists ff_h_pvs_base_tableentrypositive. ff_h_pvs_base_tableentrypositive + S (dst_positive_base_table) = S ((S (dst_index_base_table)) * dst_positive_scale_base_table)) /\ exists ff_q_pvs_base_tableentrypositive. dst_positive_code_base_table = ff_q_pvs_base_tableentrypositive * S ((S (dst_index_base_table)) * dst_positive_scale_base_table) + (dst_positive_base_table))) /\ (((((exists ff_h_pvs_base_tableentrynegative. ff_h_pvs_base_tableentrynegative + S (dst_negative_base_table) = S ((S (dst_index_base_table)) * dst_negative_scale_base_table)) /\ exists ff_q_pvs_base_tableentrynegative. dst_negative_code_base_table = ff_q_pvs_base_tableentrynegative * S ((S (dst_index_base_table)) * dst_negative_scale_base_table) + (dst_negative_base_table))) /\ (exists ge_balance_positive_base_tableentryvalue ge_balance_negative_base_tableentryvalue. (((((dst_value_base_table) = 2 * (ge_balance_positive_base_tableentryvalue) /\ (ge_balance_negative_base_tableentryvalue) = 0) \/ exists ge_signed_half_base_tableentryvaluedecode. (((dst_value_base_table) = 2 * ge_signed_half_base_tableentryvaluedecode + 1 /\ (ge_balance_positive_base_tableentryvalue) = 0) /\ (ge_balance_negative_base_tableentryvalue) = S ge_signed_half_base_tableentryvaluedecode))) /\ ((dst_positive_base_table) + ge_balance_negative_base_tableentryvalue = (dst_negative_base_table) + ge_balance_positive_base_tableentryvalue))))))))) -> (exists dst_positive_code_base_zero dst_positive_scale_base_zero dst_negative_code_base_zero dst_negative_scale_base_zero dst_positive_base_zero dst_negative_base_zero. (((F) = (((((dst_positive_code_base_zero) + (dst_positive_scale_base_zero)) * S ((dst_positive_code_base_zero) + (dst_positive_scale_base_zero)) + ((dst_positive_scale_base_zero) + (dst_positive_scale_base_zero))) + (((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) * S ((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) + ((dst_negative_scale_base_zero) + (dst_negative_scale_base_zero)))) * S ((((dst_positive_code_base_zero) + (dst_positive_scale_base_zero)) * S ((dst_positive_code_base_zero) + (dst_positive_scale_base_zero)) + ((dst_positive_scale_base_zero) + (dst_positive_scale_base_zero))) + (((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) * S ((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) + ((dst_negative_scale_base_zero) + (dst_negative_scale_base_zero)))) + ((((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) * S ((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) + ((dst_negative_scale_base_zero) + (dst_negative_scale_base_zero))) + (((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) * S ((dst_negative_code_base_zero) + (dst_negative_scale_base_zero)) + ((dst_negative_scale_base_zero) + (dst_negative_scale_base_zero)))))) /\ (((((exists ff_h_pvs_base_zeropositive. ff_h_pvs_base_zeropositive + S (dst_positive_base_zero) = S ((S (0)) * dst_positive_scale_base_zero)) /\ exists ff_q_pvs_base_zeropositive. dst_positive_code_base_zero = ff_q_pvs_base_zeropositive * S ((S (0)) * dst_positive_scale_base_zero) + (dst_positive_base_zero))) /\ (((((exists ff_h_pvs_base_zeronegative. ff_h_pvs_base_zeronegative + S (dst_negative_base_zero) = S ((S (0)) * dst_negative_scale_base_zero)) /\ exists ff_q_pvs_base_zeronegative. dst_negative_code_base_zero = ff_q_pvs_base_zeronegative * S ((S (0)) * dst_negative_scale_base_zero) + (dst_negative_base_zero))) /\ (exists ge_balance_positive_base_zerovalue ge_balance_negative_base_zerovalue. (((((0) = 2 * (ge_balance_positive_base_zerovalue) /\ (ge_balance_negative_base_zerovalue) = 0) \/ exists ge_signed_half_base_zerovaluedecode. (((0) = 2 * ge_signed_half_base_zerovaluedecode + 1 /\ (ge_balance_positive_base_zerovalue) = 0) /\ (ge_balance_negative_base_zerovalue) = S ge_signed_half_base_zerovaluedecode))) /\ ((dst_positive_base_zero) + ge_balance_negative_base_zerovalue = (dst_negative_base_zero) + ge_balance_positive_base_zerovalue))))))))) -> (((exists dst_positive_code_base_resulttable dst_positive_scale_base_resulttable dst_negative_code_base_resulttable dst_negative_scale_base_resulttable. (((F) = (((((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) * S ((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) + ((dst_positive_scale_base_resulttable) + (dst_positive_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))) * S ((((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) * S ((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) + ((dst_positive_scale_base_resulttable) + (dst_positive_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))) + ((((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))))) /\ (forall dst_index_base_resulttable. (exists pvs_le_gap_base_resulttabledomain. pvs_le_gap_base_resulttabledomain + (dst_index_base_resulttable) = (0)) -> exists dst_positive_base_resulttable dst_negative_base_resulttable dst_value_base_resulttable. ((((exists ff_h_pvs_base_resulttableentrypositive. ff_h_pvs_base_resulttableentrypositive + S (dst_positive_base_resulttable) = S ((S (dst_index_base_resulttable)) * dst_positive_scale_base_resulttable)) /\ exists ff_q_pvs_base_resulttableentrypositive. dst_positive_code_base_resulttable = ff_q_pvs_base_resulttableentrypositive * S ((S (dst_index_base_resulttable)) * dst_positive_scale_base_resulttable) + (dst_positive_base_resulttable))) /\ (((((exists ff_h_pvs_base_resulttableentrynegative. ff_h_pvs_base_resulttableentrynegative + S (dst_negative_base_resulttable) = S ((S (dst_index_base_resulttable)) * dst_negative_scale_base_resulttable)) /\ exists ff_q_pvs_base_resulttableentrynegative. dst_negative_code_base_resulttable = ff_q_pvs_base_resulttableentrynegative * S ((S (dst_index_base_resulttable)) * dst_negative_scale_base_resulttable) + (dst_negative_base_resulttable))) /\ (exists ge_balance_positive_base_resulttableentryvalue ge_balance_negative_base_resulttableentryvalue. (((((dst_value_base_resulttable) = 2 * (ge_balance_positive_base_resulttableentryvalue) /\ (ge_balance_negative_base_resulttableentryvalue) = 0) \/ exists ge_signed_half_base_resulttableentryvaluedecode. (((dst_value_base_resulttable) = 2 * ge_signed_half_base_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_base_resulttableentryvalue) = 0) /\ (ge_balance_negative_base_resulttableentryvalue) = S ge_signed_half_base_resulttableentryvaluedecode))) /\ ((dst_positive_base_resulttable) + ge_balance_negative_base_resulttableentryvalue = (dst_negative_base_resulttable) + ge_balance_positive_base_resulttableentryvalue))))))))) /\ (((exists dst_positive_code_base_resultzero dst_positive_scale_base_resultzero dst_negative_code_base_resultzero dst_negative_scale_base_resultzero dst_positive_base_resultzero dst_negative_base_resultzero. (((F) = (((((dst_positive_code_base_resultzero) + (dst_positive_scale_base_resultzero)) * S ((dst_positive_code_base_resultzero) + (dst_positive_scale_base_resultzero)) + ((dst_positive_scale_base_resultzero) + (dst_positive_scale_base_resultzero))) + (((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) * S ((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) + ((dst_negative_scale_base_resultzero) + (dst_negative_scale_base_resultzero)))) * S ((((dst_positive_code_base_resultzero) + (dst_positive_scale_base_resultzero)) * S ((dst_positive_code_base_resultzero) + (dst_positive_scale_base_resultzero)) + ((dst_positive_scale_base_resultzero) + (dst_positive_scale_base_resultzero))) + (((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) * S ((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) + ((dst_negative_scale_base_resultzero) + (dst_negative_scale_base_resultzero)))) + ((((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) * S ((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) + ((dst_negative_scale_base_resultzero) + (dst_negative_scale_base_resultzero))) + (((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) * S ((dst_negative_code_base_resultzero) + (dst_negative_scale_base_resultzero)) + ((dst_negative_scale_base_resultzero) + (dst_negative_scale_base_resultzero)))))) /\ (((((exists ff_h_pvs_base_resultzeropositive. ff_h_pvs_base_resultzeropositive + S (dst_positive_base_resultzero) = S ((S (0)) * dst_positive_scale_base_resultzero)) /\ exists ff_q_pvs_base_resultzeropositive. dst_positive_code_base_resultzero = ff_q_pvs_base_resultzeropositive * S ((S (0)) * dst_positive_scale_base_resultzero) + (dst_positive_base_resultzero))) /\ (((((exists ff_h_pvs_base_resultzeronegative. ff_h_pvs_base_resultzeronegative + S (dst_negative_base_resultzero) = S ((S (0)) * dst_negative_scale_base_resultzero)) /\ exists ff_q_pvs_base_resultzeronegative. dst_negative_code_base_resultzero = ff_q_pvs_base_resultzeronegative * S ((S (0)) * dst_negative_scale_base_resultzero) + (dst_negative_base_resultzero))) /\ (exists ge_balance_positive_base_resultzerovalue ge_balance_negative_base_resultzerovalue. (((((0) = 2 * (ge_balance_positive_base_resultzerovalue) /\ (ge_balance_negative_base_resultzerovalue) = 0) \/ exists ge_signed_half_base_resultzerovaluedecode. (((0) = 2 * ge_signed_half_base_resultzerovaluedecode + 1 /\ (ge_balance_positive_base_resultzerovalue) = 0) /\ (ge_balance_negative_base_resultzerovalue) = S ge_signed_half_base_resultzerovaluedecode))) /\ ((dst_positive_base_resultzero) + ge_balance_negative_base_resultzerovalue = (dst_negative_base_resultzero) + ge_balance_positive_base_resultzerovalue))))))))) /\ (forall mt_index_base_result mt_value_base_result. ~(mt_index_base_result=0) -> (exists pvs_le_gap_base_resultdomain. pvs_le_gap_base_resultdomain + (mt_index_base_result) = (0)) -> (exists dst_positive_code_base_resultentry dst_positive_scale_base_resultentry dst_negative_code_base_resultentry dst_negative_scale_base_resultentry dst_positive_base_resultentry dst_negative_base_resultentry. (((F) = (((((dst_positive_code_base_resultentry) + (dst_positive_scale_base_resultentry)) * S ((dst_positive_code_base_resultentry) + (dst_positive_scale_base_resultentry)) + ((dst_positive_scale_base_resultentry) + (dst_positive_scale_base_resultentry))) + (((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) * S ((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) + ((dst_negative_scale_base_resultentry) + (dst_negative_scale_base_resultentry)))) * S ((((dst_positive_code_base_resultentry) + (dst_positive_scale_base_resultentry)) * S ((dst_positive_code_base_resultentry) + (dst_positive_scale_base_resultentry)) + ((dst_positive_scale_base_resultentry) + (dst_positive_scale_base_resultentry))) + (((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) * S ((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) + ((dst_negative_scale_base_resultentry) + (dst_negative_scale_base_resultentry)))) + ((((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) * S ((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) + ((dst_negative_scale_base_resultentry) + (dst_negative_scale_base_resultentry))) + (((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) * S ((dst_negative_code_base_resultentry) + (dst_negative_scale_base_resultentry)) + ((dst_negative_scale_base_resultentry) + (dst_negative_scale_base_resultentry)))))) /\ (((((exists ff_h_pvs_base_resultentrypositive. ff_h_pvs_base_resultentrypositive + S (dst_positive_base_resultentry) = S ((S (mt_index_base_result)) * dst_positive_scale_base_resultentry)) /\ exists ff_q_pvs_base_resultentrypositive. dst_positive_code_base_resultentry = ff_q_pvs_base_resultentrypositive * S ((S (mt_index_base_result)) * dst_positive_scale_base_resultentry) + (dst_positive_base_resultentry))) /\ (((((exists ff_h_pvs_base_resultentrynegative. ff_h_pvs_base_resultentrynegative + S (dst_negative_base_resultentry) = S ((S (mt_index_base_result)) * dst_negative_scale_base_resultentry)) /\ exists ff_q_pvs_base_resultentrynegative. dst_negative_code_base_resultentry = ff_q_pvs_base_resultentrynegative * S ((S (mt_index_base_result)) * dst_negative_scale_base_resultentry) + (dst_negative_base_resultentry))) /\ (exists ge_balance_positive_base_resultentryvalue ge_balance_negative_base_resultentryvalue. (((((mt_value_base_result) = 2 * (ge_balance_positive_base_resultentryvalue) /\ (ge_balance_negative_base_resultentryvalue) = 0) \/ exists ge_signed_half_base_resultentryvaluedecode. (((mt_value_base_result) = 2 * ge_signed_half_base_resultentryvaluedecode + 1 /\ (ge_balance_positive_base_resultentryvalue) = 0) /\ (ge_balance_negative_base_resultentryvalue) = S ge_signed_half_base_resultentryvaluedecode))) /\ ((dst_positive_base_resultentry) + ge_balance_negative_base_resultentryvalue = (dst_negative_base_resultentry) + ge_balance_positive_base_resultentryvalue))))))))) -> (((~((mt_index_base_result) = 0)) /\ ((((exists mv_square_prime_base_resultvaluesquare. ((~((mv_square_prime_base_resultvaluesquare) = 1) /\ forall pvs_left_base_resultvaluesquareprime pvs_right_base_resultvaluesquareprime. (mv_square_prime_base_resultvaluesquare) = pvs_left_base_resultvaluesquareprime * pvs_right_base_resultvaluesquareprime -> pvs_left_base_resultvaluesquareprime = 1 \/ pvs_right_base_resultvaluesquareprime = 1) /\ (exists pvs_factor_base_resultvaluesquaredivisor. (mt_index_base_result) = (mv_square_prime_base_resultvaluesquare * mv_square_prime_base_resultvaluesquare) * pvs_factor_base_resultvaluesquaredivisor))) /\ ((mt_value_base_result) = 0))) \/ (((((~((mt_index_base_result) = 0)) /\ (forall sfd_prime_base_resultvaluesquarefree. (~((sfd_prime_base_resultvaluesquarefree) = 1) /\ forall pvs_left_base_resultvaluesquarefreedomain pvs_right_base_resultvaluesquarefreedomain. (sfd_prime_base_resultvaluesquarefree) = pvs_left_base_resultvaluesquarefreedomain * pvs_right_base_resultvaluesquarefreedomain -> pvs_left_base_resultvaluesquarefreedomain = 1 \/ pvs_right_base_resultvaluesquarefreedomain = 1) -> (exists pvs_le_gap_base_resultvaluesquarefreebound. pvs_le_gap_base_resultvaluesquarefreebound + (sfd_prime_base_resultvaluesquarefree) = (mt_index_base_result)) -> ~(exists pvs_factor_base_resultvaluesquarefreesquare. (mt_index_base_result) = (sfd_prime_base_resultvaluesquarefree * sfd_prime_base_resultvaluesquarefree) * pvs_factor_base_resultvaluesquarefreesquare)))) /\ (exists mv_factor_code_base_resultvaluefactors mv_factor_scale_base_resultvaluefactors mv_factor_count_base_resultvaluefactors. (((~(mt_index_base_result = 0) /\ ((exists ff_u_fsat_base_resultvaluefactorsfactorization_product ff_v_fsat_base_resultvaluefactorsfactorization_product. ((((exists ff_h_fsat_base_resultvaluefactorsfactorization_product_start. ff_h_fsat_base_resultvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_base_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_base_resultvaluefactorsfactorization_product_start. ff_u_fsat_base_resultvaluefactorsfactorization_product = ff_q_fsat_base_resultvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_base_resultvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_base_resultvaluefactorsfactorization_product_terminal. ff_h_fsat_base_resultvaluefactorsfactorization_product_terminal + S (mt_index_base_result) = S ((S (mv_factor_count_base_resultvaluefactors)) * ff_v_fsat_base_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_base_resultvaluefactorsfactorization_product_terminal. ff_u_fsat_base_resultvaluefactorsfactorization_product = ff_q_fsat_base_resultvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_base_resultvaluefactors)) * ff_v_fsat_base_resultvaluefactorsfactorization_product) + (mt_index_base_result))) /\ forall ff_i_fsat_base_resultvaluefactorsfactorization_product. (exists ff_lt_fsat_base_resultvaluefactorsfactorization_product_bound. ff_lt_fsat_base_resultvaluefactorsfactorization_product_bound + S ff_i_fsat_base_resultvaluefactorsfactorization_product = mv_factor_count_base_resultvaluefactors) -> exists ff_p_fsat_base_resultvaluefactorsfactorization_product ff_r_fsat_base_resultvaluefactorsfactorization_product ff_s_fsat_base_resultvaluefactorsfactorization_product. ((((exists ff_h_fsat_base_resultvaluefactorsfactorization_product_factor. ff_h_fsat_base_resultvaluefactorsfactorization_product_factor + S (ff_p_fsat_base_resultvaluefactorsfactorization_product) = S ((S (ff_i_fsat_base_resultvaluefactorsfactorization_product)) * mv_factor_scale_base_resultvaluefactors)) /\ exists ff_q_fsat_base_resultvaluefactorsfactorization_product_factor. mv_factor_code_base_resultvaluefactors = ff_q_fsat_base_resultvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_base_resultvaluefactorsfactorization_product)) * mv_factor_scale_base_resultvaluefactors) + (ff_p_fsat_base_resultvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_base_resultvaluefactorsfactorization_product_partial. ff_h_fsat_base_resultvaluefactorsfactorization_product_partial + S (ff_r_fsat_base_resultvaluefactorsfactorization_product) = S ((S (ff_i_fsat_base_resultvaluefactorsfactorization_product)) * ff_v_fsat_base_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_base_resultvaluefactorsfactorization_product_partial. ff_u_fsat_base_resultvaluefactorsfactorization_product = ff_q_fsat_base_resultvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_base_resultvaluefactorsfactorization_product)) * ff_v_fsat_base_resultvaluefactorsfactorization_product) + (ff_r_fsat_base_resultvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_base_resultvaluefactorsfactorization_product_successor. ff_h_fsat_base_resultvaluefactorsfactorization_product_successor + S (ff_s_fsat_base_resultvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_base_resultvaluefactorsfactorization_product)) * ff_v_fsat_base_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_base_resultvaluefactorsfactorization_product_successor. ff_u_fsat_base_resultvaluefactorsfactorization_product = ff_q_fsat_base_resultvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_base_resultvaluefactorsfactorization_product)) * ff_v_fsat_base_resultvaluefactorsfactorization_product) + (ff_s_fsat_base_resultvaluefactorsfactorization_product))) /\ ff_s_fsat_base_resultvaluefactorsfactorization_product = ff_r_fsat_base_resultvaluefactorsfactorization_product * ff_p_fsat_base_resultvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_base_resultvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_base_resultvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_base_resultvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_base_resultvaluefactorsfactorization_primes = (mv_factor_count_base_resultvaluefactors)) -> exists ftsf_factor_fsat_base_resultvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_base_resultvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_base_resultvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_base_resultvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_base_resultvaluefactorsfactorization_primes)) * mv_factor_scale_base_resultvaluefactors)) /\ exists ff_q_ftsf_fsat_base_resultvaluefactorsfactorization_primes_entry. mv_factor_code_base_resultvaluefactors = ff_q_ftsf_fsat_base_resultvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_base_resultvaluefactorsfactorization_primes)) * mv_factor_scale_base_resultvaluefactors) + (ftsf_factor_fsat_base_resultvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_base_resultvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_base_resultvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_base_resultvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_base_resultvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_base_resultvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_base_resultvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_base_resultvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_base_resultvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_base_resultvaluefactorsparityeven. (mv_factor_count_base_resultvaluefactors) = 2 * mv_even_half_base_resultvaluefactorsparityeven) /\ ((mt_value_base_result) = 2))) \/ (((exists mv_odd_half_base_resultvaluefactorsparityodd. (mv_factor_count_base_resultvaluefactors) = 2 * mv_odd_half_base_resultvaluefactorsparityodd + 1) /\ ((mt_value_base_result) = 1))))))))))))))))

mobius_table_append

new owned theorem · read exact theorem evidence

Bundle node 285; exact statement SHA-256 c76f820bd1cf5219ee1c3d37af5bcb9ccaf2a3d6a26d3f301dd72c03ddfefc84

Exact first-order statement

forall N F z. (((exists dst_positive_code_append_oldtable dst_positive_scale_append_oldtable dst_negative_code_append_oldtable dst_negative_scale_append_oldtable. (((F) = (((((dst_positive_code_append_oldtable) + (dst_positive_scale_append_oldtable)) * S ((dst_positive_code_append_oldtable) + (dst_positive_scale_append_oldtable)) + ((dst_positive_scale_append_oldtable) + (dst_positive_scale_append_oldtable))) + (((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) * S ((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) + ((dst_negative_scale_append_oldtable) + (dst_negative_scale_append_oldtable)))) * S ((((dst_positive_code_append_oldtable) + (dst_positive_scale_append_oldtable)) * S ((dst_positive_code_append_oldtable) + (dst_positive_scale_append_oldtable)) + ((dst_positive_scale_append_oldtable) + (dst_positive_scale_append_oldtable))) + (((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) * S ((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) + ((dst_negative_scale_append_oldtable) + (dst_negative_scale_append_oldtable)))) + ((((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) * S ((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) + ((dst_negative_scale_append_oldtable) + (dst_negative_scale_append_oldtable))) + (((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) * S ((dst_negative_code_append_oldtable) + (dst_negative_scale_append_oldtable)) + ((dst_negative_scale_append_oldtable) + (dst_negative_scale_append_oldtable)))))) /\ (forall dst_index_append_oldtable. (exists pvs_le_gap_append_oldtabledomain. pvs_le_gap_append_oldtabledomain + (dst_index_append_oldtable) = (N)) -> exists dst_positive_append_oldtable dst_negative_append_oldtable dst_value_append_oldtable. ((((exists ff_h_pvs_append_oldtableentrypositive. ff_h_pvs_append_oldtableentrypositive + S (dst_positive_append_oldtable) = S ((S (dst_index_append_oldtable)) * dst_positive_scale_append_oldtable)) /\ exists ff_q_pvs_append_oldtableentrypositive. dst_positive_code_append_oldtable = ff_q_pvs_append_oldtableentrypositive * S ((S (dst_index_append_oldtable)) * dst_positive_scale_append_oldtable) + (dst_positive_append_oldtable))) /\ (((((exists ff_h_pvs_append_oldtableentrynegative. ff_h_pvs_append_oldtableentrynegative + S (dst_negative_append_oldtable) = S ((S (dst_index_append_oldtable)) * dst_negative_scale_append_oldtable)) /\ exists ff_q_pvs_append_oldtableentrynegative. dst_negative_code_append_oldtable = ff_q_pvs_append_oldtableentrynegative * S ((S (dst_index_append_oldtable)) * dst_negative_scale_append_oldtable) + (dst_negative_append_oldtable))) /\ (exists ge_balance_positive_append_oldtableentryvalue ge_balance_negative_append_oldtableentryvalue. (((((dst_value_append_oldtable) = 2 * (ge_balance_positive_append_oldtableentryvalue) /\ (ge_balance_negative_append_oldtableentryvalue) = 0) \/ exists ge_signed_half_append_oldtableentryvaluedecode. (((dst_value_append_oldtable) = 2 * ge_signed_half_append_oldtableentryvaluedecode + 1 /\ (ge_balance_positive_append_oldtableentryvalue) = 0) /\ (ge_balance_negative_append_oldtableentryvalue) = S ge_signed_half_append_oldtableentryvaluedecode))) /\ ((dst_positive_append_oldtable) + ge_balance_negative_append_oldtableentryvalue = (dst_negative_append_oldtable) + ge_balance_positive_append_oldtableentryvalue))))))))) /\ (((exists dst_positive_code_append_oldzero dst_positive_scale_append_oldzero dst_negative_code_append_oldzero dst_negative_scale_append_oldzero dst_positive_append_oldzero dst_negative_append_oldzero. (((F) = (((((dst_positive_code_append_oldzero) + (dst_positive_scale_append_oldzero)) * S ((dst_positive_code_append_oldzero) + (dst_positive_scale_append_oldzero)) + ((dst_positive_scale_append_oldzero) + (dst_positive_scale_append_oldzero))) + (((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) * S ((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) + ((dst_negative_scale_append_oldzero) + (dst_negative_scale_append_oldzero)))) * S ((((dst_positive_code_append_oldzero) + (dst_positive_scale_append_oldzero)) * S ((dst_positive_code_append_oldzero) + (dst_positive_scale_append_oldzero)) + ((dst_positive_scale_append_oldzero) + (dst_positive_scale_append_oldzero))) + (((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) * S ((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) + ((dst_negative_scale_append_oldzero) + (dst_negative_scale_append_oldzero)))) + ((((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) * S ((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) + ((dst_negative_scale_append_oldzero) + (dst_negative_scale_append_oldzero))) + (((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) * S ((dst_negative_code_append_oldzero) + (dst_negative_scale_append_oldzero)) + ((dst_negative_scale_append_oldzero) + (dst_negative_scale_append_oldzero)))))) /\ (((((exists ff_h_pvs_append_oldzeropositive. ff_h_pvs_append_oldzeropositive + S (dst_positive_append_oldzero) = S ((S (0)) * dst_positive_scale_append_oldzero)) /\ exists ff_q_pvs_append_oldzeropositive. dst_positive_code_append_oldzero = ff_q_pvs_append_oldzeropositive * S ((S (0)) * dst_positive_scale_append_oldzero) + (dst_positive_append_oldzero))) /\ (((((exists ff_h_pvs_append_oldzeronegative. ff_h_pvs_append_oldzeronegative + S (dst_negative_append_oldzero) = S ((S (0)) * dst_negative_scale_append_oldzero)) /\ exists ff_q_pvs_append_oldzeronegative. dst_negative_code_append_oldzero = ff_q_pvs_append_oldzeronegative * S ((S (0)) * dst_negative_scale_append_oldzero) + (dst_negative_append_oldzero))) /\ (exists ge_balance_positive_append_oldzerovalue ge_balance_negative_append_oldzerovalue. (((((0) = 2 * (ge_balance_positive_append_oldzerovalue) /\ (ge_balance_negative_append_oldzerovalue) = 0) \/ exists ge_signed_half_append_oldzerovaluedecode. (((0) = 2 * ge_signed_half_append_oldzerovaluedecode + 1 /\ (ge_balance_positive_append_oldzerovalue) = 0) /\ (ge_balance_negative_append_oldzerovalue) = S ge_signed_half_append_oldzerovaluedecode))) /\ ((dst_positive_append_oldzero) + ge_balance_negative_append_oldzerovalue = (dst_negative_append_oldzero) + ge_balance_positive_append_oldzerovalue))))))))) /\ (forall mt_index_append_old mt_value_append_old. ~(mt_index_append_old=0) -> (exists pvs_le_gap_append_olddomain. pvs_le_gap_append_olddomain + (mt_index_append_old) = (N)) -> (exists dst_positive_code_append_oldentry dst_positive_scale_append_oldentry dst_negative_code_append_oldentry dst_negative_scale_append_oldentry dst_positive_append_oldentry dst_negative_append_oldentry. (((F) = (((((dst_positive_code_append_oldentry) + (dst_positive_scale_append_oldentry)) * S ((dst_positive_code_append_oldentry) + (dst_positive_scale_append_oldentry)) + ((dst_positive_scale_append_oldentry) + (dst_positive_scale_append_oldentry))) + (((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) * S ((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) + ((dst_negative_scale_append_oldentry) + (dst_negative_scale_append_oldentry)))) * S ((((dst_positive_code_append_oldentry) + (dst_positive_scale_append_oldentry)) * S ((dst_positive_code_append_oldentry) + (dst_positive_scale_append_oldentry)) + ((dst_positive_scale_append_oldentry) + (dst_positive_scale_append_oldentry))) + (((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) * S ((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) + ((dst_negative_scale_append_oldentry) + (dst_negative_scale_append_oldentry)))) + ((((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) * S ((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) + ((dst_negative_scale_append_oldentry) + (dst_negative_scale_append_oldentry))) + (((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) * S ((dst_negative_code_append_oldentry) + (dst_negative_scale_append_oldentry)) + ((dst_negative_scale_append_oldentry) + (dst_negative_scale_append_oldentry)))))) /\ (((((exists ff_h_pvs_append_oldentrypositive. ff_h_pvs_append_oldentrypositive + S (dst_positive_append_oldentry) = S ((S (mt_index_append_old)) * dst_positive_scale_append_oldentry)) /\ exists ff_q_pvs_append_oldentrypositive. dst_positive_code_append_oldentry = ff_q_pvs_append_oldentrypositive * S ((S (mt_index_append_old)) * dst_positive_scale_append_oldentry) + (dst_positive_append_oldentry))) /\ (((((exists ff_h_pvs_append_oldentrynegative. ff_h_pvs_append_oldentrynegative + S (dst_negative_append_oldentry) = S ((S (mt_index_append_old)) * dst_negative_scale_append_oldentry)) /\ exists ff_q_pvs_append_oldentrynegative. dst_negative_code_append_oldentry = ff_q_pvs_append_oldentrynegative * S ((S (mt_index_append_old)) * dst_negative_scale_append_oldentry) + (dst_negative_append_oldentry))) /\ (exists ge_balance_positive_append_oldentryvalue ge_balance_negative_append_oldentryvalue. (((((mt_value_append_old) = 2 * (ge_balance_positive_append_oldentryvalue) /\ (ge_balance_negative_append_oldentryvalue) = 0) \/ exists ge_signed_half_append_oldentryvaluedecode. (((mt_value_append_old) = 2 * ge_signed_half_append_oldentryvaluedecode + 1 /\ (ge_balance_positive_append_oldentryvalue) = 0) /\ (ge_balance_negative_append_oldentryvalue) = S ge_signed_half_append_oldentryvaluedecode))) /\ ((dst_positive_append_oldentry) + ge_balance_negative_append_oldentryvalue = (dst_negative_append_oldentry) + ge_balance_positive_append_oldentryvalue))))))))) -> (((~((mt_index_append_old) = 0)) /\ ((((exists mv_square_prime_append_oldvaluesquare. ((~((mv_square_prime_append_oldvaluesquare) = 1) /\ forall pvs_left_append_oldvaluesquareprime pvs_right_append_oldvaluesquareprime. (mv_square_prime_append_oldvaluesquare) = pvs_left_append_oldvaluesquareprime * pvs_right_append_oldvaluesquareprime -> pvs_left_append_oldvaluesquareprime = 1 \/ pvs_right_append_oldvaluesquareprime = 1) /\ (exists pvs_factor_append_oldvaluesquaredivisor. (mt_index_append_old) = (mv_square_prime_append_oldvaluesquare * mv_square_prime_append_oldvaluesquare) * pvs_factor_append_oldvaluesquaredivisor))) /\ ((mt_value_append_old) = 0))) \/ (((((~((mt_index_append_old) = 0)) /\ (forall sfd_prime_append_oldvaluesquarefree. (~((sfd_prime_append_oldvaluesquarefree) = 1) /\ forall pvs_left_append_oldvaluesquarefreedomain pvs_right_append_oldvaluesquarefreedomain. (sfd_prime_append_oldvaluesquarefree) = pvs_left_append_oldvaluesquarefreedomain * pvs_right_append_oldvaluesquarefreedomain -> pvs_left_append_oldvaluesquarefreedomain = 1 \/ pvs_right_append_oldvaluesquarefreedomain = 1) -> (exists pvs_le_gap_append_oldvaluesquarefreebound. pvs_le_gap_append_oldvaluesquarefreebound + (sfd_prime_append_oldvaluesquarefree) = (mt_index_append_old)) -> ~(exists pvs_factor_append_oldvaluesquarefreesquare. (mt_index_append_old) = (sfd_prime_append_oldvaluesquarefree * sfd_prime_append_oldvaluesquarefree) * pvs_factor_append_oldvaluesquarefreesquare)))) /\ (exists mv_factor_code_append_oldvaluefactors mv_factor_scale_append_oldvaluefactors mv_factor_count_append_oldvaluefactors. (((~(mt_index_append_old = 0) /\ ((exists ff_u_fsat_append_oldvaluefactorsfactorization_product ff_v_fsat_append_oldvaluefactorsfactorization_product. ((((exists ff_h_fsat_append_oldvaluefactorsfactorization_product_start. ff_h_fsat_append_oldvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_append_oldvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_oldvaluefactorsfactorization_product_start. ff_u_fsat_append_oldvaluefactorsfactorization_product = ff_q_fsat_append_oldvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_append_oldvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_append_oldvaluefactorsfactorization_product_terminal. ff_h_fsat_append_oldvaluefactorsfactorization_product_terminal + S (mt_index_append_old) = S ((S (mv_factor_count_append_oldvaluefactors)) * ff_v_fsat_append_oldvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_oldvaluefactorsfactorization_product_terminal. ff_u_fsat_append_oldvaluefactorsfactorization_product = ff_q_fsat_append_oldvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_append_oldvaluefactors)) * ff_v_fsat_append_oldvaluefactorsfactorization_product) + (mt_index_append_old))) /\ forall ff_i_fsat_append_oldvaluefactorsfactorization_product. (exists ff_lt_fsat_append_oldvaluefactorsfactorization_product_bound. ff_lt_fsat_append_oldvaluefactorsfactorization_product_bound + S ff_i_fsat_append_oldvaluefactorsfactorization_product = mv_factor_count_append_oldvaluefactors) -> exists ff_p_fsat_append_oldvaluefactorsfactorization_product ff_r_fsat_append_oldvaluefactorsfactorization_product ff_s_fsat_append_oldvaluefactorsfactorization_product. ((((exists ff_h_fsat_append_oldvaluefactorsfactorization_product_factor. ff_h_fsat_append_oldvaluefactorsfactorization_product_factor + S (ff_p_fsat_append_oldvaluefactorsfactorization_product) = S ((S (ff_i_fsat_append_oldvaluefactorsfactorization_product)) * mv_factor_scale_append_oldvaluefactors)) /\ exists ff_q_fsat_append_oldvaluefactorsfactorization_product_factor. mv_factor_code_append_oldvaluefactors = ff_q_fsat_append_oldvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_append_oldvaluefactorsfactorization_product)) * mv_factor_scale_append_oldvaluefactors) + (ff_p_fsat_append_oldvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_append_oldvaluefactorsfactorization_product_partial. ff_h_fsat_append_oldvaluefactorsfactorization_product_partial + S (ff_r_fsat_append_oldvaluefactorsfactorization_product) = S ((S (ff_i_fsat_append_oldvaluefactorsfactorization_product)) * ff_v_fsat_append_oldvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_oldvaluefactorsfactorization_product_partial. ff_u_fsat_append_oldvaluefactorsfactorization_product = ff_q_fsat_append_oldvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_append_oldvaluefactorsfactorization_product)) * ff_v_fsat_append_oldvaluefactorsfactorization_product) + (ff_r_fsat_append_oldvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_append_oldvaluefactorsfactorization_product_successor. ff_h_fsat_append_oldvaluefactorsfactorization_product_successor + S (ff_s_fsat_append_oldvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_append_oldvaluefactorsfactorization_product)) * ff_v_fsat_append_oldvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_oldvaluefactorsfactorization_product_successor. ff_u_fsat_append_oldvaluefactorsfactorization_product = ff_q_fsat_append_oldvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_append_oldvaluefactorsfactorization_product)) * ff_v_fsat_append_oldvaluefactorsfactorization_product) + (ff_s_fsat_append_oldvaluefactorsfactorization_product))) /\ ff_s_fsat_append_oldvaluefactorsfactorization_product = ff_r_fsat_append_oldvaluefactorsfactorization_product * ff_p_fsat_append_oldvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_append_oldvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_append_oldvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_append_oldvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_append_oldvaluefactorsfactorization_primes = (mv_factor_count_append_oldvaluefactors)) -> exists ftsf_factor_fsat_append_oldvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_append_oldvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_append_oldvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_append_oldvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_append_oldvaluefactorsfactorization_primes)) * mv_factor_scale_append_oldvaluefactors)) /\ exists ff_q_ftsf_fsat_append_oldvaluefactorsfactorization_primes_entry. mv_factor_code_append_oldvaluefactors = ff_q_ftsf_fsat_append_oldvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_append_oldvaluefactorsfactorization_primes)) * mv_factor_scale_append_oldvaluefactors) + (ftsf_factor_fsat_append_oldvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_append_oldvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_append_oldvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_append_oldvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_append_oldvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_append_oldvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_append_oldvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_append_oldvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_append_oldvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_append_oldvaluefactorsparityeven. (mv_factor_count_append_oldvaluefactors) = 2 * mv_even_half_append_oldvaluefactorsparityeven) /\ ((mt_value_append_old) = 2))) \/ (((exists mv_odd_half_append_oldvaluefactorsparityodd. (mv_factor_count_append_oldvaluefactors) = 2 * mv_odd_half_append_oldvaluefactorsparityodd + 1) /\ ((mt_value_append_old) = 1)))))))))))))))) -> (((~((S N) = 0)) /\ ((((exists mv_square_prime_append_valuesquare. ((~((mv_square_prime_append_valuesquare) = 1) /\ forall pvs_left_append_valuesquareprime pvs_right_append_valuesquareprime. (mv_square_prime_append_valuesquare) = pvs_left_append_valuesquareprime * pvs_right_append_valuesquareprime -> pvs_left_append_valuesquareprime = 1 \/ pvs_right_append_valuesquareprime = 1) /\ (exists pvs_factor_append_valuesquaredivisor. (S N) = (mv_square_prime_append_valuesquare * mv_square_prime_append_valuesquare) * pvs_factor_append_valuesquaredivisor))) /\ ((z) = 0))) \/ (((((~((S N) = 0)) /\ (forall sfd_prime_append_valuesquarefree. (~((sfd_prime_append_valuesquarefree) = 1) /\ forall pvs_left_append_valuesquarefreedomain pvs_right_append_valuesquarefreedomain. (sfd_prime_append_valuesquarefree) = pvs_left_append_valuesquarefreedomain * pvs_right_append_valuesquarefreedomain -> pvs_left_append_valuesquarefreedomain = 1 \/ pvs_right_append_valuesquarefreedomain = 1) -> (exists pvs_le_gap_append_valuesquarefreebound. pvs_le_gap_append_valuesquarefreebound + (sfd_prime_append_valuesquarefree) = (S N)) -> ~(exists pvs_factor_append_valuesquarefreesquare. (S N) = (sfd_prime_append_valuesquarefree * sfd_prime_append_valuesquarefree) * pvs_factor_append_valuesquarefreesquare)))) /\ (exists mv_factor_code_append_valuefactors mv_factor_scale_append_valuefactors mv_factor_count_append_valuefactors. (((~(S N = 0) /\ ((exists ff_u_fsat_append_valuefactorsfactorization_product ff_v_fsat_append_valuefactorsfactorization_product. ((((exists ff_h_fsat_append_valuefactorsfactorization_product_start. ff_h_fsat_append_valuefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_append_valuefactorsfactorization_product)) /\ exists ff_q_fsat_append_valuefactorsfactorization_product_start. ff_u_fsat_append_valuefactorsfactorization_product = ff_q_fsat_append_valuefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_append_valuefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_append_valuefactorsfactorization_product_terminal. ff_h_fsat_append_valuefactorsfactorization_product_terminal + S (S N) = S ((S (mv_factor_count_append_valuefactors)) * ff_v_fsat_append_valuefactorsfactorization_product)) /\ exists ff_q_fsat_append_valuefactorsfactorization_product_terminal. ff_u_fsat_append_valuefactorsfactorization_product = ff_q_fsat_append_valuefactorsfactorization_product_terminal * S ((S (mv_factor_count_append_valuefactors)) * ff_v_fsat_append_valuefactorsfactorization_product) + (S N))) /\ forall ff_i_fsat_append_valuefactorsfactorization_product. (exists ff_lt_fsat_append_valuefactorsfactorization_product_bound. ff_lt_fsat_append_valuefactorsfactorization_product_bound + S ff_i_fsat_append_valuefactorsfactorization_product = mv_factor_count_append_valuefactors) -> exists ff_p_fsat_append_valuefactorsfactorization_product ff_r_fsat_append_valuefactorsfactorization_product ff_s_fsat_append_valuefactorsfactorization_product. ((((exists ff_h_fsat_append_valuefactorsfactorization_product_factor. ff_h_fsat_append_valuefactorsfactorization_product_factor + S (ff_p_fsat_append_valuefactorsfactorization_product) = S ((S (ff_i_fsat_append_valuefactorsfactorization_product)) * mv_factor_scale_append_valuefactors)) /\ exists ff_q_fsat_append_valuefactorsfactorization_product_factor. mv_factor_code_append_valuefactors = ff_q_fsat_append_valuefactorsfactorization_product_factor * S ((S (ff_i_fsat_append_valuefactorsfactorization_product)) * mv_factor_scale_append_valuefactors) + (ff_p_fsat_append_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_append_valuefactorsfactorization_product_partial. ff_h_fsat_append_valuefactorsfactorization_product_partial + S (ff_r_fsat_append_valuefactorsfactorization_product) = S ((S (ff_i_fsat_append_valuefactorsfactorization_product)) * ff_v_fsat_append_valuefactorsfactorization_product)) /\ exists ff_q_fsat_append_valuefactorsfactorization_product_partial. ff_u_fsat_append_valuefactorsfactorization_product = ff_q_fsat_append_valuefactorsfactorization_product_partial * S ((S (ff_i_fsat_append_valuefactorsfactorization_product)) * ff_v_fsat_append_valuefactorsfactorization_product) + (ff_r_fsat_append_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_append_valuefactorsfactorization_product_successor. ff_h_fsat_append_valuefactorsfactorization_product_successor + S (ff_s_fsat_append_valuefactorsfactorization_product) = S ((S (S ff_i_fsat_append_valuefactorsfactorization_product)) * ff_v_fsat_append_valuefactorsfactorization_product)) /\ exists ff_q_fsat_append_valuefactorsfactorization_product_successor. ff_u_fsat_append_valuefactorsfactorization_product = ff_q_fsat_append_valuefactorsfactorization_product_successor * S ((S (S ff_i_fsat_append_valuefactorsfactorization_product)) * ff_v_fsat_append_valuefactorsfactorization_product) + (ff_s_fsat_append_valuefactorsfactorization_product))) /\ ff_s_fsat_append_valuefactorsfactorization_product = ff_r_fsat_append_valuefactorsfactorization_product * ff_p_fsat_append_valuefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_append_valuefactorsfactorization_primes. (exists ftsf_gap_fsat_append_valuefactorsfactorization_primes_bound. ftsf_gap_fsat_append_valuefactorsfactorization_primes_bound + S ftsf_index_fsat_append_valuefactorsfactorization_primes = (mv_factor_count_append_valuefactors)) -> exists ftsf_factor_fsat_append_valuefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_append_valuefactorsfactorization_primes_entry. ff_h_ftsf_fsat_append_valuefactorsfactorization_primes_entry + S (ftsf_factor_fsat_append_valuefactorsfactorization_primes) = S ((S (ftsf_index_fsat_append_valuefactorsfactorization_primes)) * mv_factor_scale_append_valuefactors)) /\ exists ff_q_ftsf_fsat_append_valuefactorsfactorization_primes_entry. mv_factor_code_append_valuefactors = ff_q_ftsf_fsat_append_valuefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_append_valuefactorsfactorization_primes)) * mv_factor_scale_append_valuefactors) + (ftsf_factor_fsat_append_valuefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_append_valuefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_append_valuefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_append_valuefactorsfactorization_primes_prime. ftsf_factor_fsat_append_valuefactorsfactorization_primes = frm_prime_left_ftsf_fsat_append_valuefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_append_valuefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_append_valuefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_append_valuefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_append_valuefactorsparityeven. (mv_factor_count_append_valuefactors) = 2 * mv_even_half_append_valuefactorsparityeven) /\ ((z) = 2))) \/ (((exists mv_odd_half_append_valuefactorsparityodd. (mv_factor_count_append_valuefactors) = 2 * mv_odd_half_append_valuefactorsparityodd + 1) /\ ((z) = 1))))))))))) -> exists G. (((exists dst_positive_code_append_newtable dst_positive_scale_append_newtable dst_negative_code_append_newtable dst_negative_scale_append_newtable. (((G) = (((((dst_positive_code_append_newtable) + (dst_positive_scale_append_newtable)) * S ((dst_positive_code_append_newtable) + (dst_positive_scale_append_newtable)) + ((dst_positive_scale_append_newtable) + (dst_positive_scale_append_newtable))) + (((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) * S ((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) + ((dst_negative_scale_append_newtable) + (dst_negative_scale_append_newtable)))) * S ((((dst_positive_code_append_newtable) + (dst_positive_scale_append_newtable)) * S ((dst_positive_code_append_newtable) + (dst_positive_scale_append_newtable)) + ((dst_positive_scale_append_newtable) + (dst_positive_scale_append_newtable))) + (((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) * S ((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) + ((dst_negative_scale_append_newtable) + (dst_negative_scale_append_newtable)))) + ((((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) * S ((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) + ((dst_negative_scale_append_newtable) + (dst_negative_scale_append_newtable))) + (((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) * S ((dst_negative_code_append_newtable) + (dst_negative_scale_append_newtable)) + ((dst_negative_scale_append_newtable) + (dst_negative_scale_append_newtable)))))) /\ (forall dst_index_append_newtable. (exists pvs_le_gap_append_newtabledomain. pvs_le_gap_append_newtabledomain + (dst_index_append_newtable) = (S N)) -> exists dst_positive_append_newtable dst_negative_append_newtable dst_value_append_newtable. ((((exists ff_h_pvs_append_newtableentrypositive. ff_h_pvs_append_newtableentrypositive + S (dst_positive_append_newtable) = S ((S (dst_index_append_newtable)) * dst_positive_scale_append_newtable)) /\ exists ff_q_pvs_append_newtableentrypositive. dst_positive_code_append_newtable = ff_q_pvs_append_newtableentrypositive * S ((S (dst_index_append_newtable)) * dst_positive_scale_append_newtable) + (dst_positive_append_newtable))) /\ (((((exists ff_h_pvs_append_newtableentrynegative. ff_h_pvs_append_newtableentrynegative + S (dst_negative_append_newtable) = S ((S (dst_index_append_newtable)) * dst_negative_scale_append_newtable)) /\ exists ff_q_pvs_append_newtableentrynegative. dst_negative_code_append_newtable = ff_q_pvs_append_newtableentrynegative * S ((S (dst_index_append_newtable)) * dst_negative_scale_append_newtable) + (dst_negative_append_newtable))) /\ (exists ge_balance_positive_append_newtableentryvalue ge_balance_negative_append_newtableentryvalue. (((((dst_value_append_newtable) = 2 * (ge_balance_positive_append_newtableentryvalue) /\ (ge_balance_negative_append_newtableentryvalue) = 0) \/ exists ge_signed_half_append_newtableentryvaluedecode. (((dst_value_append_newtable) = 2 * ge_signed_half_append_newtableentryvaluedecode + 1 /\ (ge_balance_positive_append_newtableentryvalue) = 0) /\ (ge_balance_negative_append_newtableentryvalue) = S ge_signed_half_append_newtableentryvaluedecode))) /\ ((dst_positive_append_newtable) + ge_balance_negative_append_newtableentryvalue = (dst_negative_append_newtable) + ge_balance_positive_append_newtableentryvalue))))))))) /\ (((exists dst_positive_code_append_newzero dst_positive_scale_append_newzero dst_negative_code_append_newzero dst_negative_scale_append_newzero dst_positive_append_newzero dst_negative_append_newzero. (((G) = (((((dst_positive_code_append_newzero) + (dst_positive_scale_append_newzero)) * S ((dst_positive_code_append_newzero) + (dst_positive_scale_append_newzero)) + ((dst_positive_scale_append_newzero) + (dst_positive_scale_append_newzero))) + (((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) * S ((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) + ((dst_negative_scale_append_newzero) + (dst_negative_scale_append_newzero)))) * S ((((dst_positive_code_append_newzero) + (dst_positive_scale_append_newzero)) * S ((dst_positive_code_append_newzero) + (dst_positive_scale_append_newzero)) + ((dst_positive_scale_append_newzero) + (dst_positive_scale_append_newzero))) + (((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) * S ((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) + ((dst_negative_scale_append_newzero) + (dst_negative_scale_append_newzero)))) + ((((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) * S ((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) + ((dst_negative_scale_append_newzero) + (dst_negative_scale_append_newzero))) + (((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) * S ((dst_negative_code_append_newzero) + (dst_negative_scale_append_newzero)) + ((dst_negative_scale_append_newzero) + (dst_negative_scale_append_newzero)))))) /\ (((((exists ff_h_pvs_append_newzeropositive. ff_h_pvs_append_newzeropositive + S (dst_positive_append_newzero) = S ((S (0)) * dst_positive_scale_append_newzero)) /\ exists ff_q_pvs_append_newzeropositive. dst_positive_code_append_newzero = ff_q_pvs_append_newzeropositive * S ((S (0)) * dst_positive_scale_append_newzero) + (dst_positive_append_newzero))) /\ (((((exists ff_h_pvs_append_newzeronegative. ff_h_pvs_append_newzeronegative + S (dst_negative_append_newzero) = S ((S (0)) * dst_negative_scale_append_newzero)) /\ exists ff_q_pvs_append_newzeronegative. dst_negative_code_append_newzero = ff_q_pvs_append_newzeronegative * S ((S (0)) * dst_negative_scale_append_newzero) + (dst_negative_append_newzero))) /\ (exists ge_balance_positive_append_newzerovalue ge_balance_negative_append_newzerovalue. (((((0) = 2 * (ge_balance_positive_append_newzerovalue) /\ (ge_balance_negative_append_newzerovalue) = 0) \/ exists ge_signed_half_append_newzerovaluedecode. (((0) = 2 * ge_signed_half_append_newzerovaluedecode + 1 /\ (ge_balance_positive_append_newzerovalue) = 0) /\ (ge_balance_negative_append_newzerovalue) = S ge_signed_half_append_newzerovaluedecode))) /\ ((dst_positive_append_newzero) + ge_balance_negative_append_newzerovalue = (dst_negative_append_newzero) + ge_balance_positive_append_newzerovalue))))))))) /\ (forall mt_index_append_new mt_value_append_new. ~(mt_index_append_new=0) -> (exists pvs_le_gap_append_newdomain. pvs_le_gap_append_newdomain + (mt_index_append_new) = (S N)) -> (exists dst_positive_code_append_newentry dst_positive_scale_append_newentry dst_negative_code_append_newentry dst_negative_scale_append_newentry dst_positive_append_newentry dst_negative_append_newentry. (((G) = (((((dst_positive_code_append_newentry) + (dst_positive_scale_append_newentry)) * S ((dst_positive_code_append_newentry) + (dst_positive_scale_append_newentry)) + ((dst_positive_scale_append_newentry) + (dst_positive_scale_append_newentry))) + (((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) * S ((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) + ((dst_negative_scale_append_newentry) + (dst_negative_scale_append_newentry)))) * S ((((dst_positive_code_append_newentry) + (dst_positive_scale_append_newentry)) * S ((dst_positive_code_append_newentry) + (dst_positive_scale_append_newentry)) + ((dst_positive_scale_append_newentry) + (dst_positive_scale_append_newentry))) + (((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) * S ((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) + ((dst_negative_scale_append_newentry) + (dst_negative_scale_append_newentry)))) + ((((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) * S ((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) + ((dst_negative_scale_append_newentry) + (dst_negative_scale_append_newentry))) + (((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) * S ((dst_negative_code_append_newentry) + (dst_negative_scale_append_newentry)) + ((dst_negative_scale_append_newentry) + (dst_negative_scale_append_newentry)))))) /\ (((((exists ff_h_pvs_append_newentrypositive. ff_h_pvs_append_newentrypositive + S (dst_positive_append_newentry) = S ((S (mt_index_append_new)) * dst_positive_scale_append_newentry)) /\ exists ff_q_pvs_append_newentrypositive. dst_positive_code_append_newentry = ff_q_pvs_append_newentrypositive * S ((S (mt_index_append_new)) * dst_positive_scale_append_newentry) + (dst_positive_append_newentry))) /\ (((((exists ff_h_pvs_append_newentrynegative. ff_h_pvs_append_newentrynegative + S (dst_negative_append_newentry) = S ((S (mt_index_append_new)) * dst_negative_scale_append_newentry)) /\ exists ff_q_pvs_append_newentrynegative. dst_negative_code_append_newentry = ff_q_pvs_append_newentrynegative * S ((S (mt_index_append_new)) * dst_negative_scale_append_newentry) + (dst_negative_append_newentry))) /\ (exists ge_balance_positive_append_newentryvalue ge_balance_negative_append_newentryvalue. (((((mt_value_append_new) = 2 * (ge_balance_positive_append_newentryvalue) /\ (ge_balance_negative_append_newentryvalue) = 0) \/ exists ge_signed_half_append_newentryvaluedecode. (((mt_value_append_new) = 2 * ge_signed_half_append_newentryvaluedecode + 1 /\ (ge_balance_positive_append_newentryvalue) = 0) /\ (ge_balance_negative_append_newentryvalue) = S ge_signed_half_append_newentryvaluedecode))) /\ ((dst_positive_append_newentry) + ge_balance_negative_append_newentryvalue = (dst_negative_append_newentry) + ge_balance_positive_append_newentryvalue))))))))) -> (((~((mt_index_append_new) = 0)) /\ ((((exists mv_square_prime_append_newvaluesquare. ((~((mv_square_prime_append_newvaluesquare) = 1) /\ forall pvs_left_append_newvaluesquareprime pvs_right_append_newvaluesquareprime. (mv_square_prime_append_newvaluesquare) = pvs_left_append_newvaluesquareprime * pvs_right_append_newvaluesquareprime -> pvs_left_append_newvaluesquareprime = 1 \/ pvs_right_append_newvaluesquareprime = 1) /\ (exists pvs_factor_append_newvaluesquaredivisor. (mt_index_append_new) = (mv_square_prime_append_newvaluesquare * mv_square_prime_append_newvaluesquare) * pvs_factor_append_newvaluesquaredivisor))) /\ ((mt_value_append_new) = 0))) \/ (((((~((mt_index_append_new) = 0)) /\ (forall sfd_prime_append_newvaluesquarefree. (~((sfd_prime_append_newvaluesquarefree) = 1) /\ forall pvs_left_append_newvaluesquarefreedomain pvs_right_append_newvaluesquarefreedomain. (sfd_prime_append_newvaluesquarefree) = pvs_left_append_newvaluesquarefreedomain * pvs_right_append_newvaluesquarefreedomain -> pvs_left_append_newvaluesquarefreedomain = 1 \/ pvs_right_append_newvaluesquarefreedomain = 1) -> (exists pvs_le_gap_append_newvaluesquarefreebound. pvs_le_gap_append_newvaluesquarefreebound + (sfd_prime_append_newvaluesquarefree) = (mt_index_append_new)) -> ~(exists pvs_factor_append_newvaluesquarefreesquare. (mt_index_append_new) = (sfd_prime_append_newvaluesquarefree * sfd_prime_append_newvaluesquarefree) * pvs_factor_append_newvaluesquarefreesquare)))) /\ (exists mv_factor_code_append_newvaluefactors mv_factor_scale_append_newvaluefactors mv_factor_count_append_newvaluefactors. (((~(mt_index_append_new = 0) /\ ((exists ff_u_fsat_append_newvaluefactorsfactorization_product ff_v_fsat_append_newvaluefactorsfactorization_product. ((((exists ff_h_fsat_append_newvaluefactorsfactorization_product_start. ff_h_fsat_append_newvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_append_newvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_newvaluefactorsfactorization_product_start. ff_u_fsat_append_newvaluefactorsfactorization_product = ff_q_fsat_append_newvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_append_newvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_append_newvaluefactorsfactorization_product_terminal. ff_h_fsat_append_newvaluefactorsfactorization_product_terminal + S (mt_index_append_new) = S ((S (mv_factor_count_append_newvaluefactors)) * ff_v_fsat_append_newvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_newvaluefactorsfactorization_product_terminal. ff_u_fsat_append_newvaluefactorsfactorization_product = ff_q_fsat_append_newvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_append_newvaluefactors)) * ff_v_fsat_append_newvaluefactorsfactorization_product) + (mt_index_append_new))) /\ forall ff_i_fsat_append_newvaluefactorsfactorization_product. (exists ff_lt_fsat_append_newvaluefactorsfactorization_product_bound. ff_lt_fsat_append_newvaluefactorsfactorization_product_bound + S ff_i_fsat_append_newvaluefactorsfactorization_product = mv_factor_count_append_newvaluefactors) -> exists ff_p_fsat_append_newvaluefactorsfactorization_product ff_r_fsat_append_newvaluefactorsfactorization_product ff_s_fsat_append_newvaluefactorsfactorization_product. ((((exists ff_h_fsat_append_newvaluefactorsfactorization_product_factor. ff_h_fsat_append_newvaluefactorsfactorization_product_factor + S (ff_p_fsat_append_newvaluefactorsfactorization_product) = S ((S (ff_i_fsat_append_newvaluefactorsfactorization_product)) * mv_factor_scale_append_newvaluefactors)) /\ exists ff_q_fsat_append_newvaluefactorsfactorization_product_factor. mv_factor_code_append_newvaluefactors = ff_q_fsat_append_newvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_append_newvaluefactorsfactorization_product)) * mv_factor_scale_append_newvaluefactors) + (ff_p_fsat_append_newvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_append_newvaluefactorsfactorization_product_partial. ff_h_fsat_append_newvaluefactorsfactorization_product_partial + S (ff_r_fsat_append_newvaluefactorsfactorization_product) = S ((S (ff_i_fsat_append_newvaluefactorsfactorization_product)) * ff_v_fsat_append_newvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_newvaluefactorsfactorization_product_partial. ff_u_fsat_append_newvaluefactorsfactorization_product = ff_q_fsat_append_newvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_append_newvaluefactorsfactorization_product)) * ff_v_fsat_append_newvaluefactorsfactorization_product) + (ff_r_fsat_append_newvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_append_newvaluefactorsfactorization_product_successor. ff_h_fsat_append_newvaluefactorsfactorization_product_successor + S (ff_s_fsat_append_newvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_append_newvaluefactorsfactorization_product)) * ff_v_fsat_append_newvaluefactorsfactorization_product)) /\ exists ff_q_fsat_append_newvaluefactorsfactorization_product_successor. ff_u_fsat_append_newvaluefactorsfactorization_product = ff_q_fsat_append_newvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_append_newvaluefactorsfactorization_product)) * ff_v_fsat_append_newvaluefactorsfactorization_product) + (ff_s_fsat_append_newvaluefactorsfactorization_product))) /\ ff_s_fsat_append_newvaluefactorsfactorization_product = ff_r_fsat_append_newvaluefactorsfactorization_product * ff_p_fsat_append_newvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_append_newvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_append_newvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_append_newvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_append_newvaluefactorsfactorization_primes = (mv_factor_count_append_newvaluefactors)) -> exists ftsf_factor_fsat_append_newvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_append_newvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_append_newvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_append_newvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_append_newvaluefactorsfactorization_primes)) * mv_factor_scale_append_newvaluefactors)) /\ exists ff_q_ftsf_fsat_append_newvaluefactorsfactorization_primes_entry. mv_factor_code_append_newvaluefactors = ff_q_ftsf_fsat_append_newvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_append_newvaluefactorsfactorization_primes)) * mv_factor_scale_append_newvaluefactors) + (ftsf_factor_fsat_append_newvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_append_newvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_append_newvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_append_newvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_append_newvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_append_newvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_append_newvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_append_newvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_append_newvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_append_newvaluefactorsparityeven. (mv_factor_count_append_newvaluefactors) = 2 * mv_even_half_append_newvaluefactorsparityeven) /\ ((mt_value_append_new) = 2))) \/ (((exists mv_odd_half_append_newvaluefactorsparityodd. (mv_factor_count_append_newvaluefactors) = 2 * mv_odd_half_append_newvaluefactorsparityodd + 1) /\ ((mt_value_append_new) = 1)))))))))))))))) /\ (forall dst_index_append_preserved dst_first_append_preserved dst_second_append_preserved. (exists pvs_gap_append_preservedbound. pvs_gap_append_preservedbound + S (dst_index_append_preserved) = (S N)) -> (exists dst_positive_code_append_preservedfirst dst_positive_scale_append_preservedfirst dst_negative_code_append_preservedfirst dst_negative_scale_append_preservedfirst dst_positive_append_preservedfirst dst_negative_append_preservedfirst. (((F) = (((((dst_positive_code_append_preservedfirst) + (dst_positive_scale_append_preservedfirst)) * S ((dst_positive_code_append_preservedfirst) + (dst_positive_scale_append_preservedfirst)) + ((dst_positive_scale_append_preservedfirst) + (dst_positive_scale_append_preservedfirst))) + (((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) * S ((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) + ((dst_negative_scale_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)))) * S ((((dst_positive_code_append_preservedfirst) + (dst_positive_scale_append_preservedfirst)) * S ((dst_positive_code_append_preservedfirst) + (dst_positive_scale_append_preservedfirst)) + ((dst_positive_scale_append_preservedfirst) + (dst_positive_scale_append_preservedfirst))) + (((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) * S ((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) + ((dst_negative_scale_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)))) + ((((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) * S ((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) + ((dst_negative_scale_append_preservedfirst) + (dst_negative_scale_append_preservedfirst))) + (((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) * S ((dst_negative_code_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)) + ((dst_negative_scale_append_preservedfirst) + (dst_negative_scale_append_preservedfirst)))))) /\ (((((exists ff_h_pvs_append_preservedfirstpositive. ff_h_pvs_append_preservedfirstpositive + S (dst_positive_append_preservedfirst) = S ((S (dst_index_append_preserved)) * dst_positive_scale_append_preservedfirst)) /\ exists ff_q_pvs_append_preservedfirstpositive. dst_positive_code_append_preservedfirst = ff_q_pvs_append_preservedfirstpositive * S ((S (dst_index_append_preserved)) * dst_positive_scale_append_preservedfirst) + (dst_positive_append_preservedfirst))) /\ (((((exists ff_h_pvs_append_preservedfirstnegative. ff_h_pvs_append_preservedfirstnegative + S (dst_negative_append_preservedfirst) = S ((S (dst_index_append_preserved)) * dst_negative_scale_append_preservedfirst)) /\ exists ff_q_pvs_append_preservedfirstnegative. dst_negative_code_append_preservedfirst = ff_q_pvs_append_preservedfirstnegative * S ((S (dst_index_append_preserved)) * dst_negative_scale_append_preservedfirst) + (dst_negative_append_preservedfirst))) /\ (exists ge_balance_positive_append_preservedfirstvalue ge_balance_negative_append_preservedfirstvalue. (((((dst_first_append_preserved) = 2 * (ge_balance_positive_append_preservedfirstvalue) /\ (ge_balance_negative_append_preservedfirstvalue) = 0) \/ exists ge_signed_half_append_preservedfirstvaluedecode. (((dst_first_append_preserved) = 2 * ge_signed_half_append_preservedfirstvaluedecode + 1 /\ (ge_balance_positive_append_preservedfirstvalue) = 0) /\ (ge_balance_negative_append_preservedfirstvalue) = S ge_signed_half_append_preservedfirstvaluedecode))) /\ ((dst_positive_append_preservedfirst) + ge_balance_negative_append_preservedfirstvalue = (dst_negative_append_preservedfirst) + ge_balance_positive_append_preservedfirstvalue))))))))) -> (exists dst_positive_code_append_preservedsecond dst_positive_scale_append_preservedsecond dst_negative_code_append_preservedsecond dst_negative_scale_append_preservedsecond dst_positive_append_preservedsecond dst_negative_append_preservedsecond. (((G) = (((((dst_positive_code_append_preservedsecond) + (dst_positive_scale_append_preservedsecond)) * S ((dst_positive_code_append_preservedsecond) + (dst_positive_scale_append_preservedsecond)) + ((dst_positive_scale_append_preservedsecond) + (dst_positive_scale_append_preservedsecond))) + (((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) * S ((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) + ((dst_negative_scale_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)))) * S ((((dst_positive_code_append_preservedsecond) + (dst_positive_scale_append_preservedsecond)) * S ((dst_positive_code_append_preservedsecond) + (dst_positive_scale_append_preservedsecond)) + ((dst_positive_scale_append_preservedsecond) + (dst_positive_scale_append_preservedsecond))) + (((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) * S ((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) + ((dst_negative_scale_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)))) + ((((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) * S ((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) + ((dst_negative_scale_append_preservedsecond) + (dst_negative_scale_append_preservedsecond))) + (((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) * S ((dst_negative_code_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)) + ((dst_negative_scale_append_preservedsecond) + (dst_negative_scale_append_preservedsecond)))))) /\ (((((exists ff_h_pvs_append_preservedsecondpositive. ff_h_pvs_append_preservedsecondpositive + S (dst_positive_append_preservedsecond) = S ((S (dst_index_append_preserved)) * dst_positive_scale_append_preservedsecond)) /\ exists ff_q_pvs_append_preservedsecondpositive. dst_positive_code_append_preservedsecond = ff_q_pvs_append_preservedsecondpositive * S ((S (dst_index_append_preserved)) * dst_positive_scale_append_preservedsecond) + (dst_positive_append_preservedsecond))) /\ (((((exists ff_h_pvs_append_preservedsecondnegative. ff_h_pvs_append_preservedsecondnegative + S (dst_negative_append_preservedsecond) = S ((S (dst_index_append_preserved)) * dst_negative_scale_append_preservedsecond)) /\ exists ff_q_pvs_append_preservedsecondnegative. dst_negative_code_append_preservedsecond = ff_q_pvs_append_preservedsecondnegative * S ((S (dst_index_append_preserved)) * dst_negative_scale_append_preservedsecond) + (dst_negative_append_preservedsecond))) /\ (exists ge_balance_positive_append_preservedsecondvalue ge_balance_negative_append_preservedsecondvalue. (((((dst_second_append_preserved) = 2 * (ge_balance_positive_append_preservedsecondvalue) /\ (ge_balance_negative_append_preservedsecondvalue) = 0) \/ exists ge_signed_half_append_preservedsecondvaluedecode. (((dst_second_append_preserved) = 2 * ge_signed_half_append_preservedsecondvaluedecode + 1 /\ (ge_balance_positive_append_preservedsecondvalue) = 0) /\ (ge_balance_negative_append_preservedsecondvalue) = S ge_signed_half_append_preservedsecondvaluedecode))) /\ ((dst_positive_append_preservedsecond) + ge_balance_negative_append_preservedsecondvalue = (dst_negative_append_preservedsecond) + ge_balance_positive_append_preservedsecondvalue))))))))) -> dst_first_append_preserved = dst_second_append_preserved)

mobius_table_exists

new owned theorem · read exact theorem evidence

Bundle node 286; exact statement SHA-256 9d90a11bd987bfe516272671293b30a0d264fe613d2632c628b5701634cf5dd3

Exact first-order statement

forall N. exists M. (((exists dst_positive_code_exists_resulttable dst_positive_scale_exists_resulttable dst_negative_code_exists_resulttable dst_negative_scale_exists_resulttable. (((M) = (((((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) * S ((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) + ((dst_positive_scale_exists_resulttable) + (dst_positive_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))) * S ((((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) * S ((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) + ((dst_positive_scale_exists_resulttable) + (dst_positive_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))) + ((((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))))) /\ (forall dst_index_exists_resulttable. (exists pvs_le_gap_exists_resulttabledomain. pvs_le_gap_exists_resulttabledomain + (dst_index_exists_resulttable) = (N)) -> exists dst_positive_exists_resulttable dst_negative_exists_resulttable dst_value_exists_resulttable. ((((exists ff_h_pvs_exists_resulttableentrypositive. ff_h_pvs_exists_resulttableentrypositive + S (dst_positive_exists_resulttable) = S ((S (dst_index_exists_resulttable)) * dst_positive_scale_exists_resulttable)) /\ exists ff_q_pvs_exists_resulttableentrypositive. dst_positive_code_exists_resulttable = ff_q_pvs_exists_resulttableentrypositive * S ((S (dst_index_exists_resulttable)) * dst_positive_scale_exists_resulttable) + (dst_positive_exists_resulttable))) /\ (((((exists ff_h_pvs_exists_resulttableentrynegative. ff_h_pvs_exists_resulttableentrynegative + S (dst_negative_exists_resulttable) = S ((S (dst_index_exists_resulttable)) * dst_negative_scale_exists_resulttable)) /\ exists ff_q_pvs_exists_resulttableentrynegative. dst_negative_code_exists_resulttable = ff_q_pvs_exists_resulttableentrynegative * S ((S (dst_index_exists_resulttable)) * dst_negative_scale_exists_resulttable) + (dst_negative_exists_resulttable))) /\ (exists ge_balance_positive_exists_resulttableentryvalue ge_balance_negative_exists_resulttableentryvalue. (((((dst_value_exists_resulttable) = 2 * (ge_balance_positive_exists_resulttableentryvalue) /\ (ge_balance_negative_exists_resulttableentryvalue) = 0) \/ exists ge_signed_half_exists_resulttableentryvaluedecode. (((dst_value_exists_resulttable) = 2 * ge_signed_half_exists_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_exists_resulttableentryvalue) = 0) /\ (ge_balance_negative_exists_resulttableentryvalue) = S ge_signed_half_exists_resulttableentryvaluedecode))) /\ ((dst_positive_exists_resulttable) + ge_balance_negative_exists_resulttableentryvalue = (dst_negative_exists_resulttable) + ge_balance_positive_exists_resulttableentryvalue))))))))) /\ (((exists dst_positive_code_exists_resultzero dst_positive_scale_exists_resultzero dst_negative_code_exists_resultzero dst_negative_scale_exists_resultzero dst_positive_exists_resultzero dst_negative_exists_resultzero. (((M) = (((((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) * S ((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) + ((dst_positive_scale_exists_resultzero) + (dst_positive_scale_exists_resultzero))) + (((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero)))) * S ((((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) * S ((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) + ((dst_positive_scale_exists_resultzero) + (dst_positive_scale_exists_resultzero))) + (((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero)))) + ((((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero))) + (((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero)))))) /\ (((((exists ff_h_pvs_exists_resultzeropositive. ff_h_pvs_exists_resultzeropositive + S (dst_positive_exists_resultzero) = S ((S (0)) * dst_positive_scale_exists_resultzero)) /\ exists ff_q_pvs_exists_resultzeropositive. dst_positive_code_exists_resultzero = ff_q_pvs_exists_resultzeropositive * S ((S (0)) * dst_positive_scale_exists_resultzero) + (dst_positive_exists_resultzero))) /\ (((((exists ff_h_pvs_exists_resultzeronegative. ff_h_pvs_exists_resultzeronegative + S (dst_negative_exists_resultzero) = S ((S (0)) * dst_negative_scale_exists_resultzero)) /\ exists ff_q_pvs_exists_resultzeronegative. dst_negative_code_exists_resultzero = ff_q_pvs_exists_resultzeronegative * S ((S (0)) * dst_negative_scale_exists_resultzero) + (dst_negative_exists_resultzero))) /\ (exists ge_balance_positive_exists_resultzerovalue ge_balance_negative_exists_resultzerovalue. (((((0) = 2 * (ge_balance_positive_exists_resultzerovalue) /\ (ge_balance_negative_exists_resultzerovalue) = 0) \/ exists ge_signed_half_exists_resultzerovaluedecode. (((0) = 2 * ge_signed_half_exists_resultzerovaluedecode + 1 /\ (ge_balance_positive_exists_resultzerovalue) = 0) /\ (ge_balance_negative_exists_resultzerovalue) = S ge_signed_half_exists_resultzerovaluedecode))) /\ ((dst_positive_exists_resultzero) + ge_balance_negative_exists_resultzerovalue = (dst_negative_exists_resultzero) + ge_balance_positive_exists_resultzerovalue))))))))) /\ (forall mt_index_exists_result mt_value_exists_result. ~(mt_index_exists_result=0) -> (exists pvs_le_gap_exists_resultdomain. pvs_le_gap_exists_resultdomain + (mt_index_exists_result) = (N)) -> (exists dst_positive_code_exists_resultentry dst_positive_scale_exists_resultentry dst_negative_code_exists_resultentry dst_negative_scale_exists_resultentry dst_positive_exists_resultentry dst_negative_exists_resultentry. (((M) = (((((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) * S ((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) + ((dst_positive_scale_exists_resultentry) + (dst_positive_scale_exists_resultentry))) + (((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry)))) * S ((((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) * S ((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) + ((dst_positive_scale_exists_resultentry) + (dst_positive_scale_exists_resultentry))) + (((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry)))) + ((((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry))) + (((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry)))))) /\ (((((exists ff_h_pvs_exists_resultentrypositive. ff_h_pvs_exists_resultentrypositive + S (dst_positive_exists_resultentry) = S ((S (mt_index_exists_result)) * dst_positive_scale_exists_resultentry)) /\ exists ff_q_pvs_exists_resultentrypositive. dst_positive_code_exists_resultentry = ff_q_pvs_exists_resultentrypositive * S ((S (mt_index_exists_result)) * dst_positive_scale_exists_resultentry) + (dst_positive_exists_resultentry))) /\ (((((exists ff_h_pvs_exists_resultentrynegative. ff_h_pvs_exists_resultentrynegative + S (dst_negative_exists_resultentry) = S ((S (mt_index_exists_result)) * dst_negative_scale_exists_resultentry)) /\ exists ff_q_pvs_exists_resultentrynegative. dst_negative_code_exists_resultentry = ff_q_pvs_exists_resultentrynegative * S ((S (mt_index_exists_result)) * dst_negative_scale_exists_resultentry) + (dst_negative_exists_resultentry))) /\ (exists ge_balance_positive_exists_resultentryvalue ge_balance_negative_exists_resultentryvalue. (((((mt_value_exists_result) = 2 * (ge_balance_positive_exists_resultentryvalue) /\ (ge_balance_negative_exists_resultentryvalue) = 0) \/ exists ge_signed_half_exists_resultentryvaluedecode. (((mt_value_exists_result) = 2 * ge_signed_half_exists_resultentryvaluedecode + 1 /\ (ge_balance_positive_exists_resultentryvalue) = 0) /\ (ge_balance_negative_exists_resultentryvalue) = S ge_signed_half_exists_resultentryvaluedecode))) /\ ((dst_positive_exists_resultentry) + ge_balance_negative_exists_resultentryvalue = (dst_negative_exists_resultentry) + ge_balance_positive_exists_resultentryvalue))))))))) -> (((~((mt_index_exists_result) = 0)) /\ ((((exists mv_square_prime_exists_resultvaluesquare. ((~((mv_square_prime_exists_resultvaluesquare) = 1) /\ forall pvs_left_exists_resultvaluesquareprime pvs_right_exists_resultvaluesquareprime. (mv_square_prime_exists_resultvaluesquare) = pvs_left_exists_resultvaluesquareprime * pvs_right_exists_resultvaluesquareprime -> pvs_left_exists_resultvaluesquareprime = 1 \/ pvs_right_exists_resultvaluesquareprime = 1) /\ (exists pvs_factor_exists_resultvaluesquaredivisor. (mt_index_exists_result) = (mv_square_prime_exists_resultvaluesquare * mv_square_prime_exists_resultvaluesquare) * pvs_factor_exists_resultvaluesquaredivisor))) /\ ((mt_value_exists_result) = 0))) \/ (((((~((mt_index_exists_result) = 0)) /\ (forall sfd_prime_exists_resultvaluesquarefree. (~((sfd_prime_exists_resultvaluesquarefree) = 1) /\ forall pvs_left_exists_resultvaluesquarefreedomain pvs_right_exists_resultvaluesquarefreedomain. (sfd_prime_exists_resultvaluesquarefree) = pvs_left_exists_resultvaluesquarefreedomain * pvs_right_exists_resultvaluesquarefreedomain -> pvs_left_exists_resultvaluesquarefreedomain = 1 \/ pvs_right_exists_resultvaluesquarefreedomain = 1) -> (exists pvs_le_gap_exists_resultvaluesquarefreebound. pvs_le_gap_exists_resultvaluesquarefreebound + (sfd_prime_exists_resultvaluesquarefree) = (mt_index_exists_result)) -> ~(exists pvs_factor_exists_resultvaluesquarefreesquare. (mt_index_exists_result) = (sfd_prime_exists_resultvaluesquarefree * sfd_prime_exists_resultvaluesquarefree) * pvs_factor_exists_resultvaluesquarefreesquare)))) /\ (exists mv_factor_code_exists_resultvaluefactors mv_factor_scale_exists_resultvaluefactors mv_factor_count_exists_resultvaluefactors. (((~(mt_index_exists_result = 0) /\ ((exists ff_u_fsat_exists_resultvaluefactorsfactorization_product ff_v_fsat_exists_resultvaluefactorsfactorization_product. ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_start. ff_h_fsat_exists_resultvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_start. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_terminal. ff_h_fsat_exists_resultvaluefactorsfactorization_product_terminal + S (mt_index_exists_result) = S ((S (mv_factor_count_exists_resultvaluefactors)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_terminal. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_exists_resultvaluefactors)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (mt_index_exists_result))) /\ forall ff_i_fsat_exists_resultvaluefactorsfactorization_product. (exists ff_lt_fsat_exists_resultvaluefactorsfactorization_product_bound. ff_lt_fsat_exists_resultvaluefactorsfactorization_product_bound + S ff_i_fsat_exists_resultvaluefactorsfactorization_product = mv_factor_count_exists_resultvaluefactors) -> exists ff_p_fsat_exists_resultvaluefactorsfactorization_product ff_r_fsat_exists_resultvaluefactorsfactorization_product ff_s_fsat_exists_resultvaluefactorsfactorization_product. ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_factor. ff_h_fsat_exists_resultvaluefactorsfactorization_product_factor + S (ff_p_fsat_exists_resultvaluefactorsfactorization_product) = S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * mv_factor_scale_exists_resultvaluefactors)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_factor. mv_factor_code_exists_resultvaluefactors = ff_q_fsat_exists_resultvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * mv_factor_scale_exists_resultvaluefactors) + (ff_p_fsat_exists_resultvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_partial. ff_h_fsat_exists_resultvaluefactorsfactorization_product_partial + S (ff_r_fsat_exists_resultvaluefactorsfactorization_product) = S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_partial. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (ff_r_fsat_exists_resultvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_successor. ff_h_fsat_exists_resultvaluefactorsfactorization_product_successor + S (ff_s_fsat_exists_resultvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_successor. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (ff_s_fsat_exists_resultvaluefactorsfactorization_product))) /\ ff_s_fsat_exists_resultvaluefactorsfactorization_product = ff_r_fsat_exists_resultvaluefactorsfactorization_product * ff_p_fsat_exists_resultvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_exists_resultvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_exists_resultvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes = (mv_factor_count_exists_resultvaluefactors)) -> exists ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes)) * mv_factor_scale_exists_resultvaluefactors)) /\ exists ff_q_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry. mv_factor_code_exists_resultvaluefactors = ff_q_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes)) * mv_factor_scale_exists_resultvaluefactors) + (ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_exists_resultvaluefactorsparityeven. (mv_factor_count_exists_resultvaluefactors) = 2 * mv_even_half_exists_resultvaluefactorsparityeven) /\ ((mt_value_exists_result) = 2))) \/ (((exists mv_odd_half_exists_resultvaluefactorsparityodd. (mv_factor_count_exists_resultvaluefactors) = 2 * mv_odd_half_exists_resultvaluefactorsparityodd + 1) /\ ((mt_value_exists_result) = 1))))))))))))))))

mobius_table_lookup

new owned theorem · read exact theorem evidence

Bundle node 287; exact statement SHA-256 0d5b87c939d6bf38b66d5b369e910f5166170fa8346f17043444c3b7767d9359

Exact first-order statement

forall N M i. (((exists dst_positive_code_lookup_sourcetable dst_positive_scale_lookup_sourcetable dst_negative_code_lookup_sourcetable dst_negative_scale_lookup_sourcetable. (((M) = (((((dst_positive_code_lookup_sourcetable) + (dst_positive_scale_lookup_sourcetable)) * S ((dst_positive_code_lookup_sourcetable) + (dst_positive_scale_lookup_sourcetable)) + ((dst_positive_scale_lookup_sourcetable) + (dst_positive_scale_lookup_sourcetable))) + (((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) * S ((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) + ((dst_negative_scale_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)))) * S ((((dst_positive_code_lookup_sourcetable) + (dst_positive_scale_lookup_sourcetable)) * S ((dst_positive_code_lookup_sourcetable) + (dst_positive_scale_lookup_sourcetable)) + ((dst_positive_scale_lookup_sourcetable) + (dst_positive_scale_lookup_sourcetable))) + (((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) * S ((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) + ((dst_negative_scale_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)))) + ((((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) * S ((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) + ((dst_negative_scale_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable))) + (((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) * S ((dst_negative_code_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)) + ((dst_negative_scale_lookup_sourcetable) + (dst_negative_scale_lookup_sourcetable)))))) /\ (forall dst_index_lookup_sourcetable. (exists pvs_le_gap_lookup_sourcetabledomain. pvs_le_gap_lookup_sourcetabledomain + (dst_index_lookup_sourcetable) = (N)) -> exists dst_positive_lookup_sourcetable dst_negative_lookup_sourcetable dst_value_lookup_sourcetable. ((((exists ff_h_pvs_lookup_sourcetableentrypositive. ff_h_pvs_lookup_sourcetableentrypositive + S (dst_positive_lookup_sourcetable) = S ((S (dst_index_lookup_sourcetable)) * dst_positive_scale_lookup_sourcetable)) /\ exists ff_q_pvs_lookup_sourcetableentrypositive. dst_positive_code_lookup_sourcetable = ff_q_pvs_lookup_sourcetableentrypositive * S ((S (dst_index_lookup_sourcetable)) * dst_positive_scale_lookup_sourcetable) + (dst_positive_lookup_sourcetable))) /\ (((((exists ff_h_pvs_lookup_sourcetableentrynegative. ff_h_pvs_lookup_sourcetableentrynegative + S (dst_negative_lookup_sourcetable) = S ((S (dst_index_lookup_sourcetable)) * dst_negative_scale_lookup_sourcetable)) /\ exists ff_q_pvs_lookup_sourcetableentrynegative. dst_negative_code_lookup_sourcetable = ff_q_pvs_lookup_sourcetableentrynegative * S ((S (dst_index_lookup_sourcetable)) * dst_negative_scale_lookup_sourcetable) + (dst_negative_lookup_sourcetable))) /\ (exists ge_balance_positive_lookup_sourcetableentryvalue ge_balance_negative_lookup_sourcetableentryvalue. (((((dst_value_lookup_sourcetable) = 2 * (ge_balance_positive_lookup_sourcetableentryvalue) /\ (ge_balance_negative_lookup_sourcetableentryvalue) = 0) \/ exists ge_signed_half_lookup_sourcetableentryvaluedecode. (((dst_value_lookup_sourcetable) = 2 * ge_signed_half_lookup_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_sourcetableentryvalue) = 0) /\ (ge_balance_negative_lookup_sourcetableentryvalue) = S ge_signed_half_lookup_sourcetableentryvaluedecode))) /\ ((dst_positive_lookup_sourcetable) + ge_balance_negative_lookup_sourcetableentryvalue = (dst_negative_lookup_sourcetable) + ge_balance_positive_lookup_sourcetableentryvalue))))))))) /\ (((exists dst_positive_code_lookup_sourcezero dst_positive_scale_lookup_sourcezero dst_negative_code_lookup_sourcezero dst_negative_scale_lookup_sourcezero dst_positive_lookup_sourcezero dst_negative_lookup_sourcezero. (((M) = (((((dst_positive_code_lookup_sourcezero) + (dst_positive_scale_lookup_sourcezero)) * S ((dst_positive_code_lookup_sourcezero) + (dst_positive_scale_lookup_sourcezero)) + ((dst_positive_scale_lookup_sourcezero) + (dst_positive_scale_lookup_sourcezero))) + (((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) * S ((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) + ((dst_negative_scale_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)))) * S ((((dst_positive_code_lookup_sourcezero) + (dst_positive_scale_lookup_sourcezero)) * S ((dst_positive_code_lookup_sourcezero) + (dst_positive_scale_lookup_sourcezero)) + ((dst_positive_scale_lookup_sourcezero) + (dst_positive_scale_lookup_sourcezero))) + (((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) * S ((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) + ((dst_negative_scale_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)))) + ((((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) * S ((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) + ((dst_negative_scale_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero))) + (((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) * S ((dst_negative_code_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)) + ((dst_negative_scale_lookup_sourcezero) + (dst_negative_scale_lookup_sourcezero)))))) /\ (((((exists ff_h_pvs_lookup_sourcezeropositive. ff_h_pvs_lookup_sourcezeropositive + S (dst_positive_lookup_sourcezero) = S ((S (0)) * dst_positive_scale_lookup_sourcezero)) /\ exists ff_q_pvs_lookup_sourcezeropositive. dst_positive_code_lookup_sourcezero = ff_q_pvs_lookup_sourcezeropositive * S ((S (0)) * dst_positive_scale_lookup_sourcezero) + (dst_positive_lookup_sourcezero))) /\ (((((exists ff_h_pvs_lookup_sourcezeronegative. ff_h_pvs_lookup_sourcezeronegative + S (dst_negative_lookup_sourcezero) = S ((S (0)) * dst_negative_scale_lookup_sourcezero)) /\ exists ff_q_pvs_lookup_sourcezeronegative. dst_negative_code_lookup_sourcezero = ff_q_pvs_lookup_sourcezeronegative * S ((S (0)) * dst_negative_scale_lookup_sourcezero) + (dst_negative_lookup_sourcezero))) /\ (exists ge_balance_positive_lookup_sourcezerovalue ge_balance_negative_lookup_sourcezerovalue. (((((0) = 2 * (ge_balance_positive_lookup_sourcezerovalue) /\ (ge_balance_negative_lookup_sourcezerovalue) = 0) \/ exists ge_signed_half_lookup_sourcezerovaluedecode. (((0) = 2 * ge_signed_half_lookup_sourcezerovaluedecode + 1 /\ (ge_balance_positive_lookup_sourcezerovalue) = 0) /\ (ge_balance_negative_lookup_sourcezerovalue) = S ge_signed_half_lookup_sourcezerovaluedecode))) /\ ((dst_positive_lookup_sourcezero) + ge_balance_negative_lookup_sourcezerovalue = (dst_negative_lookup_sourcezero) + ge_balance_positive_lookup_sourcezerovalue))))))))) /\ (forall mt_index_lookup_source mt_value_lookup_source. ~(mt_index_lookup_source=0) -> (exists pvs_le_gap_lookup_sourcedomain. pvs_le_gap_lookup_sourcedomain + (mt_index_lookup_source) = (N)) -> (exists dst_positive_code_lookup_sourceentry dst_positive_scale_lookup_sourceentry dst_negative_code_lookup_sourceentry dst_negative_scale_lookup_sourceentry dst_positive_lookup_sourceentry dst_negative_lookup_sourceentry. (((M) = (((((dst_positive_code_lookup_sourceentry) + (dst_positive_scale_lookup_sourceentry)) * S ((dst_positive_code_lookup_sourceentry) + (dst_positive_scale_lookup_sourceentry)) + ((dst_positive_scale_lookup_sourceentry) + (dst_positive_scale_lookup_sourceentry))) + (((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) * S ((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) + ((dst_negative_scale_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)))) * S ((((dst_positive_code_lookup_sourceentry) + (dst_positive_scale_lookup_sourceentry)) * S ((dst_positive_code_lookup_sourceentry) + (dst_positive_scale_lookup_sourceentry)) + ((dst_positive_scale_lookup_sourceentry) + (dst_positive_scale_lookup_sourceentry))) + (((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) * S ((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) + ((dst_negative_scale_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)))) + ((((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) * S ((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) + ((dst_negative_scale_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry))) + (((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) * S ((dst_negative_code_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)) + ((dst_negative_scale_lookup_sourceentry) + (dst_negative_scale_lookup_sourceentry)))))) /\ (((((exists ff_h_pvs_lookup_sourceentrypositive. ff_h_pvs_lookup_sourceentrypositive + S (dst_positive_lookup_sourceentry) = S ((S (mt_index_lookup_source)) * dst_positive_scale_lookup_sourceentry)) /\ exists ff_q_pvs_lookup_sourceentrypositive. dst_positive_code_lookup_sourceentry = ff_q_pvs_lookup_sourceentrypositive * S ((S (mt_index_lookup_source)) * dst_positive_scale_lookup_sourceentry) + (dst_positive_lookup_sourceentry))) /\ (((((exists ff_h_pvs_lookup_sourceentrynegative. ff_h_pvs_lookup_sourceentrynegative + S (dst_negative_lookup_sourceentry) = S ((S (mt_index_lookup_source)) * dst_negative_scale_lookup_sourceentry)) /\ exists ff_q_pvs_lookup_sourceentrynegative. dst_negative_code_lookup_sourceentry = ff_q_pvs_lookup_sourceentrynegative * S ((S (mt_index_lookup_source)) * dst_negative_scale_lookup_sourceentry) + (dst_negative_lookup_sourceentry))) /\ (exists ge_balance_positive_lookup_sourceentryvalue ge_balance_negative_lookup_sourceentryvalue. (((((mt_value_lookup_source) = 2 * (ge_balance_positive_lookup_sourceentryvalue) /\ (ge_balance_negative_lookup_sourceentryvalue) = 0) \/ exists ge_signed_half_lookup_sourceentryvaluedecode. (((mt_value_lookup_source) = 2 * ge_signed_half_lookup_sourceentryvaluedecode + 1 /\ (ge_balance_positive_lookup_sourceentryvalue) = 0) /\ (ge_balance_negative_lookup_sourceentryvalue) = S ge_signed_half_lookup_sourceentryvaluedecode))) /\ ((dst_positive_lookup_sourceentry) + ge_balance_negative_lookup_sourceentryvalue = (dst_negative_lookup_sourceentry) + ge_balance_positive_lookup_sourceentryvalue))))))))) -> (((~((mt_index_lookup_source) = 0)) /\ ((((exists mv_square_prime_lookup_sourcevaluesquare. ((~((mv_square_prime_lookup_sourcevaluesquare) = 1) /\ forall pvs_left_lookup_sourcevaluesquareprime pvs_right_lookup_sourcevaluesquareprime. (mv_square_prime_lookup_sourcevaluesquare) = pvs_left_lookup_sourcevaluesquareprime * pvs_right_lookup_sourcevaluesquareprime -> pvs_left_lookup_sourcevaluesquareprime = 1 \/ pvs_right_lookup_sourcevaluesquareprime = 1) /\ (exists pvs_factor_lookup_sourcevaluesquaredivisor. (mt_index_lookup_source) = (mv_square_prime_lookup_sourcevaluesquare * mv_square_prime_lookup_sourcevaluesquare) * pvs_factor_lookup_sourcevaluesquaredivisor))) /\ ((mt_value_lookup_source) = 0))) \/ (((((~((mt_index_lookup_source) = 0)) /\ (forall sfd_prime_lookup_sourcevaluesquarefree. (~((sfd_prime_lookup_sourcevaluesquarefree) = 1) /\ forall pvs_left_lookup_sourcevaluesquarefreedomain pvs_right_lookup_sourcevaluesquarefreedomain. (sfd_prime_lookup_sourcevaluesquarefree) = pvs_left_lookup_sourcevaluesquarefreedomain * pvs_right_lookup_sourcevaluesquarefreedomain -> pvs_left_lookup_sourcevaluesquarefreedomain = 1 \/ pvs_right_lookup_sourcevaluesquarefreedomain = 1) -> (exists pvs_le_gap_lookup_sourcevaluesquarefreebound. pvs_le_gap_lookup_sourcevaluesquarefreebound + (sfd_prime_lookup_sourcevaluesquarefree) = (mt_index_lookup_source)) -> ~(exists pvs_factor_lookup_sourcevaluesquarefreesquare. (mt_index_lookup_source) = (sfd_prime_lookup_sourcevaluesquarefree * sfd_prime_lookup_sourcevaluesquarefree) * pvs_factor_lookup_sourcevaluesquarefreesquare)))) /\ (exists mv_factor_code_lookup_sourcevaluefactors mv_factor_scale_lookup_sourcevaluefactors mv_factor_count_lookup_sourcevaluefactors. (((~(mt_index_lookup_source = 0) /\ ((exists ff_u_fsat_lookup_sourcevaluefactorsfactorization_product ff_v_fsat_lookup_sourcevaluefactorsfactorization_product. ((((exists ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_start. ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_start. ff_u_fsat_lookup_sourcevaluefactorsfactorization_product = ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_terminal. ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_terminal + S (mt_index_lookup_source) = S ((S (mv_factor_count_lookup_sourcevaluefactors)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_terminal. ff_u_fsat_lookup_sourcevaluefactorsfactorization_product = ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_lookup_sourcevaluefactors)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product) + (mt_index_lookup_source))) /\ forall ff_i_fsat_lookup_sourcevaluefactorsfactorization_product. (exists ff_lt_fsat_lookup_sourcevaluefactorsfactorization_product_bound. ff_lt_fsat_lookup_sourcevaluefactorsfactorization_product_bound + S ff_i_fsat_lookup_sourcevaluefactorsfactorization_product = mv_factor_count_lookup_sourcevaluefactors) -> exists ff_p_fsat_lookup_sourcevaluefactorsfactorization_product ff_r_fsat_lookup_sourcevaluefactorsfactorization_product ff_s_fsat_lookup_sourcevaluefactorsfactorization_product. ((((exists ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_factor. ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_factor + S (ff_p_fsat_lookup_sourcevaluefactorsfactorization_product) = S ((S (ff_i_fsat_lookup_sourcevaluefactorsfactorization_product)) * mv_factor_scale_lookup_sourcevaluefactors)) /\ exists ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_factor. mv_factor_code_lookup_sourcevaluefactors = ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_lookup_sourcevaluefactorsfactorization_product)) * mv_factor_scale_lookup_sourcevaluefactors) + (ff_p_fsat_lookup_sourcevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_partial. ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_partial + S (ff_r_fsat_lookup_sourcevaluefactorsfactorization_product) = S ((S (ff_i_fsat_lookup_sourcevaluefactorsfactorization_product)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_partial. ff_u_fsat_lookup_sourcevaluefactorsfactorization_product = ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_lookup_sourcevaluefactorsfactorization_product)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product) + (ff_r_fsat_lookup_sourcevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_successor. ff_h_fsat_lookup_sourcevaluefactorsfactorization_product_successor + S (ff_s_fsat_lookup_sourcevaluefactorsfactorization_product) = S ((S (S ff_i_fsat_lookup_sourcevaluefactorsfactorization_product)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_successor. ff_u_fsat_lookup_sourcevaluefactorsfactorization_product = ff_q_fsat_lookup_sourcevaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_lookup_sourcevaluefactorsfactorization_product)) * ff_v_fsat_lookup_sourcevaluefactorsfactorization_product) + (ff_s_fsat_lookup_sourcevaluefactorsfactorization_product))) /\ ff_s_fsat_lookup_sourcevaluefactorsfactorization_product = ff_r_fsat_lookup_sourcevaluefactorsfactorization_product * ff_p_fsat_lookup_sourcevaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_lookup_sourcevaluefactorsfactorization_primes. (exists ftsf_gap_fsat_lookup_sourcevaluefactorsfactorization_primes_bound. ftsf_gap_fsat_lookup_sourcevaluefactorsfactorization_primes_bound + S ftsf_index_fsat_lookup_sourcevaluefactorsfactorization_primes = (mv_factor_count_lookup_sourcevaluefactors)) -> exists ftsf_factor_fsat_lookup_sourcevaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_lookup_sourcevaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_lookup_sourcevaluefactorsfactorization_primes)) * mv_factor_scale_lookup_sourcevaluefactors)) /\ exists ff_q_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_entry. mv_factor_code_lookup_sourcevaluefactors = ff_q_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_lookup_sourcevaluefactorsfactorization_primes)) * mv_factor_scale_lookup_sourcevaluefactors) + (ftsf_factor_fsat_lookup_sourcevaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_lookup_sourcevaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_prime. ftsf_factor_fsat_lookup_sourcevaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_lookup_sourcevaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_lookup_sourcevaluefactorsparityeven. (mv_factor_count_lookup_sourcevaluefactors) = 2 * mv_even_half_lookup_sourcevaluefactorsparityeven) /\ ((mt_value_lookup_source) = 2))) \/ (((exists mv_odd_half_lookup_sourcevaluefactorsparityodd. (mv_factor_count_lookup_sourcevaluefactors) = 2 * mv_odd_half_lookup_sourcevaluefactorsparityodd + 1) /\ ((mt_value_lookup_source) = 1)))))))))))))))) -> ~(i=0) -> (exists pvs_le_gap_lookup_bound. pvs_le_gap_lookup_bound + (i) = (N)) -> exists z. (exists dst_positive_code_lookup_entry dst_positive_scale_lookup_entry dst_negative_code_lookup_entry dst_negative_scale_lookup_entry dst_positive_lookup_entry dst_negative_lookup_entry. (((M) = (((((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) * S ((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) + ((dst_positive_scale_lookup_entry) + (dst_positive_scale_lookup_entry))) + (((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry)))) * S ((((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) * S ((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) + ((dst_positive_scale_lookup_entry) + (dst_positive_scale_lookup_entry))) + (((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry)))) + ((((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry))) + (((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry)))))) /\ (((((exists ff_h_pvs_lookup_entrypositive. ff_h_pvs_lookup_entrypositive + S (dst_positive_lookup_entry) = S ((S (i)) * dst_positive_scale_lookup_entry)) /\ exists ff_q_pvs_lookup_entrypositive. dst_positive_code_lookup_entry = ff_q_pvs_lookup_entrypositive * S ((S (i)) * dst_positive_scale_lookup_entry) + (dst_positive_lookup_entry))) /\ (((((exists ff_h_pvs_lookup_entrynegative. ff_h_pvs_lookup_entrynegative + S (dst_negative_lookup_entry) = S ((S (i)) * dst_negative_scale_lookup_entry)) /\ exists ff_q_pvs_lookup_entrynegative. dst_negative_code_lookup_entry = ff_q_pvs_lookup_entrynegative * S ((S (i)) * dst_negative_scale_lookup_entry) + (dst_negative_lookup_entry))) /\ (exists ge_balance_positive_lookup_entryvalue ge_balance_negative_lookup_entryvalue. (((((z) = 2 * (ge_balance_positive_lookup_entryvalue) /\ (ge_balance_negative_lookup_entryvalue) = 0) \/ exists ge_signed_half_lookup_entryvaluedecode. (((z) = 2 * ge_signed_half_lookup_entryvaluedecode + 1 /\ (ge_balance_positive_lookup_entryvalue) = 0) /\ (ge_balance_negative_lookup_entryvalue) = S ge_signed_half_lookup_entryvaluedecode))) /\ ((dst_positive_lookup_entry) + ge_balance_negative_lookup_entryvalue = (dst_negative_lookup_entry) + ge_balance_positive_lookup_entryvalue))))))))) /\ (((~((i) = 0)) /\ ((((exists mv_square_prime_lookup_valuesquare. ((~((mv_square_prime_lookup_valuesquare) = 1) /\ forall pvs_left_lookup_valuesquareprime pvs_right_lookup_valuesquareprime. (mv_square_prime_lookup_valuesquare) = pvs_left_lookup_valuesquareprime * pvs_right_lookup_valuesquareprime -> pvs_left_lookup_valuesquareprime = 1 \/ pvs_right_lookup_valuesquareprime = 1) /\ (exists pvs_factor_lookup_valuesquaredivisor. (i) = (mv_square_prime_lookup_valuesquare * mv_square_prime_lookup_valuesquare) * pvs_factor_lookup_valuesquaredivisor))) /\ ((z) = 0))) \/ (((((~((i) = 0)) /\ (forall sfd_prime_lookup_valuesquarefree. (~((sfd_prime_lookup_valuesquarefree) = 1) /\ forall pvs_left_lookup_valuesquarefreedomain pvs_right_lookup_valuesquarefreedomain. (sfd_prime_lookup_valuesquarefree) = pvs_left_lookup_valuesquarefreedomain * pvs_right_lookup_valuesquarefreedomain -> pvs_left_lookup_valuesquarefreedomain = 1 \/ pvs_right_lookup_valuesquarefreedomain = 1) -> (exists pvs_le_gap_lookup_valuesquarefreebound. pvs_le_gap_lookup_valuesquarefreebound + (sfd_prime_lookup_valuesquarefree) = (i)) -> ~(exists pvs_factor_lookup_valuesquarefreesquare. (i) = (sfd_prime_lookup_valuesquarefree * sfd_prime_lookup_valuesquarefree) * pvs_factor_lookup_valuesquarefreesquare)))) /\ (exists mv_factor_code_lookup_valuefactors mv_factor_scale_lookup_valuefactors mv_factor_count_lookup_valuefactors. (((~(i = 0) /\ ((exists ff_u_fsat_lookup_valuefactorsfactorization_product ff_v_fsat_lookup_valuefactorsfactorization_product. ((((exists ff_h_fsat_lookup_valuefactorsfactorization_product_start. ff_h_fsat_lookup_valuefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_lookup_valuefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_valuefactorsfactorization_product_start. ff_u_fsat_lookup_valuefactorsfactorization_product = ff_q_fsat_lookup_valuefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_lookup_valuefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_lookup_valuefactorsfactorization_product_terminal. ff_h_fsat_lookup_valuefactorsfactorization_product_terminal + S (i) = S ((S (mv_factor_count_lookup_valuefactors)) * ff_v_fsat_lookup_valuefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_valuefactorsfactorization_product_terminal. ff_u_fsat_lookup_valuefactorsfactorization_product = ff_q_fsat_lookup_valuefactorsfactorization_product_terminal * S ((S (mv_factor_count_lookup_valuefactors)) * ff_v_fsat_lookup_valuefactorsfactorization_product) + (i))) /\ forall ff_i_fsat_lookup_valuefactorsfactorization_product. (exists ff_lt_fsat_lookup_valuefactorsfactorization_product_bound. ff_lt_fsat_lookup_valuefactorsfactorization_product_bound + S ff_i_fsat_lookup_valuefactorsfactorization_product = mv_factor_count_lookup_valuefactors) -> exists ff_p_fsat_lookup_valuefactorsfactorization_product ff_r_fsat_lookup_valuefactorsfactorization_product ff_s_fsat_lookup_valuefactorsfactorization_product. ((((exists ff_h_fsat_lookup_valuefactorsfactorization_product_factor. ff_h_fsat_lookup_valuefactorsfactorization_product_factor + S (ff_p_fsat_lookup_valuefactorsfactorization_product) = S ((S (ff_i_fsat_lookup_valuefactorsfactorization_product)) * mv_factor_scale_lookup_valuefactors)) /\ exists ff_q_fsat_lookup_valuefactorsfactorization_product_factor. mv_factor_code_lookup_valuefactors = ff_q_fsat_lookup_valuefactorsfactorization_product_factor * S ((S (ff_i_fsat_lookup_valuefactorsfactorization_product)) * mv_factor_scale_lookup_valuefactors) + (ff_p_fsat_lookup_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_lookup_valuefactorsfactorization_product_partial. ff_h_fsat_lookup_valuefactorsfactorization_product_partial + S (ff_r_fsat_lookup_valuefactorsfactorization_product) = S ((S (ff_i_fsat_lookup_valuefactorsfactorization_product)) * ff_v_fsat_lookup_valuefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_valuefactorsfactorization_product_partial. ff_u_fsat_lookup_valuefactorsfactorization_product = ff_q_fsat_lookup_valuefactorsfactorization_product_partial * S ((S (ff_i_fsat_lookup_valuefactorsfactorization_product)) * ff_v_fsat_lookup_valuefactorsfactorization_product) + (ff_r_fsat_lookup_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_lookup_valuefactorsfactorization_product_successor. ff_h_fsat_lookup_valuefactorsfactorization_product_successor + S (ff_s_fsat_lookup_valuefactorsfactorization_product) = S ((S (S ff_i_fsat_lookup_valuefactorsfactorization_product)) * ff_v_fsat_lookup_valuefactorsfactorization_product)) /\ exists ff_q_fsat_lookup_valuefactorsfactorization_product_successor. ff_u_fsat_lookup_valuefactorsfactorization_product = ff_q_fsat_lookup_valuefactorsfactorization_product_successor * S ((S (S ff_i_fsat_lookup_valuefactorsfactorization_product)) * ff_v_fsat_lookup_valuefactorsfactorization_product) + (ff_s_fsat_lookup_valuefactorsfactorization_product))) /\ ff_s_fsat_lookup_valuefactorsfactorization_product = ff_r_fsat_lookup_valuefactorsfactorization_product * ff_p_fsat_lookup_valuefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_lookup_valuefactorsfactorization_primes. (exists ftsf_gap_fsat_lookup_valuefactorsfactorization_primes_bound. ftsf_gap_fsat_lookup_valuefactorsfactorization_primes_bound + S ftsf_index_fsat_lookup_valuefactorsfactorization_primes = (mv_factor_count_lookup_valuefactors)) -> exists ftsf_factor_fsat_lookup_valuefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_lookup_valuefactorsfactorization_primes_entry. ff_h_ftsf_fsat_lookup_valuefactorsfactorization_primes_entry + S (ftsf_factor_fsat_lookup_valuefactorsfactorization_primes) = S ((S (ftsf_index_fsat_lookup_valuefactorsfactorization_primes)) * mv_factor_scale_lookup_valuefactors)) /\ exists ff_q_ftsf_fsat_lookup_valuefactorsfactorization_primes_entry. mv_factor_code_lookup_valuefactors = ff_q_ftsf_fsat_lookup_valuefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_lookup_valuefactorsfactorization_primes)) * mv_factor_scale_lookup_valuefactors) + (ftsf_factor_fsat_lookup_valuefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_lookup_valuefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_lookup_valuefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_lookup_valuefactorsfactorization_primes_prime. ftsf_factor_fsat_lookup_valuefactorsfactorization_primes = frm_prime_left_ftsf_fsat_lookup_valuefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_lookup_valuefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_lookup_valuefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_lookup_valuefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_lookup_valuefactorsparityeven. (mv_factor_count_lookup_valuefactors) = 2 * mv_even_half_lookup_valuefactorsparityeven) /\ ((z) = 2))) \/ (((exists mv_odd_half_lookup_valuefactorsparityodd. (mv_factor_count_lookup_valuefactors) = 2 * mv_odd_half_lookup_valuefactorsparityodd + 1) /\ ((z) = 1)))))))))))

mobius_table_entry_iff

new owned theorem · read exact theorem evidence

Bundle node 288; exact statement SHA-256 86fe55ee79551634cbea612ac100812d79dd9058550132293520a2b328b57cdd

Exact first-order statement

forall N M i z. (((exists dst_positive_code_iff_tabletable dst_positive_scale_iff_tabletable dst_negative_code_iff_tabletable dst_negative_scale_iff_tabletable. (((M) = (((((dst_positive_code_iff_tabletable) + (dst_positive_scale_iff_tabletable)) * S ((dst_positive_code_iff_tabletable) + (dst_positive_scale_iff_tabletable)) + ((dst_positive_scale_iff_tabletable) + (dst_positive_scale_iff_tabletable))) + (((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) * S ((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) + ((dst_negative_scale_iff_tabletable) + (dst_negative_scale_iff_tabletable)))) * S ((((dst_positive_code_iff_tabletable) + (dst_positive_scale_iff_tabletable)) * S ((dst_positive_code_iff_tabletable) + (dst_positive_scale_iff_tabletable)) + ((dst_positive_scale_iff_tabletable) + (dst_positive_scale_iff_tabletable))) + (((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) * S ((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) + ((dst_negative_scale_iff_tabletable) + (dst_negative_scale_iff_tabletable)))) + ((((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) * S ((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) + ((dst_negative_scale_iff_tabletable) + (dst_negative_scale_iff_tabletable))) + (((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) * S ((dst_negative_code_iff_tabletable) + (dst_negative_scale_iff_tabletable)) + ((dst_negative_scale_iff_tabletable) + (dst_negative_scale_iff_tabletable)))))) /\ (forall dst_index_iff_tabletable. (exists pvs_le_gap_iff_tabletabledomain. pvs_le_gap_iff_tabletabledomain + (dst_index_iff_tabletable) = (N)) -> exists dst_positive_iff_tabletable dst_negative_iff_tabletable dst_value_iff_tabletable. ((((exists ff_h_pvs_iff_tabletableentrypositive. ff_h_pvs_iff_tabletableentrypositive + S (dst_positive_iff_tabletable) = S ((S (dst_index_iff_tabletable)) * dst_positive_scale_iff_tabletable)) /\ exists ff_q_pvs_iff_tabletableentrypositive. dst_positive_code_iff_tabletable = ff_q_pvs_iff_tabletableentrypositive * S ((S (dst_index_iff_tabletable)) * dst_positive_scale_iff_tabletable) + (dst_positive_iff_tabletable))) /\ (((((exists ff_h_pvs_iff_tabletableentrynegative. ff_h_pvs_iff_tabletableentrynegative + S (dst_negative_iff_tabletable) = S ((S (dst_index_iff_tabletable)) * dst_negative_scale_iff_tabletable)) /\ exists ff_q_pvs_iff_tabletableentrynegative. dst_negative_code_iff_tabletable = ff_q_pvs_iff_tabletableentrynegative * S ((S (dst_index_iff_tabletable)) * dst_negative_scale_iff_tabletable) + (dst_negative_iff_tabletable))) /\ (exists ge_balance_positive_iff_tabletableentryvalue ge_balance_negative_iff_tabletableentryvalue. (((((dst_value_iff_tabletable) = 2 * (ge_balance_positive_iff_tabletableentryvalue) /\ (ge_balance_negative_iff_tabletableentryvalue) = 0) \/ exists ge_signed_half_iff_tabletableentryvaluedecode. (((dst_value_iff_tabletable) = 2 * ge_signed_half_iff_tabletableentryvaluedecode + 1 /\ (ge_balance_positive_iff_tabletableentryvalue) = 0) /\ (ge_balance_negative_iff_tabletableentryvalue) = S ge_signed_half_iff_tabletableentryvaluedecode))) /\ ((dst_positive_iff_tabletable) + ge_balance_negative_iff_tabletableentryvalue = (dst_negative_iff_tabletable) + ge_balance_positive_iff_tabletableentryvalue))))))))) /\ (((exists dst_positive_code_iff_tablezero dst_positive_scale_iff_tablezero dst_negative_code_iff_tablezero dst_negative_scale_iff_tablezero dst_positive_iff_tablezero dst_negative_iff_tablezero. (((M) = (((((dst_positive_code_iff_tablezero) + (dst_positive_scale_iff_tablezero)) * S ((dst_positive_code_iff_tablezero) + (dst_positive_scale_iff_tablezero)) + ((dst_positive_scale_iff_tablezero) + (dst_positive_scale_iff_tablezero))) + (((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) * S ((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) + ((dst_negative_scale_iff_tablezero) + (dst_negative_scale_iff_tablezero)))) * S ((((dst_positive_code_iff_tablezero) + (dst_positive_scale_iff_tablezero)) * S ((dst_positive_code_iff_tablezero) + (dst_positive_scale_iff_tablezero)) + ((dst_positive_scale_iff_tablezero) + (dst_positive_scale_iff_tablezero))) + (((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) * S ((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) + ((dst_negative_scale_iff_tablezero) + (dst_negative_scale_iff_tablezero)))) + ((((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) * S ((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) + ((dst_negative_scale_iff_tablezero) + (dst_negative_scale_iff_tablezero))) + (((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) * S ((dst_negative_code_iff_tablezero) + (dst_negative_scale_iff_tablezero)) + ((dst_negative_scale_iff_tablezero) + (dst_negative_scale_iff_tablezero)))))) /\ (((((exists ff_h_pvs_iff_tablezeropositive. ff_h_pvs_iff_tablezeropositive + S (dst_positive_iff_tablezero) = S ((S (0)) * dst_positive_scale_iff_tablezero)) /\ exists ff_q_pvs_iff_tablezeropositive. dst_positive_code_iff_tablezero = ff_q_pvs_iff_tablezeropositive * S ((S (0)) * dst_positive_scale_iff_tablezero) + (dst_positive_iff_tablezero))) /\ (((((exists ff_h_pvs_iff_tablezeronegative. ff_h_pvs_iff_tablezeronegative + S (dst_negative_iff_tablezero) = S ((S (0)) * dst_negative_scale_iff_tablezero)) /\ exists ff_q_pvs_iff_tablezeronegative. dst_negative_code_iff_tablezero = ff_q_pvs_iff_tablezeronegative * S ((S (0)) * dst_negative_scale_iff_tablezero) + (dst_negative_iff_tablezero))) /\ (exists ge_balance_positive_iff_tablezerovalue ge_balance_negative_iff_tablezerovalue. (((((0) = 2 * (ge_balance_positive_iff_tablezerovalue) /\ (ge_balance_negative_iff_tablezerovalue) = 0) \/ exists ge_signed_half_iff_tablezerovaluedecode. (((0) = 2 * ge_signed_half_iff_tablezerovaluedecode + 1 /\ (ge_balance_positive_iff_tablezerovalue) = 0) /\ (ge_balance_negative_iff_tablezerovalue) = S ge_signed_half_iff_tablezerovaluedecode))) /\ ((dst_positive_iff_tablezero) + ge_balance_negative_iff_tablezerovalue = (dst_negative_iff_tablezero) + ge_balance_positive_iff_tablezerovalue))))))))) /\ (forall mt_index_iff_table mt_value_iff_table. ~(mt_index_iff_table=0) -> (exists pvs_le_gap_iff_tabledomain. pvs_le_gap_iff_tabledomain + (mt_index_iff_table) = (N)) -> (exists dst_positive_code_iff_tableentry dst_positive_scale_iff_tableentry dst_negative_code_iff_tableentry dst_negative_scale_iff_tableentry dst_positive_iff_tableentry dst_negative_iff_tableentry. (((M) = (((((dst_positive_code_iff_tableentry) + (dst_positive_scale_iff_tableentry)) * S ((dst_positive_code_iff_tableentry) + (dst_positive_scale_iff_tableentry)) + ((dst_positive_scale_iff_tableentry) + (dst_positive_scale_iff_tableentry))) + (((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) * S ((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) + ((dst_negative_scale_iff_tableentry) + (dst_negative_scale_iff_tableentry)))) * S ((((dst_positive_code_iff_tableentry) + (dst_positive_scale_iff_tableentry)) * S ((dst_positive_code_iff_tableentry) + (dst_positive_scale_iff_tableentry)) + ((dst_positive_scale_iff_tableentry) + (dst_positive_scale_iff_tableentry))) + (((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) * S ((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) + ((dst_negative_scale_iff_tableentry) + (dst_negative_scale_iff_tableentry)))) + ((((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) * S ((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) + ((dst_negative_scale_iff_tableentry) + (dst_negative_scale_iff_tableentry))) + (((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) * S ((dst_negative_code_iff_tableentry) + (dst_negative_scale_iff_tableentry)) + ((dst_negative_scale_iff_tableentry) + (dst_negative_scale_iff_tableentry)))))) /\ (((((exists ff_h_pvs_iff_tableentrypositive. ff_h_pvs_iff_tableentrypositive + S (dst_positive_iff_tableentry) = S ((S (mt_index_iff_table)) * dst_positive_scale_iff_tableentry)) /\ exists ff_q_pvs_iff_tableentrypositive. dst_positive_code_iff_tableentry = ff_q_pvs_iff_tableentrypositive * S ((S (mt_index_iff_table)) * dst_positive_scale_iff_tableentry) + (dst_positive_iff_tableentry))) /\ (((((exists ff_h_pvs_iff_tableentrynegative. ff_h_pvs_iff_tableentrynegative + S (dst_negative_iff_tableentry) = S ((S (mt_index_iff_table)) * dst_negative_scale_iff_tableentry)) /\ exists ff_q_pvs_iff_tableentrynegative. dst_negative_code_iff_tableentry = ff_q_pvs_iff_tableentrynegative * S ((S (mt_index_iff_table)) * dst_negative_scale_iff_tableentry) + (dst_negative_iff_tableentry))) /\ (exists ge_balance_positive_iff_tableentryvalue ge_balance_negative_iff_tableentryvalue. (((((mt_value_iff_table) = 2 * (ge_balance_positive_iff_tableentryvalue) /\ (ge_balance_negative_iff_tableentryvalue) = 0) \/ exists ge_signed_half_iff_tableentryvaluedecode. (((mt_value_iff_table) = 2 * ge_signed_half_iff_tableentryvaluedecode + 1 /\ (ge_balance_positive_iff_tableentryvalue) = 0) /\ (ge_balance_negative_iff_tableentryvalue) = S ge_signed_half_iff_tableentryvaluedecode))) /\ ((dst_positive_iff_tableentry) + ge_balance_negative_iff_tableentryvalue = (dst_negative_iff_tableentry) + ge_balance_positive_iff_tableentryvalue))))))))) -> (((~((mt_index_iff_table) = 0)) /\ ((((exists mv_square_prime_iff_tablevaluesquare. ((~((mv_square_prime_iff_tablevaluesquare) = 1) /\ forall pvs_left_iff_tablevaluesquareprime pvs_right_iff_tablevaluesquareprime. (mv_square_prime_iff_tablevaluesquare) = pvs_left_iff_tablevaluesquareprime * pvs_right_iff_tablevaluesquareprime -> pvs_left_iff_tablevaluesquareprime = 1 \/ pvs_right_iff_tablevaluesquareprime = 1) /\ (exists pvs_factor_iff_tablevaluesquaredivisor. (mt_index_iff_table) = (mv_square_prime_iff_tablevaluesquare * mv_square_prime_iff_tablevaluesquare) * pvs_factor_iff_tablevaluesquaredivisor))) /\ ((mt_value_iff_table) = 0))) \/ (((((~((mt_index_iff_table) = 0)) /\ (forall sfd_prime_iff_tablevaluesquarefree. (~((sfd_prime_iff_tablevaluesquarefree) = 1) /\ forall pvs_left_iff_tablevaluesquarefreedomain pvs_right_iff_tablevaluesquarefreedomain. (sfd_prime_iff_tablevaluesquarefree) = pvs_left_iff_tablevaluesquarefreedomain * pvs_right_iff_tablevaluesquarefreedomain -> pvs_left_iff_tablevaluesquarefreedomain = 1 \/ pvs_right_iff_tablevaluesquarefreedomain = 1) -> (exists pvs_le_gap_iff_tablevaluesquarefreebound. pvs_le_gap_iff_tablevaluesquarefreebound + (sfd_prime_iff_tablevaluesquarefree) = (mt_index_iff_table)) -> ~(exists pvs_factor_iff_tablevaluesquarefreesquare. (mt_index_iff_table) = (sfd_prime_iff_tablevaluesquarefree * sfd_prime_iff_tablevaluesquarefree) * pvs_factor_iff_tablevaluesquarefreesquare)))) /\ (exists mv_factor_code_iff_tablevaluefactors mv_factor_scale_iff_tablevaluefactors mv_factor_count_iff_tablevaluefactors. (((~(mt_index_iff_table = 0) /\ ((exists ff_u_fsat_iff_tablevaluefactorsfactorization_product ff_v_fsat_iff_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_iff_tablevaluefactorsfactorization_product_start. ff_h_fsat_iff_tablevaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_iff_tablevaluefactorsfactorization_product_start. ff_u_fsat_iff_tablevaluefactorsfactorization_product = ff_q_fsat_iff_tablevaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_iff_tablevaluefactorsfactorization_product_terminal. ff_h_fsat_iff_tablevaluefactorsfactorization_product_terminal + S (mt_index_iff_table) = S ((S (mv_factor_count_iff_tablevaluefactors)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_iff_tablevaluefactorsfactorization_product_terminal. ff_u_fsat_iff_tablevaluefactorsfactorization_product = ff_q_fsat_iff_tablevaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_iff_tablevaluefactors)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product) + (mt_index_iff_table))) /\ forall ff_i_fsat_iff_tablevaluefactorsfactorization_product. (exists ff_lt_fsat_iff_tablevaluefactorsfactorization_product_bound. ff_lt_fsat_iff_tablevaluefactorsfactorization_product_bound + S ff_i_fsat_iff_tablevaluefactorsfactorization_product = mv_factor_count_iff_tablevaluefactors) -> exists ff_p_fsat_iff_tablevaluefactorsfactorization_product ff_r_fsat_iff_tablevaluefactorsfactorization_product ff_s_fsat_iff_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_iff_tablevaluefactorsfactorization_product_factor. ff_h_fsat_iff_tablevaluefactorsfactorization_product_factor + S (ff_p_fsat_iff_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_iff_tablevaluefactorsfactorization_product)) * mv_factor_scale_iff_tablevaluefactors)) /\ exists ff_q_fsat_iff_tablevaluefactorsfactorization_product_factor. mv_factor_code_iff_tablevaluefactors = ff_q_fsat_iff_tablevaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_iff_tablevaluefactorsfactorization_product)) * mv_factor_scale_iff_tablevaluefactors) + (ff_p_fsat_iff_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_iff_tablevaluefactorsfactorization_product_partial. ff_h_fsat_iff_tablevaluefactorsfactorization_product_partial + S (ff_r_fsat_iff_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_iff_tablevaluefactorsfactorization_product)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_iff_tablevaluefactorsfactorization_product_partial. ff_u_fsat_iff_tablevaluefactorsfactorization_product = ff_q_fsat_iff_tablevaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_iff_tablevaluefactorsfactorization_product)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product) + (ff_r_fsat_iff_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_iff_tablevaluefactorsfactorization_product_successor. ff_h_fsat_iff_tablevaluefactorsfactorization_product_successor + S (ff_s_fsat_iff_tablevaluefactorsfactorization_product) = S ((S (S ff_i_fsat_iff_tablevaluefactorsfactorization_product)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_iff_tablevaluefactorsfactorization_product_successor. ff_u_fsat_iff_tablevaluefactorsfactorization_product = ff_q_fsat_iff_tablevaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_iff_tablevaluefactorsfactorization_product)) * ff_v_fsat_iff_tablevaluefactorsfactorization_product) + (ff_s_fsat_iff_tablevaluefactorsfactorization_product))) /\ ff_s_fsat_iff_tablevaluefactorsfactorization_product = ff_r_fsat_iff_tablevaluefactorsfactorization_product * ff_p_fsat_iff_tablevaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_iff_tablevaluefactorsfactorization_primes. (exists ftsf_gap_fsat_iff_tablevaluefactorsfactorization_primes_bound. ftsf_gap_fsat_iff_tablevaluefactorsfactorization_primes_bound + S ftsf_index_fsat_iff_tablevaluefactorsfactorization_primes = (mv_factor_count_iff_tablevaluefactors)) -> exists ftsf_factor_fsat_iff_tablevaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_iff_tablevaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_iff_tablevaluefactorsfactorization_primes)) * mv_factor_scale_iff_tablevaluefactors)) /\ exists ff_q_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_entry. mv_factor_code_iff_tablevaluefactors = ff_q_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_iff_tablevaluefactorsfactorization_primes)) * mv_factor_scale_iff_tablevaluefactors) + (ftsf_factor_fsat_iff_tablevaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_iff_tablevaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_prime. ftsf_factor_fsat_iff_tablevaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_iff_tablevaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_iff_tablevaluefactorsparityeven. (mv_factor_count_iff_tablevaluefactors) = 2 * mv_even_half_iff_tablevaluefactorsparityeven) /\ ((mt_value_iff_table) = 2))) \/ (((exists mv_odd_half_iff_tablevaluefactorsparityodd. (mv_factor_count_iff_tablevaluefactors) = 2 * mv_odd_half_iff_tablevaluefactorsparityodd + 1) /\ ((mt_value_iff_table) = 1)))))))))))))))) -> ~(i=0) -> (exists pvs_le_gap_iff_bound. pvs_le_gap_iff_bound + (i) = (N)) -> ((exists dst_positive_code_iff_entry_forward dst_positive_scale_iff_entry_forward dst_negative_code_iff_entry_forward dst_negative_scale_iff_entry_forward dst_positive_iff_entry_forward dst_negative_iff_entry_forward. (((M) = (((((dst_positive_code_iff_entry_forward) + (dst_positive_scale_iff_entry_forward)) * S ((dst_positive_code_iff_entry_forward) + (dst_positive_scale_iff_entry_forward)) + ((dst_positive_scale_iff_entry_forward) + (dst_positive_scale_iff_entry_forward))) + (((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) * S ((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) + ((dst_negative_scale_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)))) * S ((((dst_positive_code_iff_entry_forward) + (dst_positive_scale_iff_entry_forward)) * S ((dst_positive_code_iff_entry_forward) + (dst_positive_scale_iff_entry_forward)) + ((dst_positive_scale_iff_entry_forward) + (dst_positive_scale_iff_entry_forward))) + (((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) * S ((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) + ((dst_negative_scale_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)))) + ((((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) * S ((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) + ((dst_negative_scale_iff_entry_forward) + (dst_negative_scale_iff_entry_forward))) + (((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) * S ((dst_negative_code_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)) + ((dst_negative_scale_iff_entry_forward) + (dst_negative_scale_iff_entry_forward)))))) /\ (((((exists ff_h_pvs_iff_entry_forwardpositive. ff_h_pvs_iff_entry_forwardpositive + S (dst_positive_iff_entry_forward) = S ((S (i)) * dst_positive_scale_iff_entry_forward)) /\ exists ff_q_pvs_iff_entry_forwardpositive. dst_positive_code_iff_entry_forward = ff_q_pvs_iff_entry_forwardpositive * S ((S (i)) * dst_positive_scale_iff_entry_forward) + (dst_positive_iff_entry_forward))) /\ (((((exists ff_h_pvs_iff_entry_forwardnegative. ff_h_pvs_iff_entry_forwardnegative + S (dst_negative_iff_entry_forward) = S ((S (i)) * dst_negative_scale_iff_entry_forward)) /\ exists ff_q_pvs_iff_entry_forwardnegative. dst_negative_code_iff_entry_forward = ff_q_pvs_iff_entry_forwardnegative * S ((S (i)) * dst_negative_scale_iff_entry_forward) + (dst_negative_iff_entry_forward))) /\ (exists ge_balance_positive_iff_entry_forwardvalue ge_balance_negative_iff_entry_forwardvalue. (((((z) = 2 * (ge_balance_positive_iff_entry_forwardvalue) /\ (ge_balance_negative_iff_entry_forwardvalue) = 0) \/ exists ge_signed_half_iff_entry_forwardvaluedecode. (((z) = 2 * ge_signed_half_iff_entry_forwardvaluedecode + 1 /\ (ge_balance_positive_iff_entry_forwardvalue) = 0) /\ (ge_balance_negative_iff_entry_forwardvalue) = S ge_signed_half_iff_entry_forwardvaluedecode))) /\ ((dst_positive_iff_entry_forward) + ge_balance_negative_iff_entry_forwardvalue = (dst_negative_iff_entry_forward) + ge_balance_positive_iff_entry_forwardvalue))))))))) -> (((~((i) = 0)) /\ ((((exists mv_square_prime_iff_value_forwardsquare. ((~((mv_square_prime_iff_value_forwardsquare) = 1) /\ forall pvs_left_iff_value_forwardsquareprime pvs_right_iff_value_forwardsquareprime. (mv_square_prime_iff_value_forwardsquare) = pvs_left_iff_value_forwardsquareprime * pvs_right_iff_value_forwardsquareprime -> pvs_left_iff_value_forwardsquareprime = 1 \/ pvs_right_iff_value_forwardsquareprime = 1) /\ (exists pvs_factor_iff_value_forwardsquaredivisor. (i) = (mv_square_prime_iff_value_forwardsquare * mv_square_prime_iff_value_forwardsquare) * pvs_factor_iff_value_forwardsquaredivisor))) /\ ((z) = 0))) \/ (((((~((i) = 0)) /\ (forall sfd_prime_iff_value_forwardsquarefree. (~((sfd_prime_iff_value_forwardsquarefree) = 1) /\ forall pvs_left_iff_value_forwardsquarefreedomain pvs_right_iff_value_forwardsquarefreedomain. (sfd_prime_iff_value_forwardsquarefree) = pvs_left_iff_value_forwardsquarefreedomain * pvs_right_iff_value_forwardsquarefreedomain -> pvs_left_iff_value_forwardsquarefreedomain = 1 \/ pvs_right_iff_value_forwardsquarefreedomain = 1) -> (exists pvs_le_gap_iff_value_forwardsquarefreebound. pvs_le_gap_iff_value_forwardsquarefreebound + (sfd_prime_iff_value_forwardsquarefree) = (i)) -> ~(exists pvs_factor_iff_value_forwardsquarefreesquare. (i) = (sfd_prime_iff_value_forwardsquarefree * sfd_prime_iff_value_forwardsquarefree) * pvs_factor_iff_value_forwardsquarefreesquare)))) /\ (exists mv_factor_code_iff_value_forwardfactors mv_factor_scale_iff_value_forwardfactors mv_factor_count_iff_value_forwardfactors. (((~(i = 0) /\ ((exists ff_u_fsat_iff_value_forwardfactorsfactorization_product ff_v_fsat_iff_value_forwardfactorsfactorization_product. ((((exists ff_h_fsat_iff_value_forwardfactorsfactorization_product_start. ff_h_fsat_iff_value_forwardfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_forwardfactorsfactorization_product_start. ff_u_fsat_iff_value_forwardfactorsfactorization_product = ff_q_fsat_iff_value_forwardfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_iff_value_forwardfactorsfactorization_product_terminal. ff_h_fsat_iff_value_forwardfactorsfactorization_product_terminal + S (i) = S ((S (mv_factor_count_iff_value_forwardfactors)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_forwardfactorsfactorization_product_terminal. ff_u_fsat_iff_value_forwardfactorsfactorization_product = ff_q_fsat_iff_value_forwardfactorsfactorization_product_terminal * S ((S (mv_factor_count_iff_value_forwardfactors)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product) + (i))) /\ forall ff_i_fsat_iff_value_forwardfactorsfactorization_product. (exists ff_lt_fsat_iff_value_forwardfactorsfactorization_product_bound. ff_lt_fsat_iff_value_forwardfactorsfactorization_product_bound + S ff_i_fsat_iff_value_forwardfactorsfactorization_product = mv_factor_count_iff_value_forwardfactors) -> exists ff_p_fsat_iff_value_forwardfactorsfactorization_product ff_r_fsat_iff_value_forwardfactorsfactorization_product ff_s_fsat_iff_value_forwardfactorsfactorization_product. ((((exists ff_h_fsat_iff_value_forwardfactorsfactorization_product_factor. ff_h_fsat_iff_value_forwardfactorsfactorization_product_factor + S (ff_p_fsat_iff_value_forwardfactorsfactorization_product) = S ((S (ff_i_fsat_iff_value_forwardfactorsfactorization_product)) * mv_factor_scale_iff_value_forwardfactors)) /\ exists ff_q_fsat_iff_value_forwardfactorsfactorization_product_factor. mv_factor_code_iff_value_forwardfactors = ff_q_fsat_iff_value_forwardfactorsfactorization_product_factor * S ((S (ff_i_fsat_iff_value_forwardfactorsfactorization_product)) * mv_factor_scale_iff_value_forwardfactors) + (ff_p_fsat_iff_value_forwardfactorsfactorization_product))) /\ ((((exists ff_h_fsat_iff_value_forwardfactorsfactorization_product_partial. ff_h_fsat_iff_value_forwardfactorsfactorization_product_partial + S (ff_r_fsat_iff_value_forwardfactorsfactorization_product) = S ((S (ff_i_fsat_iff_value_forwardfactorsfactorization_product)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_forwardfactorsfactorization_product_partial. ff_u_fsat_iff_value_forwardfactorsfactorization_product = ff_q_fsat_iff_value_forwardfactorsfactorization_product_partial * S ((S (ff_i_fsat_iff_value_forwardfactorsfactorization_product)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product) + (ff_r_fsat_iff_value_forwardfactorsfactorization_product))) /\ ((((exists ff_h_fsat_iff_value_forwardfactorsfactorization_product_successor. ff_h_fsat_iff_value_forwardfactorsfactorization_product_successor + S (ff_s_fsat_iff_value_forwardfactorsfactorization_product) = S ((S (S ff_i_fsat_iff_value_forwardfactorsfactorization_product)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_forwardfactorsfactorization_product_successor. ff_u_fsat_iff_value_forwardfactorsfactorization_product = ff_q_fsat_iff_value_forwardfactorsfactorization_product_successor * S ((S (S ff_i_fsat_iff_value_forwardfactorsfactorization_product)) * ff_v_fsat_iff_value_forwardfactorsfactorization_product) + (ff_s_fsat_iff_value_forwardfactorsfactorization_product))) /\ ff_s_fsat_iff_value_forwardfactorsfactorization_product = ff_r_fsat_iff_value_forwardfactorsfactorization_product * ff_p_fsat_iff_value_forwardfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_iff_value_forwardfactorsfactorization_primes. (exists ftsf_gap_fsat_iff_value_forwardfactorsfactorization_primes_bound. ftsf_gap_fsat_iff_value_forwardfactorsfactorization_primes_bound + S ftsf_index_fsat_iff_value_forwardfactorsfactorization_primes = (mv_factor_count_iff_value_forwardfactors)) -> exists ftsf_factor_fsat_iff_value_forwardfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_entry. ff_h_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_entry + S (ftsf_factor_fsat_iff_value_forwardfactorsfactorization_primes) = S ((S (ftsf_index_fsat_iff_value_forwardfactorsfactorization_primes)) * mv_factor_scale_iff_value_forwardfactors)) /\ exists ff_q_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_entry. mv_factor_code_iff_value_forwardfactors = ff_q_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_iff_value_forwardfactorsfactorization_primes)) * mv_factor_scale_iff_value_forwardfactors) + (ftsf_factor_fsat_iff_value_forwardfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_iff_value_forwardfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_prime. ftsf_factor_fsat_iff_value_forwardfactorsfactorization_primes = frm_prime_left_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_iff_value_forwardfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_iff_value_forwardfactorsparityeven. (mv_factor_count_iff_value_forwardfactors) = 2 * mv_even_half_iff_value_forwardfactorsparityeven) /\ ((z) = 2))) \/ (((exists mv_odd_half_iff_value_forwardfactorsparityodd. (mv_factor_count_iff_value_forwardfactors) = 2 * mv_odd_half_iff_value_forwardfactorsparityodd + 1) /\ ((z) = 1)))))))))))) /\ ((((~((i) = 0)) /\ ((((exists mv_square_prime_iff_value_reversesquare. ((~((mv_square_prime_iff_value_reversesquare) = 1) /\ forall pvs_left_iff_value_reversesquareprime pvs_right_iff_value_reversesquareprime. (mv_square_prime_iff_value_reversesquare) = pvs_left_iff_value_reversesquareprime * pvs_right_iff_value_reversesquareprime -> pvs_left_iff_value_reversesquareprime = 1 \/ pvs_right_iff_value_reversesquareprime = 1) /\ (exists pvs_factor_iff_value_reversesquaredivisor. (i) = (mv_square_prime_iff_value_reversesquare * mv_square_prime_iff_value_reversesquare) * pvs_factor_iff_value_reversesquaredivisor))) /\ ((z) = 0))) \/ (((((~((i) = 0)) /\ (forall sfd_prime_iff_value_reversesquarefree. (~((sfd_prime_iff_value_reversesquarefree) = 1) /\ forall pvs_left_iff_value_reversesquarefreedomain pvs_right_iff_value_reversesquarefreedomain. (sfd_prime_iff_value_reversesquarefree) = pvs_left_iff_value_reversesquarefreedomain * pvs_right_iff_value_reversesquarefreedomain -> pvs_left_iff_value_reversesquarefreedomain = 1 \/ pvs_right_iff_value_reversesquarefreedomain = 1) -> (exists pvs_le_gap_iff_value_reversesquarefreebound. pvs_le_gap_iff_value_reversesquarefreebound + (sfd_prime_iff_value_reversesquarefree) = (i)) -> ~(exists pvs_factor_iff_value_reversesquarefreesquare. (i) = (sfd_prime_iff_value_reversesquarefree * sfd_prime_iff_value_reversesquarefree) * pvs_factor_iff_value_reversesquarefreesquare)))) /\ (exists mv_factor_code_iff_value_reversefactors mv_factor_scale_iff_value_reversefactors mv_factor_count_iff_value_reversefactors. (((~(i = 0) /\ ((exists ff_u_fsat_iff_value_reversefactorsfactorization_product ff_v_fsat_iff_value_reversefactorsfactorization_product. ((((exists ff_h_fsat_iff_value_reversefactorsfactorization_product_start. ff_h_fsat_iff_value_reversefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_iff_value_reversefactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_reversefactorsfactorization_product_start. ff_u_fsat_iff_value_reversefactorsfactorization_product = ff_q_fsat_iff_value_reversefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_iff_value_reversefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_iff_value_reversefactorsfactorization_product_terminal. ff_h_fsat_iff_value_reversefactorsfactorization_product_terminal + S (i) = S ((S (mv_factor_count_iff_value_reversefactors)) * ff_v_fsat_iff_value_reversefactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_reversefactorsfactorization_product_terminal. ff_u_fsat_iff_value_reversefactorsfactorization_product = ff_q_fsat_iff_value_reversefactorsfactorization_product_terminal * S ((S (mv_factor_count_iff_value_reversefactors)) * ff_v_fsat_iff_value_reversefactorsfactorization_product) + (i))) /\ forall ff_i_fsat_iff_value_reversefactorsfactorization_product. (exists ff_lt_fsat_iff_value_reversefactorsfactorization_product_bound. ff_lt_fsat_iff_value_reversefactorsfactorization_product_bound + S ff_i_fsat_iff_value_reversefactorsfactorization_product = mv_factor_count_iff_value_reversefactors) -> exists ff_p_fsat_iff_value_reversefactorsfactorization_product ff_r_fsat_iff_value_reversefactorsfactorization_product ff_s_fsat_iff_value_reversefactorsfactorization_product. ((((exists ff_h_fsat_iff_value_reversefactorsfactorization_product_factor. ff_h_fsat_iff_value_reversefactorsfactorization_product_factor + S (ff_p_fsat_iff_value_reversefactorsfactorization_product) = S ((S (ff_i_fsat_iff_value_reversefactorsfactorization_product)) * mv_factor_scale_iff_value_reversefactors)) /\ exists ff_q_fsat_iff_value_reversefactorsfactorization_product_factor. mv_factor_code_iff_value_reversefactors = ff_q_fsat_iff_value_reversefactorsfactorization_product_factor * S ((S (ff_i_fsat_iff_value_reversefactorsfactorization_product)) * mv_factor_scale_iff_value_reversefactors) + (ff_p_fsat_iff_value_reversefactorsfactorization_product))) /\ ((((exists ff_h_fsat_iff_value_reversefactorsfactorization_product_partial. ff_h_fsat_iff_value_reversefactorsfactorization_product_partial + S (ff_r_fsat_iff_value_reversefactorsfactorization_product) = S ((S (ff_i_fsat_iff_value_reversefactorsfactorization_product)) * ff_v_fsat_iff_value_reversefactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_reversefactorsfactorization_product_partial. ff_u_fsat_iff_value_reversefactorsfactorization_product = ff_q_fsat_iff_value_reversefactorsfactorization_product_partial * S ((S (ff_i_fsat_iff_value_reversefactorsfactorization_product)) * ff_v_fsat_iff_value_reversefactorsfactorization_product) + (ff_r_fsat_iff_value_reversefactorsfactorization_product))) /\ ((((exists ff_h_fsat_iff_value_reversefactorsfactorization_product_successor. ff_h_fsat_iff_value_reversefactorsfactorization_product_successor + S (ff_s_fsat_iff_value_reversefactorsfactorization_product) = S ((S (S ff_i_fsat_iff_value_reversefactorsfactorization_product)) * ff_v_fsat_iff_value_reversefactorsfactorization_product)) /\ exists ff_q_fsat_iff_value_reversefactorsfactorization_product_successor. ff_u_fsat_iff_value_reversefactorsfactorization_product = ff_q_fsat_iff_value_reversefactorsfactorization_product_successor * S ((S (S ff_i_fsat_iff_value_reversefactorsfactorization_product)) * ff_v_fsat_iff_value_reversefactorsfactorization_product) + (ff_s_fsat_iff_value_reversefactorsfactorization_product))) /\ ff_s_fsat_iff_value_reversefactorsfactorization_product = ff_r_fsat_iff_value_reversefactorsfactorization_product * ff_p_fsat_iff_value_reversefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_iff_value_reversefactorsfactorization_primes. (exists ftsf_gap_fsat_iff_value_reversefactorsfactorization_primes_bound. ftsf_gap_fsat_iff_value_reversefactorsfactorization_primes_bound + S ftsf_index_fsat_iff_value_reversefactorsfactorization_primes = (mv_factor_count_iff_value_reversefactors)) -> exists ftsf_factor_fsat_iff_value_reversefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_iff_value_reversefactorsfactorization_primes_entry. ff_h_ftsf_fsat_iff_value_reversefactorsfactorization_primes_entry + S (ftsf_factor_fsat_iff_value_reversefactorsfactorization_primes) = S ((S (ftsf_index_fsat_iff_value_reversefactorsfactorization_primes)) * mv_factor_scale_iff_value_reversefactors)) /\ exists ff_q_ftsf_fsat_iff_value_reversefactorsfactorization_primes_entry. mv_factor_code_iff_value_reversefactors = ff_q_ftsf_fsat_iff_value_reversefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_iff_value_reversefactorsfactorization_primes)) * mv_factor_scale_iff_value_reversefactors) + (ftsf_factor_fsat_iff_value_reversefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_iff_value_reversefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_iff_value_reversefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_iff_value_reversefactorsfactorization_primes_prime. ftsf_factor_fsat_iff_value_reversefactorsfactorization_primes = frm_prime_left_ftsf_fsat_iff_value_reversefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_iff_value_reversefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_iff_value_reversefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_iff_value_reversefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_iff_value_reversefactorsparityeven. (mv_factor_count_iff_value_reversefactors) = 2 * mv_even_half_iff_value_reversefactorsparityeven) /\ ((z) = 2))) \/ (((exists mv_odd_half_iff_value_reversefactorsparityodd. (mv_factor_count_iff_value_reversefactors) = 2 * mv_odd_half_iff_value_reversefactorsparityodd + 1) /\ ((z) = 1))))))))))) -> (exists dst_positive_code_iff_entry_reverse dst_positive_scale_iff_entry_reverse dst_negative_code_iff_entry_reverse dst_negative_scale_iff_entry_reverse dst_positive_iff_entry_reverse dst_negative_iff_entry_reverse. (((M) = (((((dst_positive_code_iff_entry_reverse) + (dst_positive_scale_iff_entry_reverse)) * S ((dst_positive_code_iff_entry_reverse) + (dst_positive_scale_iff_entry_reverse)) + ((dst_positive_scale_iff_entry_reverse) + (dst_positive_scale_iff_entry_reverse))) + (((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) * S ((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) + ((dst_negative_scale_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)))) * S ((((dst_positive_code_iff_entry_reverse) + (dst_positive_scale_iff_entry_reverse)) * S ((dst_positive_code_iff_entry_reverse) + (dst_positive_scale_iff_entry_reverse)) + ((dst_positive_scale_iff_entry_reverse) + (dst_positive_scale_iff_entry_reverse))) + (((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) * S ((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) + ((dst_negative_scale_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)))) + ((((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) * S ((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) + ((dst_negative_scale_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse))) + (((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) * S ((dst_negative_code_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)) + ((dst_negative_scale_iff_entry_reverse) + (dst_negative_scale_iff_entry_reverse)))))) /\ (((((exists ff_h_pvs_iff_entry_reversepositive. ff_h_pvs_iff_entry_reversepositive + S (dst_positive_iff_entry_reverse) = S ((S (i)) * dst_positive_scale_iff_entry_reverse)) /\ exists ff_q_pvs_iff_entry_reversepositive. dst_positive_code_iff_entry_reverse = ff_q_pvs_iff_entry_reversepositive * S ((S (i)) * dst_positive_scale_iff_entry_reverse) + (dst_positive_iff_entry_reverse))) /\ (((((exists ff_h_pvs_iff_entry_reversenegative. ff_h_pvs_iff_entry_reversenegative + S (dst_negative_iff_entry_reverse) = S ((S (i)) * dst_negative_scale_iff_entry_reverse)) /\ exists ff_q_pvs_iff_entry_reversenegative. dst_negative_code_iff_entry_reverse = ff_q_pvs_iff_entry_reversenegative * S ((S (i)) * dst_negative_scale_iff_entry_reverse) + (dst_negative_iff_entry_reverse))) /\ (exists ge_balance_positive_iff_entry_reversevalue ge_balance_negative_iff_entry_reversevalue. (((((z) = 2 * (ge_balance_positive_iff_entry_reversevalue) /\ (ge_balance_negative_iff_entry_reversevalue) = 0) \/ exists ge_signed_half_iff_entry_reversevaluedecode. (((z) = 2 * ge_signed_half_iff_entry_reversevaluedecode + 1 /\ (ge_balance_positive_iff_entry_reversevalue) = 0) /\ (ge_balance_negative_iff_entry_reversevalue) = S ge_signed_half_iff_entry_reversevaluedecode))) /\ ((dst_positive_iff_entry_reverse) + ge_balance_negative_iff_entry_reversevalue = (dst_negative_iff_entry_reverse) + ge_balance_positive_iff_entry_reversevalue))))))))))

mobius_table_one_entry

new owned theorem · read exact theorem evidence

Bundle node 289; exact statement SHA-256 9abdcc1ef980138f90c241d3cdfaa385a2716729a4ef321463653c75f7b70ead

Exact first-order statement

forall N M. (((exists dst_positive_code_unit_tabletable dst_positive_scale_unit_tabletable dst_negative_code_unit_tabletable dst_negative_scale_unit_tabletable. (((M) = (((((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) * S ((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) + ((dst_positive_scale_unit_tabletable) + (dst_positive_scale_unit_tabletable))) + (((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable)))) * S ((((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) * S ((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) + ((dst_positive_scale_unit_tabletable) + (dst_positive_scale_unit_tabletable))) + (((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable)))) + ((((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable))) + (((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable)))))) /\ (forall dst_index_unit_tabletable. (exists pvs_le_gap_unit_tabletabledomain. pvs_le_gap_unit_tabletabledomain + (dst_index_unit_tabletable) = (N)) -> exists dst_positive_unit_tabletable dst_negative_unit_tabletable dst_value_unit_tabletable. ((((exists ff_h_pvs_unit_tabletableentrypositive. ff_h_pvs_unit_tabletableentrypositive + S (dst_positive_unit_tabletable) = S ((S (dst_index_unit_tabletable)) * dst_positive_scale_unit_tabletable)) /\ exists ff_q_pvs_unit_tabletableentrypositive. dst_positive_code_unit_tabletable = ff_q_pvs_unit_tabletableentrypositive * S ((S (dst_index_unit_tabletable)) * dst_positive_scale_unit_tabletable) + (dst_positive_unit_tabletable))) /\ (((((exists ff_h_pvs_unit_tabletableentrynegative. ff_h_pvs_unit_tabletableentrynegative + S (dst_negative_unit_tabletable) = S ((S (dst_index_unit_tabletable)) * dst_negative_scale_unit_tabletable)) /\ exists ff_q_pvs_unit_tabletableentrynegative. dst_negative_code_unit_tabletable = ff_q_pvs_unit_tabletableentrynegative * S ((S (dst_index_unit_tabletable)) * dst_negative_scale_unit_tabletable) + (dst_negative_unit_tabletable))) /\ (exists ge_balance_positive_unit_tabletableentryvalue ge_balance_negative_unit_tabletableentryvalue. (((((dst_value_unit_tabletable) = 2 * (ge_balance_positive_unit_tabletableentryvalue) /\ (ge_balance_negative_unit_tabletableentryvalue) = 0) \/ exists ge_signed_half_unit_tabletableentryvaluedecode. (((dst_value_unit_tabletable) = 2 * ge_signed_half_unit_tabletableentryvaluedecode + 1 /\ (ge_balance_positive_unit_tabletableentryvalue) = 0) /\ (ge_balance_negative_unit_tabletableentryvalue) = S ge_signed_half_unit_tabletableentryvaluedecode))) /\ ((dst_positive_unit_tabletable) + ge_balance_negative_unit_tabletableentryvalue = (dst_negative_unit_tabletable) + ge_balance_positive_unit_tabletableentryvalue))))))))) /\ (((exists dst_positive_code_unit_tablezero dst_positive_scale_unit_tablezero dst_negative_code_unit_tablezero dst_negative_scale_unit_tablezero dst_positive_unit_tablezero dst_negative_unit_tablezero. (((M) = (((((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) * S ((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) + ((dst_positive_scale_unit_tablezero) + (dst_positive_scale_unit_tablezero))) + (((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero)))) * S ((((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) * S ((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) + ((dst_positive_scale_unit_tablezero) + (dst_positive_scale_unit_tablezero))) + (((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero)))) + ((((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero))) + (((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero)))))) /\ (((((exists ff_h_pvs_unit_tablezeropositive. ff_h_pvs_unit_tablezeropositive + S (dst_positive_unit_tablezero) = S ((S (0)) * dst_positive_scale_unit_tablezero)) /\ exists ff_q_pvs_unit_tablezeropositive. dst_positive_code_unit_tablezero = ff_q_pvs_unit_tablezeropositive * S ((S (0)) * dst_positive_scale_unit_tablezero) + (dst_positive_unit_tablezero))) /\ (((((exists ff_h_pvs_unit_tablezeronegative. ff_h_pvs_unit_tablezeronegative + S (dst_negative_unit_tablezero) = S ((S (0)) * dst_negative_scale_unit_tablezero)) /\ exists ff_q_pvs_unit_tablezeronegative. dst_negative_code_unit_tablezero = ff_q_pvs_unit_tablezeronegative * S ((S (0)) * dst_negative_scale_unit_tablezero) + (dst_negative_unit_tablezero))) /\ (exists ge_balance_positive_unit_tablezerovalue ge_balance_negative_unit_tablezerovalue. (((((0) = 2 * (ge_balance_positive_unit_tablezerovalue) /\ (ge_balance_negative_unit_tablezerovalue) = 0) \/ exists ge_signed_half_unit_tablezerovaluedecode. (((0) = 2 * ge_signed_half_unit_tablezerovaluedecode + 1 /\ (ge_balance_positive_unit_tablezerovalue) = 0) /\ (ge_balance_negative_unit_tablezerovalue) = S ge_signed_half_unit_tablezerovaluedecode))) /\ ((dst_positive_unit_tablezero) + ge_balance_negative_unit_tablezerovalue = (dst_negative_unit_tablezero) + ge_balance_positive_unit_tablezerovalue))))))))) /\ (forall mt_index_unit_table mt_value_unit_table. ~(mt_index_unit_table=0) -> (exists pvs_le_gap_unit_tabledomain. pvs_le_gap_unit_tabledomain + (mt_index_unit_table) = (N)) -> (exists dst_positive_code_unit_tableentry dst_positive_scale_unit_tableentry dst_negative_code_unit_tableentry dst_negative_scale_unit_tableentry dst_positive_unit_tableentry dst_negative_unit_tableentry. (((M) = (((((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) * S ((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) + ((dst_positive_scale_unit_tableentry) + (dst_positive_scale_unit_tableentry))) + (((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry)))) * S ((((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) * S ((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) + ((dst_positive_scale_unit_tableentry) + (dst_positive_scale_unit_tableentry))) + (((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry)))) + ((((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry))) + (((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry)))))) /\ (((((exists ff_h_pvs_unit_tableentrypositive. ff_h_pvs_unit_tableentrypositive + S (dst_positive_unit_tableentry) = S ((S (mt_index_unit_table)) * dst_positive_scale_unit_tableentry)) /\ exists ff_q_pvs_unit_tableentrypositive. dst_positive_code_unit_tableentry = ff_q_pvs_unit_tableentrypositive * S ((S (mt_index_unit_table)) * dst_positive_scale_unit_tableentry) + (dst_positive_unit_tableentry))) /\ (((((exists ff_h_pvs_unit_tableentrynegative. ff_h_pvs_unit_tableentrynegative + S (dst_negative_unit_tableentry) = S ((S (mt_index_unit_table)) * dst_negative_scale_unit_tableentry)) /\ exists ff_q_pvs_unit_tableentrynegative. dst_negative_code_unit_tableentry = ff_q_pvs_unit_tableentrynegative * S ((S (mt_index_unit_table)) * dst_negative_scale_unit_tableentry) + (dst_negative_unit_tableentry))) /\ (exists ge_balance_positive_unit_tableentryvalue ge_balance_negative_unit_tableentryvalue. (((((mt_value_unit_table) = 2 * (ge_balance_positive_unit_tableentryvalue) /\ (ge_balance_negative_unit_tableentryvalue) = 0) \/ exists ge_signed_half_unit_tableentryvaluedecode. (((mt_value_unit_table) = 2 * ge_signed_half_unit_tableentryvaluedecode + 1 /\ (ge_balance_positive_unit_tableentryvalue) = 0) /\ (ge_balance_negative_unit_tableentryvalue) = S ge_signed_half_unit_tableentryvaluedecode))) /\ ((dst_positive_unit_tableentry) + ge_balance_negative_unit_tableentryvalue = (dst_negative_unit_tableentry) + ge_balance_positive_unit_tableentryvalue))))))))) -> (((~((mt_index_unit_table) = 0)) /\ ((((exists mv_square_prime_unit_tablevaluesquare. ((~((mv_square_prime_unit_tablevaluesquare) = 1) /\ forall pvs_left_unit_tablevaluesquareprime pvs_right_unit_tablevaluesquareprime. (mv_square_prime_unit_tablevaluesquare) = pvs_left_unit_tablevaluesquareprime * pvs_right_unit_tablevaluesquareprime -> pvs_left_unit_tablevaluesquareprime = 1 \/ pvs_right_unit_tablevaluesquareprime = 1) /\ (exists pvs_factor_unit_tablevaluesquaredivisor. (mt_index_unit_table) = (mv_square_prime_unit_tablevaluesquare * mv_square_prime_unit_tablevaluesquare) * pvs_factor_unit_tablevaluesquaredivisor))) /\ ((mt_value_unit_table) = 0))) \/ (((((~((mt_index_unit_table) = 0)) /\ (forall sfd_prime_unit_tablevaluesquarefree. (~((sfd_prime_unit_tablevaluesquarefree) = 1) /\ forall pvs_left_unit_tablevaluesquarefreedomain pvs_right_unit_tablevaluesquarefreedomain. (sfd_prime_unit_tablevaluesquarefree) = pvs_left_unit_tablevaluesquarefreedomain * pvs_right_unit_tablevaluesquarefreedomain -> pvs_left_unit_tablevaluesquarefreedomain = 1 \/ pvs_right_unit_tablevaluesquarefreedomain = 1) -> (exists pvs_le_gap_unit_tablevaluesquarefreebound. pvs_le_gap_unit_tablevaluesquarefreebound + (sfd_prime_unit_tablevaluesquarefree) = (mt_index_unit_table)) -> ~(exists pvs_factor_unit_tablevaluesquarefreesquare. (mt_index_unit_table) = (sfd_prime_unit_tablevaluesquarefree * sfd_prime_unit_tablevaluesquarefree) * pvs_factor_unit_tablevaluesquarefreesquare)))) /\ (exists mv_factor_code_unit_tablevaluefactors mv_factor_scale_unit_tablevaluefactors mv_factor_count_unit_tablevaluefactors. (((~(mt_index_unit_table = 0) /\ ((exists ff_u_fsat_unit_tablevaluefactorsfactorization_product ff_v_fsat_unit_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_start. ff_h_fsat_unit_tablevaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_start. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_terminal. ff_h_fsat_unit_tablevaluefactorsfactorization_product_terminal + S (mt_index_unit_table) = S ((S (mv_factor_count_unit_tablevaluefactors)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_terminal. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_unit_tablevaluefactors)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (mt_index_unit_table))) /\ forall ff_i_fsat_unit_tablevaluefactorsfactorization_product. (exists ff_lt_fsat_unit_tablevaluefactorsfactorization_product_bound. ff_lt_fsat_unit_tablevaluefactorsfactorization_product_bound + S ff_i_fsat_unit_tablevaluefactorsfactorization_product = mv_factor_count_unit_tablevaluefactors) -> exists ff_p_fsat_unit_tablevaluefactorsfactorization_product ff_r_fsat_unit_tablevaluefactorsfactorization_product ff_s_fsat_unit_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_factor. ff_h_fsat_unit_tablevaluefactorsfactorization_product_factor + S (ff_p_fsat_unit_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * mv_factor_scale_unit_tablevaluefactors)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_factor. mv_factor_code_unit_tablevaluefactors = ff_q_fsat_unit_tablevaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * mv_factor_scale_unit_tablevaluefactors) + (ff_p_fsat_unit_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_partial. ff_h_fsat_unit_tablevaluefactorsfactorization_product_partial + S (ff_r_fsat_unit_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_partial. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (ff_r_fsat_unit_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_successor. ff_h_fsat_unit_tablevaluefactorsfactorization_product_successor + S (ff_s_fsat_unit_tablevaluefactorsfactorization_product) = S ((S (S ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_successor. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (ff_s_fsat_unit_tablevaluefactorsfactorization_product))) /\ ff_s_fsat_unit_tablevaluefactorsfactorization_product = ff_r_fsat_unit_tablevaluefactorsfactorization_product * ff_p_fsat_unit_tablevaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes. (exists ftsf_gap_fsat_unit_tablevaluefactorsfactorization_primes_bound. ftsf_gap_fsat_unit_tablevaluefactorsfactorization_primes_bound + S ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes = (mv_factor_count_unit_tablevaluefactors)) -> exists ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes)) * mv_factor_scale_unit_tablevaluefactors)) /\ exists ff_q_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry. mv_factor_code_unit_tablevaluefactors = ff_q_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes)) * mv_factor_scale_unit_tablevaluefactors) + (ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime. ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_unit_tablevaluefactorsparityeven. (mv_factor_count_unit_tablevaluefactors) = 2 * mv_even_half_unit_tablevaluefactorsparityeven) /\ ((mt_value_unit_table) = 2))) \/ (((exists mv_odd_half_unit_tablevaluefactorsparityodd. (mv_factor_count_unit_tablevaluefactors) = 2 * mv_odd_half_unit_tablevaluefactorsparityodd + 1) /\ ((mt_value_unit_table) = 1)))))))))))))))) -> (exists pvs_le_gap_unit_bound. pvs_le_gap_unit_bound + (1) = (N)) -> (exists dst_positive_code_unit_entry dst_positive_scale_unit_entry dst_negative_code_unit_entry dst_negative_scale_unit_entry dst_positive_unit_entry dst_negative_unit_entry. (((M) = (((((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) * S ((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) + ((dst_positive_scale_unit_entry) + (dst_positive_scale_unit_entry))) + (((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry)))) * S ((((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) * S ((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) + ((dst_positive_scale_unit_entry) + (dst_positive_scale_unit_entry))) + (((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry)))) + ((((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry))) + (((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry)))))) /\ (((((exists ff_h_pvs_unit_entrypositive. ff_h_pvs_unit_entrypositive + S (dst_positive_unit_entry) = S ((S (1)) * dst_positive_scale_unit_entry)) /\ exists ff_q_pvs_unit_entrypositive. dst_positive_code_unit_entry = ff_q_pvs_unit_entrypositive * S ((S (1)) * dst_positive_scale_unit_entry) + (dst_positive_unit_entry))) /\ (((((exists ff_h_pvs_unit_entrynegative. ff_h_pvs_unit_entrynegative + S (dst_negative_unit_entry) = S ((S (1)) * dst_negative_scale_unit_entry)) /\ exists ff_q_pvs_unit_entrynegative. dst_negative_code_unit_entry = ff_q_pvs_unit_entrynegative * S ((S (1)) * dst_negative_scale_unit_entry) + (dst_negative_unit_entry))) /\ (exists ge_balance_positive_unit_entryvalue ge_balance_negative_unit_entryvalue. (((((2) = 2 * (ge_balance_positive_unit_entryvalue) /\ (ge_balance_negative_unit_entryvalue) = 0) \/ exists ge_signed_half_unit_entryvaluedecode. (((2) = 2 * ge_signed_half_unit_entryvaluedecode + 1 /\ (ge_balance_positive_unit_entryvalue) = 0) /\ (ge_balance_negative_unit_entryvalue) = S ge_signed_half_unit_entryvaluedecode))) /\ ((dst_positive_unit_entry) + ge_balance_negative_unit_entryvalue = (dst_negative_unit_entry) + ge_balance_positive_unit_entryvalue)))))))))

mobius_table_extensional

new owned theorem · read exact theorem evidence

Bundle node 290; exact statement SHA-256 0c5f57750d23295e30eea764f44ebd04f5a2992ed5c07f376bc370d0a67d6e40

Exact first-order statement

forall N F G. (((exists dst_positive_code_unique_firsttable dst_positive_scale_unique_firsttable dst_negative_code_unique_firsttable dst_negative_scale_unique_firsttable. (((F) = (((((dst_positive_code_unique_firsttable) + (dst_positive_scale_unique_firsttable)) * S ((dst_positive_code_unique_firsttable) + (dst_positive_scale_unique_firsttable)) + ((dst_positive_scale_unique_firsttable) + (dst_positive_scale_unique_firsttable))) + (((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) * S ((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) + ((dst_negative_scale_unique_firsttable) + (dst_negative_scale_unique_firsttable)))) * S ((((dst_positive_code_unique_firsttable) + (dst_positive_scale_unique_firsttable)) * S ((dst_positive_code_unique_firsttable) + (dst_positive_scale_unique_firsttable)) + ((dst_positive_scale_unique_firsttable) + (dst_positive_scale_unique_firsttable))) + (((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) * S ((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) + ((dst_negative_scale_unique_firsttable) + (dst_negative_scale_unique_firsttable)))) + ((((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) * S ((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) + ((dst_negative_scale_unique_firsttable) + (dst_negative_scale_unique_firsttable))) + (((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) * S ((dst_negative_code_unique_firsttable) + (dst_negative_scale_unique_firsttable)) + ((dst_negative_scale_unique_firsttable) + (dst_negative_scale_unique_firsttable)))))) /\ (forall dst_index_unique_firsttable. (exists pvs_le_gap_unique_firsttabledomain. pvs_le_gap_unique_firsttabledomain + (dst_index_unique_firsttable) = (N)) -> exists dst_positive_unique_firsttable dst_negative_unique_firsttable dst_value_unique_firsttable. ((((exists ff_h_pvs_unique_firsttableentrypositive. ff_h_pvs_unique_firsttableentrypositive + S (dst_positive_unique_firsttable) = S ((S (dst_index_unique_firsttable)) * dst_positive_scale_unique_firsttable)) /\ exists ff_q_pvs_unique_firsttableentrypositive. dst_positive_code_unique_firsttable = ff_q_pvs_unique_firsttableentrypositive * S ((S (dst_index_unique_firsttable)) * dst_positive_scale_unique_firsttable) + (dst_positive_unique_firsttable))) /\ (((((exists ff_h_pvs_unique_firsttableentrynegative. ff_h_pvs_unique_firsttableentrynegative + S (dst_negative_unique_firsttable) = S ((S (dst_index_unique_firsttable)) * dst_negative_scale_unique_firsttable)) /\ exists ff_q_pvs_unique_firsttableentrynegative. dst_negative_code_unique_firsttable = ff_q_pvs_unique_firsttableentrynegative * S ((S (dst_index_unique_firsttable)) * dst_negative_scale_unique_firsttable) + (dst_negative_unique_firsttable))) /\ (exists ge_balance_positive_unique_firsttableentryvalue ge_balance_negative_unique_firsttableentryvalue. (((((dst_value_unique_firsttable) = 2 * (ge_balance_positive_unique_firsttableentryvalue) /\ (ge_balance_negative_unique_firsttableentryvalue) = 0) \/ exists ge_signed_half_unique_firsttableentryvaluedecode. (((dst_value_unique_firsttable) = 2 * ge_signed_half_unique_firsttableentryvaluedecode + 1 /\ (ge_balance_positive_unique_firsttableentryvalue) = 0) /\ (ge_balance_negative_unique_firsttableentryvalue) = S ge_signed_half_unique_firsttableentryvaluedecode))) /\ ((dst_positive_unique_firsttable) + ge_balance_negative_unique_firsttableentryvalue = (dst_negative_unique_firsttable) + ge_balance_positive_unique_firsttableentryvalue))))))))) /\ (((exists dst_positive_code_unique_firstzero dst_positive_scale_unique_firstzero dst_negative_code_unique_firstzero dst_negative_scale_unique_firstzero dst_positive_unique_firstzero dst_negative_unique_firstzero. (((F) = (((((dst_positive_code_unique_firstzero) + (dst_positive_scale_unique_firstzero)) * S ((dst_positive_code_unique_firstzero) + (dst_positive_scale_unique_firstzero)) + ((dst_positive_scale_unique_firstzero) + (dst_positive_scale_unique_firstzero))) + (((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) * S ((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) + ((dst_negative_scale_unique_firstzero) + (dst_negative_scale_unique_firstzero)))) * S ((((dst_positive_code_unique_firstzero) + (dst_positive_scale_unique_firstzero)) * S ((dst_positive_code_unique_firstzero) + (dst_positive_scale_unique_firstzero)) + ((dst_positive_scale_unique_firstzero) + (dst_positive_scale_unique_firstzero))) + (((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) * S ((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) + ((dst_negative_scale_unique_firstzero) + (dst_negative_scale_unique_firstzero)))) + ((((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) * S ((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) + ((dst_negative_scale_unique_firstzero) + (dst_negative_scale_unique_firstzero))) + (((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) * S ((dst_negative_code_unique_firstzero) + (dst_negative_scale_unique_firstzero)) + ((dst_negative_scale_unique_firstzero) + (dst_negative_scale_unique_firstzero)))))) /\ (((((exists ff_h_pvs_unique_firstzeropositive. ff_h_pvs_unique_firstzeropositive + S (dst_positive_unique_firstzero) = S ((S (0)) * dst_positive_scale_unique_firstzero)) /\ exists ff_q_pvs_unique_firstzeropositive. dst_positive_code_unique_firstzero = ff_q_pvs_unique_firstzeropositive * S ((S (0)) * dst_positive_scale_unique_firstzero) + (dst_positive_unique_firstzero))) /\ (((((exists ff_h_pvs_unique_firstzeronegative. ff_h_pvs_unique_firstzeronegative + S (dst_negative_unique_firstzero) = S ((S (0)) * dst_negative_scale_unique_firstzero)) /\ exists ff_q_pvs_unique_firstzeronegative. dst_negative_code_unique_firstzero = ff_q_pvs_unique_firstzeronegative * S ((S (0)) * dst_negative_scale_unique_firstzero) + (dst_negative_unique_firstzero))) /\ (exists ge_balance_positive_unique_firstzerovalue ge_balance_negative_unique_firstzerovalue. (((((0) = 2 * (ge_balance_positive_unique_firstzerovalue) /\ (ge_balance_negative_unique_firstzerovalue) = 0) \/ exists ge_signed_half_unique_firstzerovaluedecode. (((0) = 2 * ge_signed_half_unique_firstzerovaluedecode + 1 /\ (ge_balance_positive_unique_firstzerovalue) = 0) /\ (ge_balance_negative_unique_firstzerovalue) = S ge_signed_half_unique_firstzerovaluedecode))) /\ ((dst_positive_unique_firstzero) + ge_balance_negative_unique_firstzerovalue = (dst_negative_unique_firstzero) + ge_balance_positive_unique_firstzerovalue))))))))) /\ (forall mt_index_unique_first mt_value_unique_first. ~(mt_index_unique_first=0) -> (exists pvs_le_gap_unique_firstdomain. pvs_le_gap_unique_firstdomain + (mt_index_unique_first) = (N)) -> (exists dst_positive_code_unique_firstentry dst_positive_scale_unique_firstentry dst_negative_code_unique_firstentry dst_negative_scale_unique_firstentry dst_positive_unique_firstentry dst_negative_unique_firstentry. (((F) = (((((dst_positive_code_unique_firstentry) + (dst_positive_scale_unique_firstentry)) * S ((dst_positive_code_unique_firstentry) + (dst_positive_scale_unique_firstentry)) + ((dst_positive_scale_unique_firstentry) + (dst_positive_scale_unique_firstentry))) + (((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) * S ((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) + ((dst_negative_scale_unique_firstentry) + (dst_negative_scale_unique_firstentry)))) * S ((((dst_positive_code_unique_firstentry) + (dst_positive_scale_unique_firstentry)) * S ((dst_positive_code_unique_firstentry) + (dst_positive_scale_unique_firstentry)) + ((dst_positive_scale_unique_firstentry) + (dst_positive_scale_unique_firstentry))) + (((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) * S ((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) + ((dst_negative_scale_unique_firstentry) + (dst_negative_scale_unique_firstentry)))) + ((((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) * S ((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) + ((dst_negative_scale_unique_firstentry) + (dst_negative_scale_unique_firstentry))) + (((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) * S ((dst_negative_code_unique_firstentry) + (dst_negative_scale_unique_firstentry)) + ((dst_negative_scale_unique_firstentry) + (dst_negative_scale_unique_firstentry)))))) /\ (((((exists ff_h_pvs_unique_firstentrypositive. ff_h_pvs_unique_firstentrypositive + S (dst_positive_unique_firstentry) = S ((S (mt_index_unique_first)) * dst_positive_scale_unique_firstentry)) /\ exists ff_q_pvs_unique_firstentrypositive. dst_positive_code_unique_firstentry = ff_q_pvs_unique_firstentrypositive * S ((S (mt_index_unique_first)) * dst_positive_scale_unique_firstentry) + (dst_positive_unique_firstentry))) /\ (((((exists ff_h_pvs_unique_firstentrynegative. ff_h_pvs_unique_firstentrynegative + S (dst_negative_unique_firstentry) = S ((S (mt_index_unique_first)) * dst_negative_scale_unique_firstentry)) /\ exists ff_q_pvs_unique_firstentrynegative. dst_negative_code_unique_firstentry = ff_q_pvs_unique_firstentrynegative * S ((S (mt_index_unique_first)) * dst_negative_scale_unique_firstentry) + (dst_negative_unique_firstentry))) /\ (exists ge_balance_positive_unique_firstentryvalue ge_balance_negative_unique_firstentryvalue. (((((mt_value_unique_first) = 2 * (ge_balance_positive_unique_firstentryvalue) /\ (ge_balance_negative_unique_firstentryvalue) = 0) \/ exists ge_signed_half_unique_firstentryvaluedecode. (((mt_value_unique_first) = 2 * ge_signed_half_unique_firstentryvaluedecode + 1 /\ (ge_balance_positive_unique_firstentryvalue) = 0) /\ (ge_balance_negative_unique_firstentryvalue) = S ge_signed_half_unique_firstentryvaluedecode))) /\ ((dst_positive_unique_firstentry) + ge_balance_negative_unique_firstentryvalue = (dst_negative_unique_firstentry) + ge_balance_positive_unique_firstentryvalue))))))))) -> (((~((mt_index_unique_first) = 0)) /\ ((((exists mv_square_prime_unique_firstvaluesquare. ((~((mv_square_prime_unique_firstvaluesquare) = 1) /\ forall pvs_left_unique_firstvaluesquareprime pvs_right_unique_firstvaluesquareprime. (mv_square_prime_unique_firstvaluesquare) = pvs_left_unique_firstvaluesquareprime * pvs_right_unique_firstvaluesquareprime -> pvs_left_unique_firstvaluesquareprime = 1 \/ pvs_right_unique_firstvaluesquareprime = 1) /\ (exists pvs_factor_unique_firstvaluesquaredivisor. (mt_index_unique_first) = (mv_square_prime_unique_firstvaluesquare * mv_square_prime_unique_firstvaluesquare) * pvs_factor_unique_firstvaluesquaredivisor))) /\ ((mt_value_unique_first) = 0))) \/ (((((~((mt_index_unique_first) = 0)) /\ (forall sfd_prime_unique_firstvaluesquarefree. (~((sfd_prime_unique_firstvaluesquarefree) = 1) /\ forall pvs_left_unique_firstvaluesquarefreedomain pvs_right_unique_firstvaluesquarefreedomain. (sfd_prime_unique_firstvaluesquarefree) = pvs_left_unique_firstvaluesquarefreedomain * pvs_right_unique_firstvaluesquarefreedomain -> pvs_left_unique_firstvaluesquarefreedomain = 1 \/ pvs_right_unique_firstvaluesquarefreedomain = 1) -> (exists pvs_le_gap_unique_firstvaluesquarefreebound. pvs_le_gap_unique_firstvaluesquarefreebound + (sfd_prime_unique_firstvaluesquarefree) = (mt_index_unique_first)) -> ~(exists pvs_factor_unique_firstvaluesquarefreesquare. (mt_index_unique_first) = (sfd_prime_unique_firstvaluesquarefree * sfd_prime_unique_firstvaluesquarefree) * pvs_factor_unique_firstvaluesquarefreesquare)))) /\ (exists mv_factor_code_unique_firstvaluefactors mv_factor_scale_unique_firstvaluefactors mv_factor_count_unique_firstvaluefactors. (((~(mt_index_unique_first = 0) /\ ((exists ff_u_fsat_unique_firstvaluefactorsfactorization_product ff_v_fsat_unique_firstvaluefactorsfactorization_product. ((((exists ff_h_fsat_unique_firstvaluefactorsfactorization_product_start. ff_h_fsat_unique_firstvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_firstvaluefactorsfactorization_product_start. ff_u_fsat_unique_firstvaluefactorsfactorization_product = ff_q_fsat_unique_firstvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_unique_firstvaluefactorsfactorization_product_terminal. ff_h_fsat_unique_firstvaluefactorsfactorization_product_terminal + S (mt_index_unique_first) = S ((S (mv_factor_count_unique_firstvaluefactors)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_firstvaluefactorsfactorization_product_terminal. ff_u_fsat_unique_firstvaluefactorsfactorization_product = ff_q_fsat_unique_firstvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_unique_firstvaluefactors)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product) + (mt_index_unique_first))) /\ forall ff_i_fsat_unique_firstvaluefactorsfactorization_product. (exists ff_lt_fsat_unique_firstvaluefactorsfactorization_product_bound. ff_lt_fsat_unique_firstvaluefactorsfactorization_product_bound + S ff_i_fsat_unique_firstvaluefactorsfactorization_product = mv_factor_count_unique_firstvaluefactors) -> exists ff_p_fsat_unique_firstvaluefactorsfactorization_product ff_r_fsat_unique_firstvaluefactorsfactorization_product ff_s_fsat_unique_firstvaluefactorsfactorization_product. ((((exists ff_h_fsat_unique_firstvaluefactorsfactorization_product_factor. ff_h_fsat_unique_firstvaluefactorsfactorization_product_factor + S (ff_p_fsat_unique_firstvaluefactorsfactorization_product) = S ((S (ff_i_fsat_unique_firstvaluefactorsfactorization_product)) * mv_factor_scale_unique_firstvaluefactors)) /\ exists ff_q_fsat_unique_firstvaluefactorsfactorization_product_factor. mv_factor_code_unique_firstvaluefactors = ff_q_fsat_unique_firstvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_unique_firstvaluefactorsfactorization_product)) * mv_factor_scale_unique_firstvaluefactors) + (ff_p_fsat_unique_firstvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unique_firstvaluefactorsfactorization_product_partial. ff_h_fsat_unique_firstvaluefactorsfactorization_product_partial + S (ff_r_fsat_unique_firstvaluefactorsfactorization_product) = S ((S (ff_i_fsat_unique_firstvaluefactorsfactorization_product)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_firstvaluefactorsfactorization_product_partial. ff_u_fsat_unique_firstvaluefactorsfactorization_product = ff_q_fsat_unique_firstvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_unique_firstvaluefactorsfactorization_product)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product) + (ff_r_fsat_unique_firstvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unique_firstvaluefactorsfactorization_product_successor. ff_h_fsat_unique_firstvaluefactorsfactorization_product_successor + S (ff_s_fsat_unique_firstvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_unique_firstvaluefactorsfactorization_product)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_firstvaluefactorsfactorization_product_successor. ff_u_fsat_unique_firstvaluefactorsfactorization_product = ff_q_fsat_unique_firstvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_unique_firstvaluefactorsfactorization_product)) * ff_v_fsat_unique_firstvaluefactorsfactorization_product) + (ff_s_fsat_unique_firstvaluefactorsfactorization_product))) /\ ff_s_fsat_unique_firstvaluefactorsfactorization_product = ff_r_fsat_unique_firstvaluefactorsfactorization_product * ff_p_fsat_unique_firstvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_unique_firstvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_unique_firstvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_unique_firstvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_unique_firstvaluefactorsfactorization_primes = (mv_factor_count_unique_firstvaluefactors)) -> exists ftsf_factor_fsat_unique_firstvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_unique_firstvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_unique_firstvaluefactorsfactorization_primes)) * mv_factor_scale_unique_firstvaluefactors)) /\ exists ff_q_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_entry. mv_factor_code_unique_firstvaluefactors = ff_q_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_unique_firstvaluefactorsfactorization_primes)) * mv_factor_scale_unique_firstvaluefactors) + (ftsf_factor_fsat_unique_firstvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_unique_firstvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_unique_firstvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_unique_firstvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_unique_firstvaluefactorsparityeven. (mv_factor_count_unique_firstvaluefactors) = 2 * mv_even_half_unique_firstvaluefactorsparityeven) /\ ((mt_value_unique_first) = 2))) \/ (((exists mv_odd_half_unique_firstvaluefactorsparityodd. (mv_factor_count_unique_firstvaluefactors) = 2 * mv_odd_half_unique_firstvaluefactorsparityodd + 1) /\ ((mt_value_unique_first) = 1)))))))))))))))) -> (((exists dst_positive_code_unique_secondtable dst_positive_scale_unique_secondtable dst_negative_code_unique_secondtable dst_negative_scale_unique_secondtable. (((G) = (((((dst_positive_code_unique_secondtable) + (dst_positive_scale_unique_secondtable)) * S ((dst_positive_code_unique_secondtable) + (dst_positive_scale_unique_secondtable)) + ((dst_positive_scale_unique_secondtable) + (dst_positive_scale_unique_secondtable))) + (((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) * S ((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) + ((dst_negative_scale_unique_secondtable) + (dst_negative_scale_unique_secondtable)))) * S ((((dst_positive_code_unique_secondtable) + (dst_positive_scale_unique_secondtable)) * S ((dst_positive_code_unique_secondtable) + (dst_positive_scale_unique_secondtable)) + ((dst_positive_scale_unique_secondtable) + (dst_positive_scale_unique_secondtable))) + (((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) * S ((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) + ((dst_negative_scale_unique_secondtable) + (dst_negative_scale_unique_secondtable)))) + ((((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) * S ((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) + ((dst_negative_scale_unique_secondtable) + (dst_negative_scale_unique_secondtable))) + (((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) * S ((dst_negative_code_unique_secondtable) + (dst_negative_scale_unique_secondtable)) + ((dst_negative_scale_unique_secondtable) + (dst_negative_scale_unique_secondtable)))))) /\ (forall dst_index_unique_secondtable. (exists pvs_le_gap_unique_secondtabledomain. pvs_le_gap_unique_secondtabledomain + (dst_index_unique_secondtable) = (N)) -> exists dst_positive_unique_secondtable dst_negative_unique_secondtable dst_value_unique_secondtable. ((((exists ff_h_pvs_unique_secondtableentrypositive. ff_h_pvs_unique_secondtableentrypositive + S (dst_positive_unique_secondtable) = S ((S (dst_index_unique_secondtable)) * dst_positive_scale_unique_secondtable)) /\ exists ff_q_pvs_unique_secondtableentrypositive. dst_positive_code_unique_secondtable = ff_q_pvs_unique_secondtableentrypositive * S ((S (dst_index_unique_secondtable)) * dst_positive_scale_unique_secondtable) + (dst_positive_unique_secondtable))) /\ (((((exists ff_h_pvs_unique_secondtableentrynegative. ff_h_pvs_unique_secondtableentrynegative + S (dst_negative_unique_secondtable) = S ((S (dst_index_unique_secondtable)) * dst_negative_scale_unique_secondtable)) /\ exists ff_q_pvs_unique_secondtableentrynegative. dst_negative_code_unique_secondtable = ff_q_pvs_unique_secondtableentrynegative * S ((S (dst_index_unique_secondtable)) * dst_negative_scale_unique_secondtable) + (dst_negative_unique_secondtable))) /\ (exists ge_balance_positive_unique_secondtableentryvalue ge_balance_negative_unique_secondtableentryvalue. (((((dst_value_unique_secondtable) = 2 * (ge_balance_positive_unique_secondtableentryvalue) /\ (ge_balance_negative_unique_secondtableentryvalue) = 0) \/ exists ge_signed_half_unique_secondtableentryvaluedecode. (((dst_value_unique_secondtable) = 2 * ge_signed_half_unique_secondtableentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondtableentryvalue) = 0) /\ (ge_balance_negative_unique_secondtableentryvalue) = S ge_signed_half_unique_secondtableentryvaluedecode))) /\ ((dst_positive_unique_secondtable) + ge_balance_negative_unique_secondtableentryvalue = (dst_negative_unique_secondtable) + ge_balance_positive_unique_secondtableentryvalue))))))))) /\ (((exists dst_positive_code_unique_secondzero dst_positive_scale_unique_secondzero dst_negative_code_unique_secondzero dst_negative_scale_unique_secondzero dst_positive_unique_secondzero dst_negative_unique_secondzero. (((G) = (((((dst_positive_code_unique_secondzero) + (dst_positive_scale_unique_secondzero)) * S ((dst_positive_code_unique_secondzero) + (dst_positive_scale_unique_secondzero)) + ((dst_positive_scale_unique_secondzero) + (dst_positive_scale_unique_secondzero))) + (((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) * S ((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) + ((dst_negative_scale_unique_secondzero) + (dst_negative_scale_unique_secondzero)))) * S ((((dst_positive_code_unique_secondzero) + (dst_positive_scale_unique_secondzero)) * S ((dst_positive_code_unique_secondzero) + (dst_positive_scale_unique_secondzero)) + ((dst_positive_scale_unique_secondzero) + (dst_positive_scale_unique_secondzero))) + (((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) * S ((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) + ((dst_negative_scale_unique_secondzero) + (dst_negative_scale_unique_secondzero)))) + ((((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) * S ((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) + ((dst_negative_scale_unique_secondzero) + (dst_negative_scale_unique_secondzero))) + (((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) * S ((dst_negative_code_unique_secondzero) + (dst_negative_scale_unique_secondzero)) + ((dst_negative_scale_unique_secondzero) + (dst_negative_scale_unique_secondzero)))))) /\ (((((exists ff_h_pvs_unique_secondzeropositive. ff_h_pvs_unique_secondzeropositive + S (dst_positive_unique_secondzero) = S ((S (0)) * dst_positive_scale_unique_secondzero)) /\ exists ff_q_pvs_unique_secondzeropositive. dst_positive_code_unique_secondzero = ff_q_pvs_unique_secondzeropositive * S ((S (0)) * dst_positive_scale_unique_secondzero) + (dst_positive_unique_secondzero))) /\ (((((exists ff_h_pvs_unique_secondzeronegative. ff_h_pvs_unique_secondzeronegative + S (dst_negative_unique_secondzero) = S ((S (0)) * dst_negative_scale_unique_secondzero)) /\ exists ff_q_pvs_unique_secondzeronegative. dst_negative_code_unique_secondzero = ff_q_pvs_unique_secondzeronegative * S ((S (0)) * dst_negative_scale_unique_secondzero) + (dst_negative_unique_secondzero))) /\ (exists ge_balance_positive_unique_secondzerovalue ge_balance_negative_unique_secondzerovalue. (((((0) = 2 * (ge_balance_positive_unique_secondzerovalue) /\ (ge_balance_negative_unique_secondzerovalue) = 0) \/ exists ge_signed_half_unique_secondzerovaluedecode. (((0) = 2 * ge_signed_half_unique_secondzerovaluedecode + 1 /\ (ge_balance_positive_unique_secondzerovalue) = 0) /\ (ge_balance_negative_unique_secondzerovalue) = S ge_signed_half_unique_secondzerovaluedecode))) /\ ((dst_positive_unique_secondzero) + ge_balance_negative_unique_secondzerovalue = (dst_negative_unique_secondzero) + ge_balance_positive_unique_secondzerovalue))))))))) /\ (forall mt_index_unique_second mt_value_unique_second. ~(mt_index_unique_second=0) -> (exists pvs_le_gap_unique_seconddomain. pvs_le_gap_unique_seconddomain + (mt_index_unique_second) = (N)) -> (exists dst_positive_code_unique_secondentry dst_positive_scale_unique_secondentry dst_negative_code_unique_secondentry dst_negative_scale_unique_secondentry dst_positive_unique_secondentry dst_negative_unique_secondentry. (((G) = (((((dst_positive_code_unique_secondentry) + (dst_positive_scale_unique_secondentry)) * S ((dst_positive_code_unique_secondentry) + (dst_positive_scale_unique_secondentry)) + ((dst_positive_scale_unique_secondentry) + (dst_positive_scale_unique_secondentry))) + (((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) * S ((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) + ((dst_negative_scale_unique_secondentry) + (dst_negative_scale_unique_secondentry)))) * S ((((dst_positive_code_unique_secondentry) + (dst_positive_scale_unique_secondentry)) * S ((dst_positive_code_unique_secondentry) + (dst_positive_scale_unique_secondentry)) + ((dst_positive_scale_unique_secondentry) + (dst_positive_scale_unique_secondentry))) + (((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) * S ((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) + ((dst_negative_scale_unique_secondentry) + (dst_negative_scale_unique_secondentry)))) + ((((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) * S ((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) + ((dst_negative_scale_unique_secondentry) + (dst_negative_scale_unique_secondentry))) + (((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) * S ((dst_negative_code_unique_secondentry) + (dst_negative_scale_unique_secondentry)) + ((dst_negative_scale_unique_secondentry) + (dst_negative_scale_unique_secondentry)))))) /\ (((((exists ff_h_pvs_unique_secondentrypositive. ff_h_pvs_unique_secondentrypositive + S (dst_positive_unique_secondentry) = S ((S (mt_index_unique_second)) * dst_positive_scale_unique_secondentry)) /\ exists ff_q_pvs_unique_secondentrypositive. dst_positive_code_unique_secondentry = ff_q_pvs_unique_secondentrypositive * S ((S (mt_index_unique_second)) * dst_positive_scale_unique_secondentry) + (dst_positive_unique_secondentry))) /\ (((((exists ff_h_pvs_unique_secondentrynegative. ff_h_pvs_unique_secondentrynegative + S (dst_negative_unique_secondentry) = S ((S (mt_index_unique_second)) * dst_negative_scale_unique_secondentry)) /\ exists ff_q_pvs_unique_secondentrynegative. dst_negative_code_unique_secondentry = ff_q_pvs_unique_secondentrynegative * S ((S (mt_index_unique_second)) * dst_negative_scale_unique_secondentry) + (dst_negative_unique_secondentry))) /\ (exists ge_balance_positive_unique_secondentryvalue ge_balance_negative_unique_secondentryvalue. (((((mt_value_unique_second) = 2 * (ge_balance_positive_unique_secondentryvalue) /\ (ge_balance_negative_unique_secondentryvalue) = 0) \/ exists ge_signed_half_unique_secondentryvaluedecode. (((mt_value_unique_second) = 2 * ge_signed_half_unique_secondentryvaluedecode + 1 /\ (ge_balance_positive_unique_secondentryvalue) = 0) /\ (ge_balance_negative_unique_secondentryvalue) = S ge_signed_half_unique_secondentryvaluedecode))) /\ ((dst_positive_unique_secondentry) + ge_balance_negative_unique_secondentryvalue = (dst_negative_unique_secondentry) + ge_balance_positive_unique_secondentryvalue))))))))) -> (((~((mt_index_unique_second) = 0)) /\ ((((exists mv_square_prime_unique_secondvaluesquare. ((~((mv_square_prime_unique_secondvaluesquare) = 1) /\ forall pvs_left_unique_secondvaluesquareprime pvs_right_unique_secondvaluesquareprime. (mv_square_prime_unique_secondvaluesquare) = pvs_left_unique_secondvaluesquareprime * pvs_right_unique_secondvaluesquareprime -> pvs_left_unique_secondvaluesquareprime = 1 \/ pvs_right_unique_secondvaluesquareprime = 1) /\ (exists pvs_factor_unique_secondvaluesquaredivisor. (mt_index_unique_second) = (mv_square_prime_unique_secondvaluesquare * mv_square_prime_unique_secondvaluesquare) * pvs_factor_unique_secondvaluesquaredivisor))) /\ ((mt_value_unique_second) = 0))) \/ (((((~((mt_index_unique_second) = 0)) /\ (forall sfd_prime_unique_secondvaluesquarefree. (~((sfd_prime_unique_secondvaluesquarefree) = 1) /\ forall pvs_left_unique_secondvaluesquarefreedomain pvs_right_unique_secondvaluesquarefreedomain. (sfd_prime_unique_secondvaluesquarefree) = pvs_left_unique_secondvaluesquarefreedomain * pvs_right_unique_secondvaluesquarefreedomain -> pvs_left_unique_secondvaluesquarefreedomain = 1 \/ pvs_right_unique_secondvaluesquarefreedomain = 1) -> (exists pvs_le_gap_unique_secondvaluesquarefreebound. pvs_le_gap_unique_secondvaluesquarefreebound + (sfd_prime_unique_secondvaluesquarefree) = (mt_index_unique_second)) -> ~(exists pvs_factor_unique_secondvaluesquarefreesquare. (mt_index_unique_second) = (sfd_prime_unique_secondvaluesquarefree * sfd_prime_unique_secondvaluesquarefree) * pvs_factor_unique_secondvaluesquarefreesquare)))) /\ (exists mv_factor_code_unique_secondvaluefactors mv_factor_scale_unique_secondvaluefactors mv_factor_count_unique_secondvaluefactors. (((~(mt_index_unique_second = 0) /\ ((exists ff_u_fsat_unique_secondvaluefactorsfactorization_product ff_v_fsat_unique_secondvaluefactorsfactorization_product. ((((exists ff_h_fsat_unique_secondvaluefactorsfactorization_product_start. ff_h_fsat_unique_secondvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_secondvaluefactorsfactorization_product_start. ff_u_fsat_unique_secondvaluefactorsfactorization_product = ff_q_fsat_unique_secondvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_unique_secondvaluefactorsfactorization_product_terminal. ff_h_fsat_unique_secondvaluefactorsfactorization_product_terminal + S (mt_index_unique_second) = S ((S (mv_factor_count_unique_secondvaluefactors)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_secondvaluefactorsfactorization_product_terminal. ff_u_fsat_unique_secondvaluefactorsfactorization_product = ff_q_fsat_unique_secondvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_unique_secondvaluefactors)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product) + (mt_index_unique_second))) /\ forall ff_i_fsat_unique_secondvaluefactorsfactorization_product. (exists ff_lt_fsat_unique_secondvaluefactorsfactorization_product_bound. ff_lt_fsat_unique_secondvaluefactorsfactorization_product_bound + S ff_i_fsat_unique_secondvaluefactorsfactorization_product = mv_factor_count_unique_secondvaluefactors) -> exists ff_p_fsat_unique_secondvaluefactorsfactorization_product ff_r_fsat_unique_secondvaluefactorsfactorization_product ff_s_fsat_unique_secondvaluefactorsfactorization_product. ((((exists ff_h_fsat_unique_secondvaluefactorsfactorization_product_factor. ff_h_fsat_unique_secondvaluefactorsfactorization_product_factor + S (ff_p_fsat_unique_secondvaluefactorsfactorization_product) = S ((S (ff_i_fsat_unique_secondvaluefactorsfactorization_product)) * mv_factor_scale_unique_secondvaluefactors)) /\ exists ff_q_fsat_unique_secondvaluefactorsfactorization_product_factor. mv_factor_code_unique_secondvaluefactors = ff_q_fsat_unique_secondvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_unique_secondvaluefactorsfactorization_product)) * mv_factor_scale_unique_secondvaluefactors) + (ff_p_fsat_unique_secondvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unique_secondvaluefactorsfactorization_product_partial. ff_h_fsat_unique_secondvaluefactorsfactorization_product_partial + S (ff_r_fsat_unique_secondvaluefactorsfactorization_product) = S ((S (ff_i_fsat_unique_secondvaluefactorsfactorization_product)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_secondvaluefactorsfactorization_product_partial. ff_u_fsat_unique_secondvaluefactorsfactorization_product = ff_q_fsat_unique_secondvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_unique_secondvaluefactorsfactorization_product)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product) + (ff_r_fsat_unique_secondvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unique_secondvaluefactorsfactorization_product_successor. ff_h_fsat_unique_secondvaluefactorsfactorization_product_successor + S (ff_s_fsat_unique_secondvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_unique_secondvaluefactorsfactorization_product)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product)) /\ exists ff_q_fsat_unique_secondvaluefactorsfactorization_product_successor. ff_u_fsat_unique_secondvaluefactorsfactorization_product = ff_q_fsat_unique_secondvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_unique_secondvaluefactorsfactorization_product)) * ff_v_fsat_unique_secondvaluefactorsfactorization_product) + (ff_s_fsat_unique_secondvaluefactorsfactorization_product))) /\ ff_s_fsat_unique_secondvaluefactorsfactorization_product = ff_r_fsat_unique_secondvaluefactorsfactorization_product * ff_p_fsat_unique_secondvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_unique_secondvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_unique_secondvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_unique_secondvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_unique_secondvaluefactorsfactorization_primes = (mv_factor_count_unique_secondvaluefactors)) -> exists ftsf_factor_fsat_unique_secondvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_unique_secondvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_unique_secondvaluefactorsfactorization_primes)) * mv_factor_scale_unique_secondvaluefactors)) /\ exists ff_q_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_entry. mv_factor_code_unique_secondvaluefactors = ff_q_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_unique_secondvaluefactorsfactorization_primes)) * mv_factor_scale_unique_secondvaluefactors) + (ftsf_factor_fsat_unique_secondvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_unique_secondvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_unique_secondvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_unique_secondvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_unique_secondvaluefactorsparityeven. (mv_factor_count_unique_secondvaluefactors) = 2 * mv_even_half_unique_secondvaluefactorsparityeven) /\ ((mt_value_unique_second) = 2))) \/ (((exists mv_odd_half_unique_secondvaluefactorsparityodd. (mv_factor_count_unique_secondvaluefactors) = 2 * mv_odd_half_unique_secondvaluefactorsparityodd + 1) /\ ((mt_value_unique_second) = 1)))))))))))))))) -> (forall dst_index_unique_values dst_first_unique_values dst_second_unique_values. (exists pvs_gap_unique_valuesbound. pvs_gap_unique_valuesbound + S (dst_index_unique_values) = (S N)) -> (exists dst_positive_code_unique_valuesfirst dst_positive_scale_unique_valuesfirst dst_negative_code_unique_valuesfirst dst_negative_scale_unique_valuesfirst dst_positive_unique_valuesfirst dst_negative_unique_valuesfirst. (((F) = (((((dst_positive_code_unique_valuesfirst) + (dst_positive_scale_unique_valuesfirst)) * S ((dst_positive_code_unique_valuesfirst) + (dst_positive_scale_unique_valuesfirst)) + ((dst_positive_scale_unique_valuesfirst) + (dst_positive_scale_unique_valuesfirst))) + (((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) * S ((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) + ((dst_negative_scale_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)))) * S ((((dst_positive_code_unique_valuesfirst) + (dst_positive_scale_unique_valuesfirst)) * S ((dst_positive_code_unique_valuesfirst) + (dst_positive_scale_unique_valuesfirst)) + ((dst_positive_scale_unique_valuesfirst) + (dst_positive_scale_unique_valuesfirst))) + (((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) * S ((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) + ((dst_negative_scale_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)))) + ((((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) * S ((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) + ((dst_negative_scale_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst))) + (((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) * S ((dst_negative_code_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)) + ((dst_negative_scale_unique_valuesfirst) + (dst_negative_scale_unique_valuesfirst)))))) /\ (((((exists ff_h_pvs_unique_valuesfirstpositive. ff_h_pvs_unique_valuesfirstpositive + S (dst_positive_unique_valuesfirst) = S ((S (dst_index_unique_values)) * dst_positive_scale_unique_valuesfirst)) /\ exists ff_q_pvs_unique_valuesfirstpositive. dst_positive_code_unique_valuesfirst = ff_q_pvs_unique_valuesfirstpositive * S ((S (dst_index_unique_values)) * dst_positive_scale_unique_valuesfirst) + (dst_positive_unique_valuesfirst))) /\ (((((exists ff_h_pvs_unique_valuesfirstnegative. ff_h_pvs_unique_valuesfirstnegative + S (dst_negative_unique_valuesfirst) = S ((S (dst_index_unique_values)) * dst_negative_scale_unique_valuesfirst)) /\ exists ff_q_pvs_unique_valuesfirstnegative. dst_negative_code_unique_valuesfirst = ff_q_pvs_unique_valuesfirstnegative * S ((S (dst_index_unique_values)) * dst_negative_scale_unique_valuesfirst) + (dst_negative_unique_valuesfirst))) /\ (exists ge_balance_positive_unique_valuesfirstvalue ge_balance_negative_unique_valuesfirstvalue. (((((dst_first_unique_values) = 2 * (ge_balance_positive_unique_valuesfirstvalue) /\ (ge_balance_negative_unique_valuesfirstvalue) = 0) \/ exists ge_signed_half_unique_valuesfirstvaluedecode. (((dst_first_unique_values) = 2 * ge_signed_half_unique_valuesfirstvaluedecode + 1 /\ (ge_balance_positive_unique_valuesfirstvalue) = 0) /\ (ge_balance_negative_unique_valuesfirstvalue) = S ge_signed_half_unique_valuesfirstvaluedecode))) /\ ((dst_positive_unique_valuesfirst) + ge_balance_negative_unique_valuesfirstvalue = (dst_negative_unique_valuesfirst) + ge_balance_positive_unique_valuesfirstvalue))))))))) -> (exists dst_positive_code_unique_valuessecond dst_positive_scale_unique_valuessecond dst_negative_code_unique_valuessecond dst_negative_scale_unique_valuessecond dst_positive_unique_valuessecond dst_negative_unique_valuessecond. (((G) = (((((dst_positive_code_unique_valuessecond) + (dst_positive_scale_unique_valuessecond)) * S ((dst_positive_code_unique_valuessecond) + (dst_positive_scale_unique_valuessecond)) + ((dst_positive_scale_unique_valuessecond) + (dst_positive_scale_unique_valuessecond))) + (((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) * S ((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) + ((dst_negative_scale_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)))) * S ((((dst_positive_code_unique_valuessecond) + (dst_positive_scale_unique_valuessecond)) * S ((dst_positive_code_unique_valuessecond) + (dst_positive_scale_unique_valuessecond)) + ((dst_positive_scale_unique_valuessecond) + (dst_positive_scale_unique_valuessecond))) + (((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) * S ((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) + ((dst_negative_scale_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)))) + ((((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) * S ((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) + ((dst_negative_scale_unique_valuessecond) + (dst_negative_scale_unique_valuessecond))) + (((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) * S ((dst_negative_code_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)) + ((dst_negative_scale_unique_valuessecond) + (dst_negative_scale_unique_valuessecond)))))) /\ (((((exists ff_h_pvs_unique_valuessecondpositive. ff_h_pvs_unique_valuessecondpositive + S (dst_positive_unique_valuessecond) = S ((S (dst_index_unique_values)) * dst_positive_scale_unique_valuessecond)) /\ exists ff_q_pvs_unique_valuessecondpositive. dst_positive_code_unique_valuessecond = ff_q_pvs_unique_valuessecondpositive * S ((S (dst_index_unique_values)) * dst_positive_scale_unique_valuessecond) + (dst_positive_unique_valuessecond))) /\ (((((exists ff_h_pvs_unique_valuessecondnegative. ff_h_pvs_unique_valuessecondnegative + S (dst_negative_unique_valuessecond) = S ((S (dst_index_unique_values)) * dst_negative_scale_unique_valuessecond)) /\ exists ff_q_pvs_unique_valuessecondnegative. dst_negative_code_unique_valuessecond = ff_q_pvs_unique_valuessecondnegative * S ((S (dst_index_unique_values)) * dst_negative_scale_unique_valuessecond) + (dst_negative_unique_valuessecond))) /\ (exists ge_balance_positive_unique_valuessecondvalue ge_balance_negative_unique_valuessecondvalue. (((((dst_second_unique_values) = 2 * (ge_balance_positive_unique_valuessecondvalue) /\ (ge_balance_negative_unique_valuessecondvalue) = 0) \/ exists ge_signed_half_unique_valuessecondvaluedecode. (((dst_second_unique_values) = 2 * ge_signed_half_unique_valuessecondvaluedecode + 1 /\ (ge_balance_positive_unique_valuessecondvalue) = 0) /\ (ge_balance_negative_unique_valuessecondvalue) = S ge_signed_half_unique_valuessecondvaluedecode))) /\ ((dst_positive_unique_valuessecond) + ge_balance_negative_unique_valuessecondvalue = (dst_negative_unique_valuessecond) + ge_balance_positive_unique_valuessecondvalue))))))))) -> dst_first_unique_values = dst_second_unique_values)

mobius_table_restrict

new owned theorem · read exact theorem evidence

Bundle node 291; exact statement SHA-256 a3d52063c215b69147b5d062ca368efd30b92d75d97c4b4d18cc8a5b8239db8f

Exact first-order statement

forall N K M. (((exists dst_positive_code_restrict_sourcetable dst_positive_scale_restrict_sourcetable dst_negative_code_restrict_sourcetable dst_negative_scale_restrict_sourcetable. (((M) = (((((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) * S ((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) + ((dst_positive_scale_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable))) + (((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)))) * S ((((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) * S ((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) + ((dst_positive_scale_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable))) + (((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)))) + ((((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable))) + (((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)))))) /\ (forall dst_index_restrict_sourcetable. (exists pvs_le_gap_restrict_sourcetabledomain. pvs_le_gap_restrict_sourcetabledomain + (dst_index_restrict_sourcetable) = (N)) -> exists dst_positive_restrict_sourcetable dst_negative_restrict_sourcetable dst_value_restrict_sourcetable. ((((exists ff_h_pvs_restrict_sourcetableentrypositive. ff_h_pvs_restrict_sourcetableentrypositive + S (dst_positive_restrict_sourcetable) = S ((S (dst_index_restrict_sourcetable)) * dst_positive_scale_restrict_sourcetable)) /\ exists ff_q_pvs_restrict_sourcetableentrypositive. dst_positive_code_restrict_sourcetable = ff_q_pvs_restrict_sourcetableentrypositive * S ((S (dst_index_restrict_sourcetable)) * dst_positive_scale_restrict_sourcetable) + (dst_positive_restrict_sourcetable))) /\ (((((exists ff_h_pvs_restrict_sourcetableentrynegative. ff_h_pvs_restrict_sourcetableentrynegative + S (dst_negative_restrict_sourcetable) = S ((S (dst_index_restrict_sourcetable)) * dst_negative_scale_restrict_sourcetable)) /\ exists ff_q_pvs_restrict_sourcetableentrynegative. dst_negative_code_restrict_sourcetable = ff_q_pvs_restrict_sourcetableentrynegative * S ((S (dst_index_restrict_sourcetable)) * dst_negative_scale_restrict_sourcetable) + (dst_negative_restrict_sourcetable))) /\ (exists ge_balance_positive_restrict_sourcetableentryvalue ge_balance_negative_restrict_sourcetableentryvalue. (((((dst_value_restrict_sourcetable) = 2 * (ge_balance_positive_restrict_sourcetableentryvalue) /\ (ge_balance_negative_restrict_sourcetableentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcetableentryvaluedecode. (((dst_value_restrict_sourcetable) = 2 * ge_signed_half_restrict_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcetableentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcetableentryvalue) = S ge_signed_half_restrict_sourcetableentryvaluedecode))) /\ ((dst_positive_restrict_sourcetable) + ge_balance_negative_restrict_sourcetableentryvalue = (dst_negative_restrict_sourcetable) + ge_balance_positive_restrict_sourcetableentryvalue))))))))) /\ (((exists dst_positive_code_restrict_sourcezero dst_positive_scale_restrict_sourcezero dst_negative_code_restrict_sourcezero dst_negative_scale_restrict_sourcezero dst_positive_restrict_sourcezero dst_negative_restrict_sourcezero. (((M) = (((((dst_positive_code_restrict_sourcezero) + (dst_positive_scale_restrict_sourcezero)) * S ((dst_positive_code_restrict_sourcezero) + (dst_positive_scale_restrict_sourcezero)) + ((dst_positive_scale_restrict_sourcezero) + (dst_positive_scale_restrict_sourcezero))) + (((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) * S ((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) + ((dst_negative_scale_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)))) * S ((((dst_positive_code_restrict_sourcezero) + (dst_positive_scale_restrict_sourcezero)) * S ((dst_positive_code_restrict_sourcezero) + (dst_positive_scale_restrict_sourcezero)) + ((dst_positive_scale_restrict_sourcezero) + (dst_positive_scale_restrict_sourcezero))) + (((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) * S ((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) + ((dst_negative_scale_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)))) + ((((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) * S ((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) + ((dst_negative_scale_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero))) + (((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) * S ((dst_negative_code_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)) + ((dst_negative_scale_restrict_sourcezero) + (dst_negative_scale_restrict_sourcezero)))))) /\ (((((exists ff_h_pvs_restrict_sourcezeropositive. ff_h_pvs_restrict_sourcezeropositive + S (dst_positive_restrict_sourcezero) = S ((S (0)) * dst_positive_scale_restrict_sourcezero)) /\ exists ff_q_pvs_restrict_sourcezeropositive. dst_positive_code_restrict_sourcezero = ff_q_pvs_restrict_sourcezeropositive * S ((S (0)) * dst_positive_scale_restrict_sourcezero) + (dst_positive_restrict_sourcezero))) /\ (((((exists ff_h_pvs_restrict_sourcezeronegative. ff_h_pvs_restrict_sourcezeronegative + S (dst_negative_restrict_sourcezero) = S ((S (0)) * dst_negative_scale_restrict_sourcezero)) /\ exists ff_q_pvs_restrict_sourcezeronegative. dst_negative_code_restrict_sourcezero = ff_q_pvs_restrict_sourcezeronegative * S ((S (0)) * dst_negative_scale_restrict_sourcezero) + (dst_negative_restrict_sourcezero))) /\ (exists ge_balance_positive_restrict_sourcezerovalue ge_balance_negative_restrict_sourcezerovalue. (((((0) = 2 * (ge_balance_positive_restrict_sourcezerovalue) /\ (ge_balance_negative_restrict_sourcezerovalue) = 0) \/ exists ge_signed_half_restrict_sourcezerovaluedecode. (((0) = 2 * ge_signed_half_restrict_sourcezerovaluedecode + 1 /\ (ge_balance_positive_restrict_sourcezerovalue) = 0) /\ (ge_balance_negative_restrict_sourcezerovalue) = S ge_signed_half_restrict_sourcezerovaluedecode))) /\ ((dst_positive_restrict_sourcezero) + ge_balance_negative_restrict_sourcezerovalue = (dst_negative_restrict_sourcezero) + ge_balance_positive_restrict_sourcezerovalue))))))))) /\ (forall mt_index_restrict_source mt_value_restrict_source. ~(mt_index_restrict_source=0) -> (exists pvs_le_gap_restrict_sourcedomain. pvs_le_gap_restrict_sourcedomain + (mt_index_restrict_source) = (N)) -> (exists dst_positive_code_restrict_sourceentry dst_positive_scale_restrict_sourceentry dst_negative_code_restrict_sourceentry dst_negative_scale_restrict_sourceentry dst_positive_restrict_sourceentry dst_negative_restrict_sourceentry. (((M) = (((((dst_positive_code_restrict_sourceentry) + (dst_positive_scale_restrict_sourceentry)) * S ((dst_positive_code_restrict_sourceentry) + (dst_positive_scale_restrict_sourceentry)) + ((dst_positive_scale_restrict_sourceentry) + (dst_positive_scale_restrict_sourceentry))) + (((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) * S ((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) + ((dst_negative_scale_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)))) * S ((((dst_positive_code_restrict_sourceentry) + (dst_positive_scale_restrict_sourceentry)) * S ((dst_positive_code_restrict_sourceentry) + (dst_positive_scale_restrict_sourceentry)) + ((dst_positive_scale_restrict_sourceentry) + (dst_positive_scale_restrict_sourceentry))) + (((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) * S ((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) + ((dst_negative_scale_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)))) + ((((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) * S ((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) + ((dst_negative_scale_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry))) + (((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) * S ((dst_negative_code_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)) + ((dst_negative_scale_restrict_sourceentry) + (dst_negative_scale_restrict_sourceentry)))))) /\ (((((exists ff_h_pvs_restrict_sourceentrypositive. ff_h_pvs_restrict_sourceentrypositive + S (dst_positive_restrict_sourceentry) = S ((S (mt_index_restrict_source)) * dst_positive_scale_restrict_sourceentry)) /\ exists ff_q_pvs_restrict_sourceentrypositive. dst_positive_code_restrict_sourceentry = ff_q_pvs_restrict_sourceentrypositive * S ((S (mt_index_restrict_source)) * dst_positive_scale_restrict_sourceentry) + (dst_positive_restrict_sourceentry))) /\ (((((exists ff_h_pvs_restrict_sourceentrynegative. ff_h_pvs_restrict_sourceentrynegative + S (dst_negative_restrict_sourceentry) = S ((S (mt_index_restrict_source)) * dst_negative_scale_restrict_sourceentry)) /\ exists ff_q_pvs_restrict_sourceentrynegative. dst_negative_code_restrict_sourceentry = ff_q_pvs_restrict_sourceentrynegative * S ((S (mt_index_restrict_source)) * dst_negative_scale_restrict_sourceentry) + (dst_negative_restrict_sourceentry))) /\ (exists ge_balance_positive_restrict_sourceentryvalue ge_balance_negative_restrict_sourceentryvalue. (((((mt_value_restrict_source) = 2 * (ge_balance_positive_restrict_sourceentryvalue) /\ (ge_balance_negative_restrict_sourceentryvalue) = 0) \/ exists ge_signed_half_restrict_sourceentryvaluedecode. (((mt_value_restrict_source) = 2 * ge_signed_half_restrict_sourceentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourceentryvalue) = 0) /\ (ge_balance_negative_restrict_sourceentryvalue) = S ge_signed_half_restrict_sourceentryvaluedecode))) /\ ((dst_positive_restrict_sourceentry) + ge_balance_negative_restrict_sourceentryvalue = (dst_negative_restrict_sourceentry) + ge_balance_positive_restrict_sourceentryvalue))))))))) -> (((~((mt_index_restrict_source) = 0)) /\ ((((exists mv_square_prime_restrict_sourcevaluesquare. ((~((mv_square_prime_restrict_sourcevaluesquare) = 1) /\ forall pvs_left_restrict_sourcevaluesquareprime pvs_right_restrict_sourcevaluesquareprime. (mv_square_prime_restrict_sourcevaluesquare) = pvs_left_restrict_sourcevaluesquareprime * pvs_right_restrict_sourcevaluesquareprime -> pvs_left_restrict_sourcevaluesquareprime = 1 \/ pvs_right_restrict_sourcevaluesquareprime = 1) /\ (exists pvs_factor_restrict_sourcevaluesquaredivisor. (mt_index_restrict_source) = (mv_square_prime_restrict_sourcevaluesquare * mv_square_prime_restrict_sourcevaluesquare) * pvs_factor_restrict_sourcevaluesquaredivisor))) /\ ((mt_value_restrict_source) = 0))) \/ (((((~((mt_index_restrict_source) = 0)) /\ (forall sfd_prime_restrict_sourcevaluesquarefree. (~((sfd_prime_restrict_sourcevaluesquarefree) = 1) /\ forall pvs_left_restrict_sourcevaluesquarefreedomain pvs_right_restrict_sourcevaluesquarefreedomain. (sfd_prime_restrict_sourcevaluesquarefree) = pvs_left_restrict_sourcevaluesquarefreedomain * pvs_right_restrict_sourcevaluesquarefreedomain -> pvs_left_restrict_sourcevaluesquarefreedomain = 1 \/ pvs_right_restrict_sourcevaluesquarefreedomain = 1) -> (exists pvs_le_gap_restrict_sourcevaluesquarefreebound. pvs_le_gap_restrict_sourcevaluesquarefreebound + (sfd_prime_restrict_sourcevaluesquarefree) = (mt_index_restrict_source)) -> ~(exists pvs_factor_restrict_sourcevaluesquarefreesquare. (mt_index_restrict_source) = (sfd_prime_restrict_sourcevaluesquarefree * sfd_prime_restrict_sourcevaluesquarefree) * pvs_factor_restrict_sourcevaluesquarefreesquare)))) /\ (exists mv_factor_code_restrict_sourcevaluefactors mv_factor_scale_restrict_sourcevaluefactors mv_factor_count_restrict_sourcevaluefactors. (((~(mt_index_restrict_source = 0) /\ ((exists ff_u_fsat_restrict_sourcevaluefactorsfactorization_product ff_v_fsat_restrict_sourcevaluefactorsfactorization_product. ((((exists ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_start. ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_start. ff_u_fsat_restrict_sourcevaluefactorsfactorization_product = ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_terminal. ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_terminal + S (mt_index_restrict_source) = S ((S (mv_factor_count_restrict_sourcevaluefactors)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_terminal. ff_u_fsat_restrict_sourcevaluefactorsfactorization_product = ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_restrict_sourcevaluefactors)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product) + (mt_index_restrict_source))) /\ forall ff_i_fsat_restrict_sourcevaluefactorsfactorization_product. (exists ff_lt_fsat_restrict_sourcevaluefactorsfactorization_product_bound. ff_lt_fsat_restrict_sourcevaluefactorsfactorization_product_bound + S ff_i_fsat_restrict_sourcevaluefactorsfactorization_product = mv_factor_count_restrict_sourcevaluefactors) -> exists ff_p_fsat_restrict_sourcevaluefactorsfactorization_product ff_r_fsat_restrict_sourcevaluefactorsfactorization_product ff_s_fsat_restrict_sourcevaluefactorsfactorization_product. ((((exists ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_factor. ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_factor + S (ff_p_fsat_restrict_sourcevaluefactorsfactorization_product) = S ((S (ff_i_fsat_restrict_sourcevaluefactorsfactorization_product)) * mv_factor_scale_restrict_sourcevaluefactors)) /\ exists ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_factor. mv_factor_code_restrict_sourcevaluefactors = ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_restrict_sourcevaluefactorsfactorization_product)) * mv_factor_scale_restrict_sourcevaluefactors) + (ff_p_fsat_restrict_sourcevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_partial. ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_partial + S (ff_r_fsat_restrict_sourcevaluefactorsfactorization_product) = S ((S (ff_i_fsat_restrict_sourcevaluefactorsfactorization_product)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_partial. ff_u_fsat_restrict_sourcevaluefactorsfactorization_product = ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_restrict_sourcevaluefactorsfactorization_product)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product) + (ff_r_fsat_restrict_sourcevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_successor. ff_h_fsat_restrict_sourcevaluefactorsfactorization_product_successor + S (ff_s_fsat_restrict_sourcevaluefactorsfactorization_product) = S ((S (S ff_i_fsat_restrict_sourcevaluefactorsfactorization_product)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_successor. ff_u_fsat_restrict_sourcevaluefactorsfactorization_product = ff_q_fsat_restrict_sourcevaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_restrict_sourcevaluefactorsfactorization_product)) * ff_v_fsat_restrict_sourcevaluefactorsfactorization_product) + (ff_s_fsat_restrict_sourcevaluefactorsfactorization_product))) /\ ff_s_fsat_restrict_sourcevaluefactorsfactorization_product = ff_r_fsat_restrict_sourcevaluefactorsfactorization_product * ff_p_fsat_restrict_sourcevaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_restrict_sourcevaluefactorsfactorization_primes. (exists ftsf_gap_fsat_restrict_sourcevaluefactorsfactorization_primes_bound. ftsf_gap_fsat_restrict_sourcevaluefactorsfactorization_primes_bound + S ftsf_index_fsat_restrict_sourcevaluefactorsfactorization_primes = (mv_factor_count_restrict_sourcevaluefactors)) -> exists ftsf_factor_fsat_restrict_sourcevaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_restrict_sourcevaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_restrict_sourcevaluefactorsfactorization_primes)) * mv_factor_scale_restrict_sourcevaluefactors)) /\ exists ff_q_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_entry. mv_factor_code_restrict_sourcevaluefactors = ff_q_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_restrict_sourcevaluefactorsfactorization_primes)) * mv_factor_scale_restrict_sourcevaluefactors) + (ftsf_factor_fsat_restrict_sourcevaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_restrict_sourcevaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_prime. ftsf_factor_fsat_restrict_sourcevaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_restrict_sourcevaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_restrict_sourcevaluefactorsparityeven. (mv_factor_count_restrict_sourcevaluefactors) = 2 * mv_even_half_restrict_sourcevaluefactorsparityeven) /\ ((mt_value_restrict_source) = 2))) \/ (((exists mv_odd_half_restrict_sourcevaluefactorsparityodd. (mv_factor_count_restrict_sourcevaluefactors) = 2 * mv_odd_half_restrict_sourcevaluefactorsparityodd + 1) /\ ((mt_value_restrict_source) = 1)))))))))))))))) -> (exists pvs_le_gap_restrict_bound. pvs_le_gap_restrict_bound + (K) = (N)) -> (((exists dst_positive_code_restrict_targettable dst_positive_scale_restrict_targettable dst_negative_code_restrict_targettable dst_negative_scale_restrict_targettable. (((M) = (((((dst_positive_code_restrict_targettable) + (dst_positive_scale_restrict_targettable)) * S ((dst_positive_code_restrict_targettable) + (dst_positive_scale_restrict_targettable)) + ((dst_positive_scale_restrict_targettable) + (dst_positive_scale_restrict_targettable))) + (((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) * S ((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) + ((dst_negative_scale_restrict_targettable) + (dst_negative_scale_restrict_targettable)))) * S ((((dst_positive_code_restrict_targettable) + (dst_positive_scale_restrict_targettable)) * S ((dst_positive_code_restrict_targettable) + (dst_positive_scale_restrict_targettable)) + ((dst_positive_scale_restrict_targettable) + (dst_positive_scale_restrict_targettable))) + (((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) * S ((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) + ((dst_negative_scale_restrict_targettable) + (dst_negative_scale_restrict_targettable)))) + ((((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) * S ((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) + ((dst_negative_scale_restrict_targettable) + (dst_negative_scale_restrict_targettable))) + (((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) * S ((dst_negative_code_restrict_targettable) + (dst_negative_scale_restrict_targettable)) + ((dst_negative_scale_restrict_targettable) + (dst_negative_scale_restrict_targettable)))))) /\ (forall dst_index_restrict_targettable. (exists pvs_le_gap_restrict_targettabledomain. pvs_le_gap_restrict_targettabledomain + (dst_index_restrict_targettable) = (K)) -> exists dst_positive_restrict_targettable dst_negative_restrict_targettable dst_value_restrict_targettable. ((((exists ff_h_pvs_restrict_targettableentrypositive. ff_h_pvs_restrict_targettableentrypositive + S (dst_positive_restrict_targettable) = S ((S (dst_index_restrict_targettable)) * dst_positive_scale_restrict_targettable)) /\ exists ff_q_pvs_restrict_targettableentrypositive. dst_positive_code_restrict_targettable = ff_q_pvs_restrict_targettableentrypositive * S ((S (dst_index_restrict_targettable)) * dst_positive_scale_restrict_targettable) + (dst_positive_restrict_targettable))) /\ (((((exists ff_h_pvs_restrict_targettableentrynegative. ff_h_pvs_restrict_targettableentrynegative + S (dst_negative_restrict_targettable) = S ((S (dst_index_restrict_targettable)) * dst_negative_scale_restrict_targettable)) /\ exists ff_q_pvs_restrict_targettableentrynegative. dst_negative_code_restrict_targettable = ff_q_pvs_restrict_targettableentrynegative * S ((S (dst_index_restrict_targettable)) * dst_negative_scale_restrict_targettable) + (dst_negative_restrict_targettable))) /\ (exists ge_balance_positive_restrict_targettableentryvalue ge_balance_negative_restrict_targettableentryvalue. (((((dst_value_restrict_targettable) = 2 * (ge_balance_positive_restrict_targettableentryvalue) /\ (ge_balance_negative_restrict_targettableentryvalue) = 0) \/ exists ge_signed_half_restrict_targettableentryvaluedecode. (((dst_value_restrict_targettable) = 2 * ge_signed_half_restrict_targettableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_targettableentryvalue) = 0) /\ (ge_balance_negative_restrict_targettableentryvalue) = S ge_signed_half_restrict_targettableentryvaluedecode))) /\ ((dst_positive_restrict_targettable) + ge_balance_negative_restrict_targettableentryvalue = (dst_negative_restrict_targettable) + ge_balance_positive_restrict_targettableentryvalue))))))))) /\ (((exists dst_positive_code_restrict_targetzero dst_positive_scale_restrict_targetzero dst_negative_code_restrict_targetzero dst_negative_scale_restrict_targetzero dst_positive_restrict_targetzero dst_negative_restrict_targetzero. (((M) = (((((dst_positive_code_restrict_targetzero) + (dst_positive_scale_restrict_targetzero)) * S ((dst_positive_code_restrict_targetzero) + (dst_positive_scale_restrict_targetzero)) + ((dst_positive_scale_restrict_targetzero) + (dst_positive_scale_restrict_targetzero))) + (((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) * S ((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) + ((dst_negative_scale_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)))) * S ((((dst_positive_code_restrict_targetzero) + (dst_positive_scale_restrict_targetzero)) * S ((dst_positive_code_restrict_targetzero) + (dst_positive_scale_restrict_targetzero)) + ((dst_positive_scale_restrict_targetzero) + (dst_positive_scale_restrict_targetzero))) + (((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) * S ((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) + ((dst_negative_scale_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)))) + ((((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) * S ((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) + ((dst_negative_scale_restrict_targetzero) + (dst_negative_scale_restrict_targetzero))) + (((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) * S ((dst_negative_code_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)) + ((dst_negative_scale_restrict_targetzero) + (dst_negative_scale_restrict_targetzero)))))) /\ (((((exists ff_h_pvs_restrict_targetzeropositive. ff_h_pvs_restrict_targetzeropositive + S (dst_positive_restrict_targetzero) = S ((S (0)) * dst_positive_scale_restrict_targetzero)) /\ exists ff_q_pvs_restrict_targetzeropositive. dst_positive_code_restrict_targetzero = ff_q_pvs_restrict_targetzeropositive * S ((S (0)) * dst_positive_scale_restrict_targetzero) + (dst_positive_restrict_targetzero))) /\ (((((exists ff_h_pvs_restrict_targetzeronegative. ff_h_pvs_restrict_targetzeronegative + S (dst_negative_restrict_targetzero) = S ((S (0)) * dst_negative_scale_restrict_targetzero)) /\ exists ff_q_pvs_restrict_targetzeronegative. dst_negative_code_restrict_targetzero = ff_q_pvs_restrict_targetzeronegative * S ((S (0)) * dst_negative_scale_restrict_targetzero) + (dst_negative_restrict_targetzero))) /\ (exists ge_balance_positive_restrict_targetzerovalue ge_balance_negative_restrict_targetzerovalue. (((((0) = 2 * (ge_balance_positive_restrict_targetzerovalue) /\ (ge_balance_negative_restrict_targetzerovalue) = 0) \/ exists ge_signed_half_restrict_targetzerovaluedecode. (((0) = 2 * ge_signed_half_restrict_targetzerovaluedecode + 1 /\ (ge_balance_positive_restrict_targetzerovalue) = 0) /\ (ge_balance_negative_restrict_targetzerovalue) = S ge_signed_half_restrict_targetzerovaluedecode))) /\ ((dst_positive_restrict_targetzero) + ge_balance_negative_restrict_targetzerovalue = (dst_negative_restrict_targetzero) + ge_balance_positive_restrict_targetzerovalue))))))))) /\ (forall mt_index_restrict_target mt_value_restrict_target. ~(mt_index_restrict_target=0) -> (exists pvs_le_gap_restrict_targetdomain. pvs_le_gap_restrict_targetdomain + (mt_index_restrict_target) = (K)) -> (exists dst_positive_code_restrict_targetentry dst_positive_scale_restrict_targetentry dst_negative_code_restrict_targetentry dst_negative_scale_restrict_targetentry dst_positive_restrict_targetentry dst_negative_restrict_targetentry. (((M) = (((((dst_positive_code_restrict_targetentry) + (dst_positive_scale_restrict_targetentry)) * S ((dst_positive_code_restrict_targetentry) + (dst_positive_scale_restrict_targetentry)) + ((dst_positive_scale_restrict_targetentry) + (dst_positive_scale_restrict_targetentry))) + (((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) * S ((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) + ((dst_negative_scale_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)))) * S ((((dst_positive_code_restrict_targetentry) + (dst_positive_scale_restrict_targetentry)) * S ((dst_positive_code_restrict_targetentry) + (dst_positive_scale_restrict_targetentry)) + ((dst_positive_scale_restrict_targetentry) + (dst_positive_scale_restrict_targetentry))) + (((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) * S ((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) + ((dst_negative_scale_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)))) + ((((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) * S ((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) + ((dst_negative_scale_restrict_targetentry) + (dst_negative_scale_restrict_targetentry))) + (((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) * S ((dst_negative_code_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)) + ((dst_negative_scale_restrict_targetentry) + (dst_negative_scale_restrict_targetentry)))))) /\ (((((exists ff_h_pvs_restrict_targetentrypositive. ff_h_pvs_restrict_targetentrypositive + S (dst_positive_restrict_targetentry) = S ((S (mt_index_restrict_target)) * dst_positive_scale_restrict_targetentry)) /\ exists ff_q_pvs_restrict_targetentrypositive. dst_positive_code_restrict_targetentry = ff_q_pvs_restrict_targetentrypositive * S ((S (mt_index_restrict_target)) * dst_positive_scale_restrict_targetentry) + (dst_positive_restrict_targetentry))) /\ (((((exists ff_h_pvs_restrict_targetentrynegative. ff_h_pvs_restrict_targetentrynegative + S (dst_negative_restrict_targetentry) = S ((S (mt_index_restrict_target)) * dst_negative_scale_restrict_targetentry)) /\ exists ff_q_pvs_restrict_targetentrynegative. dst_negative_code_restrict_targetentry = ff_q_pvs_restrict_targetentrynegative * S ((S (mt_index_restrict_target)) * dst_negative_scale_restrict_targetentry) + (dst_negative_restrict_targetentry))) /\ (exists ge_balance_positive_restrict_targetentryvalue ge_balance_negative_restrict_targetentryvalue. (((((mt_value_restrict_target) = 2 * (ge_balance_positive_restrict_targetentryvalue) /\ (ge_balance_negative_restrict_targetentryvalue) = 0) \/ exists ge_signed_half_restrict_targetentryvaluedecode. (((mt_value_restrict_target) = 2 * ge_signed_half_restrict_targetentryvaluedecode + 1 /\ (ge_balance_positive_restrict_targetentryvalue) = 0) /\ (ge_balance_negative_restrict_targetentryvalue) = S ge_signed_half_restrict_targetentryvaluedecode))) /\ ((dst_positive_restrict_targetentry) + ge_balance_negative_restrict_targetentryvalue = (dst_negative_restrict_targetentry) + ge_balance_positive_restrict_targetentryvalue))))))))) -> (((~((mt_index_restrict_target) = 0)) /\ ((((exists mv_square_prime_restrict_targetvaluesquare. ((~((mv_square_prime_restrict_targetvaluesquare) = 1) /\ forall pvs_left_restrict_targetvaluesquareprime pvs_right_restrict_targetvaluesquareprime. (mv_square_prime_restrict_targetvaluesquare) = pvs_left_restrict_targetvaluesquareprime * pvs_right_restrict_targetvaluesquareprime -> pvs_left_restrict_targetvaluesquareprime = 1 \/ pvs_right_restrict_targetvaluesquareprime = 1) /\ (exists pvs_factor_restrict_targetvaluesquaredivisor. (mt_index_restrict_target) = (mv_square_prime_restrict_targetvaluesquare * mv_square_prime_restrict_targetvaluesquare) * pvs_factor_restrict_targetvaluesquaredivisor))) /\ ((mt_value_restrict_target) = 0))) \/ (((((~((mt_index_restrict_target) = 0)) /\ (forall sfd_prime_restrict_targetvaluesquarefree. (~((sfd_prime_restrict_targetvaluesquarefree) = 1) /\ forall pvs_left_restrict_targetvaluesquarefreedomain pvs_right_restrict_targetvaluesquarefreedomain. (sfd_prime_restrict_targetvaluesquarefree) = pvs_left_restrict_targetvaluesquarefreedomain * pvs_right_restrict_targetvaluesquarefreedomain -> pvs_left_restrict_targetvaluesquarefreedomain = 1 \/ pvs_right_restrict_targetvaluesquarefreedomain = 1) -> (exists pvs_le_gap_restrict_targetvaluesquarefreebound. pvs_le_gap_restrict_targetvaluesquarefreebound + (sfd_prime_restrict_targetvaluesquarefree) = (mt_index_restrict_target)) -> ~(exists pvs_factor_restrict_targetvaluesquarefreesquare. (mt_index_restrict_target) = (sfd_prime_restrict_targetvaluesquarefree * sfd_prime_restrict_targetvaluesquarefree) * pvs_factor_restrict_targetvaluesquarefreesquare)))) /\ (exists mv_factor_code_restrict_targetvaluefactors mv_factor_scale_restrict_targetvaluefactors mv_factor_count_restrict_targetvaluefactors. (((~(mt_index_restrict_target = 0) /\ ((exists ff_u_fsat_restrict_targetvaluefactorsfactorization_product ff_v_fsat_restrict_targetvaluefactorsfactorization_product. ((((exists ff_h_fsat_restrict_targetvaluefactorsfactorization_product_start. ff_h_fsat_restrict_targetvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_targetvaluefactorsfactorization_product_start. ff_u_fsat_restrict_targetvaluefactorsfactorization_product = ff_q_fsat_restrict_targetvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_restrict_targetvaluefactorsfactorization_product_terminal. ff_h_fsat_restrict_targetvaluefactorsfactorization_product_terminal + S (mt_index_restrict_target) = S ((S (mv_factor_count_restrict_targetvaluefactors)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_targetvaluefactorsfactorization_product_terminal. ff_u_fsat_restrict_targetvaluefactorsfactorization_product = ff_q_fsat_restrict_targetvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_restrict_targetvaluefactors)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product) + (mt_index_restrict_target))) /\ forall ff_i_fsat_restrict_targetvaluefactorsfactorization_product. (exists ff_lt_fsat_restrict_targetvaluefactorsfactorization_product_bound. ff_lt_fsat_restrict_targetvaluefactorsfactorization_product_bound + S ff_i_fsat_restrict_targetvaluefactorsfactorization_product = mv_factor_count_restrict_targetvaluefactors) -> exists ff_p_fsat_restrict_targetvaluefactorsfactorization_product ff_r_fsat_restrict_targetvaluefactorsfactorization_product ff_s_fsat_restrict_targetvaluefactorsfactorization_product. ((((exists ff_h_fsat_restrict_targetvaluefactorsfactorization_product_factor. ff_h_fsat_restrict_targetvaluefactorsfactorization_product_factor + S (ff_p_fsat_restrict_targetvaluefactorsfactorization_product) = S ((S (ff_i_fsat_restrict_targetvaluefactorsfactorization_product)) * mv_factor_scale_restrict_targetvaluefactors)) /\ exists ff_q_fsat_restrict_targetvaluefactorsfactorization_product_factor. mv_factor_code_restrict_targetvaluefactors = ff_q_fsat_restrict_targetvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_restrict_targetvaluefactorsfactorization_product)) * mv_factor_scale_restrict_targetvaluefactors) + (ff_p_fsat_restrict_targetvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_restrict_targetvaluefactorsfactorization_product_partial. ff_h_fsat_restrict_targetvaluefactorsfactorization_product_partial + S (ff_r_fsat_restrict_targetvaluefactorsfactorization_product) = S ((S (ff_i_fsat_restrict_targetvaluefactorsfactorization_product)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_targetvaluefactorsfactorization_product_partial. ff_u_fsat_restrict_targetvaluefactorsfactorization_product = ff_q_fsat_restrict_targetvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_restrict_targetvaluefactorsfactorization_product)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product) + (ff_r_fsat_restrict_targetvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_restrict_targetvaluefactorsfactorization_product_successor. ff_h_fsat_restrict_targetvaluefactorsfactorization_product_successor + S (ff_s_fsat_restrict_targetvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_restrict_targetvaluefactorsfactorization_product)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product)) /\ exists ff_q_fsat_restrict_targetvaluefactorsfactorization_product_successor. ff_u_fsat_restrict_targetvaluefactorsfactorization_product = ff_q_fsat_restrict_targetvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_restrict_targetvaluefactorsfactorization_product)) * ff_v_fsat_restrict_targetvaluefactorsfactorization_product) + (ff_s_fsat_restrict_targetvaluefactorsfactorization_product))) /\ ff_s_fsat_restrict_targetvaluefactorsfactorization_product = ff_r_fsat_restrict_targetvaluefactorsfactorization_product * ff_p_fsat_restrict_targetvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_restrict_targetvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_restrict_targetvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_restrict_targetvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_restrict_targetvaluefactorsfactorization_primes = (mv_factor_count_restrict_targetvaluefactors)) -> exists ftsf_factor_fsat_restrict_targetvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_restrict_targetvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_restrict_targetvaluefactorsfactorization_primes)) * mv_factor_scale_restrict_targetvaluefactors)) /\ exists ff_q_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_entry. mv_factor_code_restrict_targetvaluefactors = ff_q_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_restrict_targetvaluefactorsfactorization_primes)) * mv_factor_scale_restrict_targetvaluefactors) + (ftsf_factor_fsat_restrict_targetvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_restrict_targetvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_restrict_targetvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_restrict_targetvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_restrict_targetvaluefactorsparityeven. (mv_factor_count_restrict_targetvaluefactors) = 2 * mv_even_half_restrict_targetvaluefactorsparityeven) /\ ((mt_value_restrict_target) = 2))) \/ (((exists mv_odd_half_restrict_targetvaluefactorsparityodd. (mv_factor_count_restrict_targetvaluefactors) = 2 * mv_odd_half_restrict_targetvaluefactorsparityodd + 1) /\ ((mt_value_restrict_target) = 1))))))))))))))))

divisor_mask_entry_zero

new owned theorem · read exact theorem evidence

Bundle node 292; exact statement SHA-256 ade51e5639462062748193ad7c090b1760664b5fda48a11e9bce31c0039cf9e5

Exact first-order statement

forall F n. ((((~((0)=0)) /\ (exists dm_quotient_zero_entry. (((n)=(0)*dm_quotient_zero_entry) /\ (exists dst_positive_code_zero_entryinput dst_positive_scale_zero_entryinput dst_negative_code_zero_entryinput dst_negative_scale_zero_entryinput dst_positive_zero_entryinput dst_negative_zero_entryinput. (((F) = (((((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) * S ((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) + ((dst_positive_scale_zero_entryinput) + (dst_positive_scale_zero_entryinput))) + (((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput)))) * S ((((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) * S ((dst_positive_code_zero_entryinput) + (dst_positive_scale_zero_entryinput)) + ((dst_positive_scale_zero_entryinput) + (dst_positive_scale_zero_entryinput))) + (((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput)))) + ((((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput))) + (((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) * S ((dst_negative_code_zero_entryinput) + (dst_negative_scale_zero_entryinput)) + ((dst_negative_scale_zero_entryinput) + (dst_negative_scale_zero_entryinput)))))) /\ (((((exists ff_h_pvs_zero_entryinputpositive. ff_h_pvs_zero_entryinputpositive + S (dst_positive_zero_entryinput) = S ((S (0)) * dst_positive_scale_zero_entryinput)) /\ exists ff_q_pvs_zero_entryinputpositive. dst_positive_code_zero_entryinput = ff_q_pvs_zero_entryinputpositive * S ((S (0)) * dst_positive_scale_zero_entryinput) + (dst_positive_zero_entryinput))) /\ (((((exists ff_h_pvs_zero_entryinputnegative. ff_h_pvs_zero_entryinputnegative + S (dst_negative_zero_entryinput) = S ((S (0)) * dst_negative_scale_zero_entryinput)) /\ exists ff_q_pvs_zero_entryinputnegative. dst_negative_code_zero_entryinput = ff_q_pvs_zero_entryinputnegative * S ((S (0)) * dst_negative_scale_zero_entryinput) + (dst_negative_zero_entryinput))) /\ (exists ge_balance_positive_zero_entryinputvalue ge_balance_negative_zero_entryinputvalue. (((((0) = 2 * (ge_balance_positive_zero_entryinputvalue) /\ (ge_balance_negative_zero_entryinputvalue) = 0) \/ exists ge_signed_half_zero_entryinputvaluedecode. (((0) = 2 * ge_signed_half_zero_entryinputvaluedecode + 1 /\ (ge_balance_positive_zero_entryinputvalue) = 0) /\ (ge_balance_negative_zero_entryinputvalue) = S ge_signed_half_zero_entryinputvaluedecode))) /\ ((dst_positive_zero_entryinput) + ge_balance_negative_zero_entryinputvalue = (dst_negative_zero_entryinput) + ge_balance_positive_zero_entryinputvalue))))))))))))) \/ ((((0)=0 \/ ~(exists pvs_factor_zero_entrynondivisor. (n) = (0) * pvs_factor_zero_entrynondivisor)) /\ ((0)=0))))

divisor_mask_entry_from_quotient

new owned theorem · read exact theorem evidence

Bundle node 293; exact statement SHA-256 cddc2f4a59dfacd4fc1c6737d33da09766f5e564e3f3fe912ea8070c45dff2d9

Exact first-order statement

forall F n d q z. ~(d=0) -> n=d*q -> (exists dst_positive_code_keep_input dst_positive_scale_keep_input dst_negative_code_keep_input dst_negative_scale_keep_input dst_positive_keep_input dst_negative_keep_input. (((F) = (((((dst_positive_code_keep_input) + (dst_positive_scale_keep_input)) * S ((dst_positive_code_keep_input) + (dst_positive_scale_keep_input)) + ((dst_positive_scale_keep_input) + (dst_positive_scale_keep_input))) + (((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) * S ((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) + ((dst_negative_scale_keep_input) + (dst_negative_scale_keep_input)))) * S ((((dst_positive_code_keep_input) + (dst_positive_scale_keep_input)) * S ((dst_positive_code_keep_input) + (dst_positive_scale_keep_input)) + ((dst_positive_scale_keep_input) + (dst_positive_scale_keep_input))) + (((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) * S ((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) + ((dst_negative_scale_keep_input) + (dst_negative_scale_keep_input)))) + ((((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) * S ((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) + ((dst_negative_scale_keep_input) + (dst_negative_scale_keep_input))) + (((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) * S ((dst_negative_code_keep_input) + (dst_negative_scale_keep_input)) + ((dst_negative_scale_keep_input) + (dst_negative_scale_keep_input)))))) /\ (((((exists ff_h_pvs_keep_inputpositive. ff_h_pvs_keep_inputpositive + S (dst_positive_keep_input) = S ((S (d)) * dst_positive_scale_keep_input)) /\ exists ff_q_pvs_keep_inputpositive. dst_positive_code_keep_input = ff_q_pvs_keep_inputpositive * S ((S (d)) * dst_positive_scale_keep_input) + (dst_positive_keep_input))) /\ (((((exists ff_h_pvs_keep_inputnegative. ff_h_pvs_keep_inputnegative + S (dst_negative_keep_input) = S ((S (d)) * dst_negative_scale_keep_input)) /\ exists ff_q_pvs_keep_inputnegative. dst_negative_code_keep_input = ff_q_pvs_keep_inputnegative * S ((S (d)) * dst_negative_scale_keep_input) + (dst_negative_keep_input))) /\ (exists ge_balance_positive_keep_inputvalue ge_balance_negative_keep_inputvalue. (((((z) = 2 * (ge_balance_positive_keep_inputvalue) /\ (ge_balance_negative_keep_inputvalue) = 0) \/ exists ge_signed_half_keep_inputvaluedecode. (((z) = 2 * ge_signed_half_keep_inputvaluedecode + 1 /\ (ge_balance_positive_keep_inputvalue) = 0) /\ (ge_balance_negative_keep_inputvalue) = S ge_signed_half_keep_inputvaluedecode))) /\ ((dst_positive_keep_input) + ge_balance_negative_keep_inputvalue = (dst_negative_keep_input) + ge_balance_positive_keep_inputvalue))))))))) -> ((((~((d)=0)) /\ (exists dm_quotient_keep_result. (((n)=(d)*dm_quotient_keep_result) /\ (exists dst_positive_code_keep_resultinput dst_positive_scale_keep_resultinput dst_negative_code_keep_resultinput dst_negative_scale_keep_resultinput dst_positive_keep_resultinput dst_negative_keep_resultinput. (((F) = (((((dst_positive_code_keep_resultinput) + (dst_positive_scale_keep_resultinput)) * S ((dst_positive_code_keep_resultinput) + (dst_positive_scale_keep_resultinput)) + ((dst_positive_scale_keep_resultinput) + (dst_positive_scale_keep_resultinput))) + (((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) * S ((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) + ((dst_negative_scale_keep_resultinput) + (dst_negative_scale_keep_resultinput)))) * S ((((dst_positive_code_keep_resultinput) + (dst_positive_scale_keep_resultinput)) * S ((dst_positive_code_keep_resultinput) + (dst_positive_scale_keep_resultinput)) + ((dst_positive_scale_keep_resultinput) + (dst_positive_scale_keep_resultinput))) + (((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) * S ((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) + ((dst_negative_scale_keep_resultinput) + (dst_negative_scale_keep_resultinput)))) + ((((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) * S ((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) + ((dst_negative_scale_keep_resultinput) + (dst_negative_scale_keep_resultinput))) + (((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) * S ((dst_negative_code_keep_resultinput) + (dst_negative_scale_keep_resultinput)) + ((dst_negative_scale_keep_resultinput) + (dst_negative_scale_keep_resultinput)))))) /\ (((((exists ff_h_pvs_keep_resultinputpositive. ff_h_pvs_keep_resultinputpositive + S (dst_positive_keep_resultinput) = S ((S (d)) * dst_positive_scale_keep_resultinput)) /\ exists ff_q_pvs_keep_resultinputpositive. dst_positive_code_keep_resultinput = ff_q_pvs_keep_resultinputpositive * S ((S (d)) * dst_positive_scale_keep_resultinput) + (dst_positive_keep_resultinput))) /\ (((((exists ff_h_pvs_keep_resultinputnegative. ff_h_pvs_keep_resultinputnegative + S (dst_negative_keep_resultinput) = S ((S (d)) * dst_negative_scale_keep_resultinput)) /\ exists ff_q_pvs_keep_resultinputnegative. dst_negative_code_keep_resultinput = ff_q_pvs_keep_resultinputnegative * S ((S (d)) * dst_negative_scale_keep_resultinput) + (dst_negative_keep_resultinput))) /\ (exists ge_balance_positive_keep_resultinputvalue ge_balance_negative_keep_resultinputvalue. (((((z) = 2 * (ge_balance_positive_keep_resultinputvalue) /\ (ge_balance_negative_keep_resultinputvalue) = 0) \/ exists ge_signed_half_keep_resultinputvaluedecode. (((z) = 2 * ge_signed_half_keep_resultinputvaluedecode + 1 /\ (ge_balance_positive_keep_resultinputvalue) = 0) /\ (ge_balance_negative_keep_resultinputvalue) = S ge_signed_half_keep_resultinputvaluedecode))) /\ ((dst_positive_keep_resultinput) + ge_balance_negative_keep_resultinputvalue = (dst_negative_keep_resultinput) + ge_balance_positive_keep_resultinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_keep_resultnondivisor. (n) = (d) * pvs_factor_keep_resultnondivisor)) /\ ((z)=0))))

divisor_mask_entry_from_nondivisor

new owned theorem · read exact theorem evidence

Bundle node 294; exact statement SHA-256 b1f12a7e7505b6a32592bf59d4c972759dcdd688212080e8b50fdaf73d16f81c

Exact first-order statement

forall F n d. ~(exists pvs_factor_omit_guard. (n) = (d) * pvs_factor_omit_guard) -> ((((~((d)=0)) /\ (exists dm_quotient_omit_result. (((n)=(d)*dm_quotient_omit_result) /\ (exists dst_positive_code_omit_resultinput dst_positive_scale_omit_resultinput dst_negative_code_omit_resultinput dst_negative_scale_omit_resultinput dst_positive_omit_resultinput dst_negative_omit_resultinput. (((F) = (((((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) * S ((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) + ((dst_positive_scale_omit_resultinput) + (dst_positive_scale_omit_resultinput))) + (((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput)))) * S ((((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) * S ((dst_positive_code_omit_resultinput) + (dst_positive_scale_omit_resultinput)) + ((dst_positive_scale_omit_resultinput) + (dst_positive_scale_omit_resultinput))) + (((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput)))) + ((((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput))) + (((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) * S ((dst_negative_code_omit_resultinput) + (dst_negative_scale_omit_resultinput)) + ((dst_negative_scale_omit_resultinput) + (dst_negative_scale_omit_resultinput)))))) /\ (((((exists ff_h_pvs_omit_resultinputpositive. ff_h_pvs_omit_resultinputpositive + S (dst_positive_omit_resultinput) = S ((S (d)) * dst_positive_scale_omit_resultinput)) /\ exists ff_q_pvs_omit_resultinputpositive. dst_positive_code_omit_resultinput = ff_q_pvs_omit_resultinputpositive * S ((S (d)) * dst_positive_scale_omit_resultinput) + (dst_positive_omit_resultinput))) /\ (((((exists ff_h_pvs_omit_resultinputnegative. ff_h_pvs_omit_resultinputnegative + S (dst_negative_omit_resultinput) = S ((S (d)) * dst_negative_scale_omit_resultinput)) /\ exists ff_q_pvs_omit_resultinputnegative. dst_negative_code_omit_resultinput = ff_q_pvs_omit_resultinputnegative * S ((S (d)) * dst_negative_scale_omit_resultinput) + (dst_negative_omit_resultinput))) /\ (exists ge_balance_positive_omit_resultinputvalue ge_balance_negative_omit_resultinputvalue. (((((0) = 2 * (ge_balance_positive_omit_resultinputvalue) /\ (ge_balance_negative_omit_resultinputvalue) = 0) \/ exists ge_signed_half_omit_resultinputvaluedecode. (((0) = 2 * ge_signed_half_omit_resultinputvaluedecode + 1 /\ (ge_balance_positive_omit_resultinputvalue) = 0) /\ (ge_balance_negative_omit_resultinputvalue) = S ge_signed_half_omit_resultinputvaluedecode))) /\ ((dst_positive_omit_resultinput) + ge_balance_negative_omit_resultinputvalue = (dst_negative_omit_resultinput) + ge_balance_positive_omit_resultinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_omit_resultnondivisor. (n) = (d) * pvs_factor_omit_resultnondivisor)) /\ ((0)=0))))

divisor_mask_entry_exists

new owned theorem · read exact theorem evidence

Bundle node 295; exact statement SHA-256 5763a7d9a0ae13e12c40786d49ae6b1a5a3cfe10abdd24f0d4b9a7a6399e70e9

Exact first-order statement

forall N F n d. (exists dst_positive_code_choice_table dst_positive_scale_choice_table dst_negative_code_choice_table dst_negative_scale_choice_table. (((F) = (((((dst_positive_code_choice_table) + (dst_positive_scale_choice_table)) * S ((dst_positive_code_choice_table) + (dst_positive_scale_choice_table)) + ((dst_positive_scale_choice_table) + (dst_positive_scale_choice_table))) + (((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) * S ((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) + ((dst_negative_scale_choice_table) + (dst_negative_scale_choice_table)))) * S ((((dst_positive_code_choice_table) + (dst_positive_scale_choice_table)) * S ((dst_positive_code_choice_table) + (dst_positive_scale_choice_table)) + ((dst_positive_scale_choice_table) + (dst_positive_scale_choice_table))) + (((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) * S ((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) + ((dst_negative_scale_choice_table) + (dst_negative_scale_choice_table)))) + ((((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) * S ((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) + ((dst_negative_scale_choice_table) + (dst_negative_scale_choice_table))) + (((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) * S ((dst_negative_code_choice_table) + (dst_negative_scale_choice_table)) + ((dst_negative_scale_choice_table) + (dst_negative_scale_choice_table)))))) /\ (forall dst_index_choice_table. (exists pvs_le_gap_choice_tabledomain. pvs_le_gap_choice_tabledomain + (dst_index_choice_table) = (N)) -> exists dst_positive_choice_table dst_negative_choice_table dst_value_choice_table. ((((exists ff_h_pvs_choice_tableentrypositive. ff_h_pvs_choice_tableentrypositive + S (dst_positive_choice_table) = S ((S (dst_index_choice_table)) * dst_positive_scale_choice_table)) /\ exists ff_q_pvs_choice_tableentrypositive. dst_positive_code_choice_table = ff_q_pvs_choice_tableentrypositive * S ((S (dst_index_choice_table)) * dst_positive_scale_choice_table) + (dst_positive_choice_table))) /\ (((((exists ff_h_pvs_choice_tableentrynegative. ff_h_pvs_choice_tableentrynegative + S (dst_negative_choice_table) = S ((S (dst_index_choice_table)) * dst_negative_scale_choice_table)) /\ exists ff_q_pvs_choice_tableentrynegative. dst_negative_code_choice_table = ff_q_pvs_choice_tableentrynegative * S ((S (dst_index_choice_table)) * dst_negative_scale_choice_table) + (dst_negative_choice_table))) /\ (exists ge_balance_positive_choice_tableentryvalue ge_balance_negative_choice_tableentryvalue. (((((dst_value_choice_table) = 2 * (ge_balance_positive_choice_tableentryvalue) /\ (ge_balance_negative_choice_tableentryvalue) = 0) \/ exists ge_signed_half_choice_tableentryvaluedecode. (((dst_value_choice_table) = 2 * ge_signed_half_choice_tableentryvaluedecode + 1 /\ (ge_balance_positive_choice_tableentryvalue) = 0) /\ (ge_balance_negative_choice_tableentryvalue) = S ge_signed_half_choice_tableentryvaluedecode))) /\ ((dst_positive_choice_table) + ge_balance_negative_choice_tableentryvalue = (dst_negative_choice_table) + ge_balance_positive_choice_tableentryvalue))))))))) -> (exists pvs_le_gap_choice_bound. pvs_le_gap_choice_bound + (d) = (N)) -> exists z. ((((~((d)=0)) /\ (exists dm_quotient_choice_result. (((n)=(d)*dm_quotient_choice_result) /\ (exists dst_positive_code_choice_resultinput dst_positive_scale_choice_resultinput dst_negative_code_choice_resultinput dst_negative_scale_choice_resultinput dst_positive_choice_resultinput dst_negative_choice_resultinput. (((F) = (((((dst_positive_code_choice_resultinput) + (dst_positive_scale_choice_resultinput)) * S ((dst_positive_code_choice_resultinput) + (dst_positive_scale_choice_resultinput)) + ((dst_positive_scale_choice_resultinput) + (dst_positive_scale_choice_resultinput))) + (((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) * S ((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) + ((dst_negative_scale_choice_resultinput) + (dst_negative_scale_choice_resultinput)))) * S ((((dst_positive_code_choice_resultinput) + (dst_positive_scale_choice_resultinput)) * S ((dst_positive_code_choice_resultinput) + (dst_positive_scale_choice_resultinput)) + ((dst_positive_scale_choice_resultinput) + (dst_positive_scale_choice_resultinput))) + (((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) * S ((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) + ((dst_negative_scale_choice_resultinput) + (dst_negative_scale_choice_resultinput)))) + ((((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) * S ((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) + ((dst_negative_scale_choice_resultinput) + (dst_negative_scale_choice_resultinput))) + (((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) * S ((dst_negative_code_choice_resultinput) + (dst_negative_scale_choice_resultinput)) + ((dst_negative_scale_choice_resultinput) + (dst_negative_scale_choice_resultinput)))))) /\ (((((exists ff_h_pvs_choice_resultinputpositive. ff_h_pvs_choice_resultinputpositive + S (dst_positive_choice_resultinput) = S ((S (d)) * dst_positive_scale_choice_resultinput)) /\ exists ff_q_pvs_choice_resultinputpositive. dst_positive_code_choice_resultinput = ff_q_pvs_choice_resultinputpositive * S ((S (d)) * dst_positive_scale_choice_resultinput) + (dst_positive_choice_resultinput))) /\ (((((exists ff_h_pvs_choice_resultinputnegative. ff_h_pvs_choice_resultinputnegative + S (dst_negative_choice_resultinput) = S ((S (d)) * dst_negative_scale_choice_resultinput)) /\ exists ff_q_pvs_choice_resultinputnegative. dst_negative_code_choice_resultinput = ff_q_pvs_choice_resultinputnegative * S ((S (d)) * dst_negative_scale_choice_resultinput) + (dst_negative_choice_resultinput))) /\ (exists ge_balance_positive_choice_resultinputvalue ge_balance_negative_choice_resultinputvalue. (((((z) = 2 * (ge_balance_positive_choice_resultinputvalue) /\ (ge_balance_negative_choice_resultinputvalue) = 0) \/ exists ge_signed_half_choice_resultinputvaluedecode. (((z) = 2 * ge_signed_half_choice_resultinputvaluedecode + 1 /\ (ge_balance_positive_choice_resultinputvalue) = 0) /\ (ge_balance_negative_choice_resultinputvalue) = S ge_signed_half_choice_resultinputvaluedecode))) /\ ((dst_positive_choice_resultinput) + ge_balance_negative_choice_resultinputvalue = (dst_negative_choice_resultinput) + ge_balance_positive_choice_resultinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_choice_resultnondivisor. (n) = (d) * pvs_factor_choice_resultnondivisor)) /\ ((z)=0))))

divisor_mask_entry_functional

new owned theorem · read exact theorem evidence

Bundle node 296; exact statement SHA-256 a6a0b4fd1ba72ea08f54bf4667cef1c1bf7e8c5a381da67a410bee395377353b

Exact first-order statement

forall F n d a b. ((((~((d)=0)) /\ (exists dm_quotient_unique_first. (((n)=(d)*dm_quotient_unique_first) /\ (exists dst_positive_code_unique_firstinput dst_positive_scale_unique_firstinput dst_negative_code_unique_firstinput dst_negative_scale_unique_firstinput dst_positive_unique_firstinput dst_negative_unique_firstinput. (((F) = (((((dst_positive_code_unique_firstinput) + (dst_positive_scale_unique_firstinput)) * S ((dst_positive_code_unique_firstinput) + (dst_positive_scale_unique_firstinput)) + ((dst_positive_scale_unique_firstinput) + (dst_positive_scale_unique_firstinput))) + (((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) * S ((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) + ((dst_negative_scale_unique_firstinput) + (dst_negative_scale_unique_firstinput)))) * S ((((dst_positive_code_unique_firstinput) + (dst_positive_scale_unique_firstinput)) * S ((dst_positive_code_unique_firstinput) + (dst_positive_scale_unique_firstinput)) + ((dst_positive_scale_unique_firstinput) + (dst_positive_scale_unique_firstinput))) + (((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) * S ((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) + ((dst_negative_scale_unique_firstinput) + (dst_negative_scale_unique_firstinput)))) + ((((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) * S ((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) + ((dst_negative_scale_unique_firstinput) + (dst_negative_scale_unique_firstinput))) + (((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) * S ((dst_negative_code_unique_firstinput) + (dst_negative_scale_unique_firstinput)) + ((dst_negative_scale_unique_firstinput) + (dst_negative_scale_unique_firstinput)))))) /\ (((((exists ff_h_pvs_unique_firstinputpositive. ff_h_pvs_unique_firstinputpositive + S (dst_positive_unique_firstinput) = S ((S (d)) * dst_positive_scale_unique_firstinput)) /\ exists ff_q_pvs_unique_firstinputpositive. dst_positive_code_unique_firstinput = ff_q_pvs_unique_firstinputpositive * S ((S (d)) * dst_positive_scale_unique_firstinput) + (dst_positive_unique_firstinput))) /\ (((((exists ff_h_pvs_unique_firstinputnegative. ff_h_pvs_unique_firstinputnegative + S (dst_negative_unique_firstinput) = S ((S (d)) * dst_negative_scale_unique_firstinput)) /\ exists ff_q_pvs_unique_firstinputnegative. dst_negative_code_unique_firstinput = ff_q_pvs_unique_firstinputnegative * S ((S (d)) * dst_negative_scale_unique_firstinput) + (dst_negative_unique_firstinput))) /\ (exists ge_balance_positive_unique_firstinputvalue ge_balance_negative_unique_firstinputvalue. (((((a) = 2 * (ge_balance_positive_unique_firstinputvalue) /\ (ge_balance_negative_unique_firstinputvalue) = 0) \/ exists ge_signed_half_unique_firstinputvaluedecode. (((a) = 2 * ge_signed_half_unique_firstinputvaluedecode + 1 /\ (ge_balance_positive_unique_firstinputvalue) = 0) /\ (ge_balance_negative_unique_firstinputvalue) = S ge_signed_half_unique_firstinputvaluedecode))) /\ ((dst_positive_unique_firstinput) + ge_balance_negative_unique_firstinputvalue = (dst_negative_unique_firstinput) + ge_balance_positive_unique_firstinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_unique_firstnondivisor. (n) = (d) * pvs_factor_unique_firstnondivisor)) /\ ((a)=0)))) -> ((((~((d)=0)) /\ (exists dm_quotient_unique_second. (((n)=(d)*dm_quotient_unique_second) /\ (exists dst_positive_code_unique_secondinput dst_positive_scale_unique_secondinput dst_negative_code_unique_secondinput dst_negative_scale_unique_secondinput dst_positive_unique_secondinput dst_negative_unique_secondinput. (((F) = (((((dst_positive_code_unique_secondinput) + (dst_positive_scale_unique_secondinput)) * S ((dst_positive_code_unique_secondinput) + (dst_positive_scale_unique_secondinput)) + ((dst_positive_scale_unique_secondinput) + (dst_positive_scale_unique_secondinput))) + (((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) * S ((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) + ((dst_negative_scale_unique_secondinput) + (dst_negative_scale_unique_secondinput)))) * S ((((dst_positive_code_unique_secondinput) + (dst_positive_scale_unique_secondinput)) * S ((dst_positive_code_unique_secondinput) + (dst_positive_scale_unique_secondinput)) + ((dst_positive_scale_unique_secondinput) + (dst_positive_scale_unique_secondinput))) + (((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) * S ((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) + ((dst_negative_scale_unique_secondinput) + (dst_negative_scale_unique_secondinput)))) + ((((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) * S ((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) + ((dst_negative_scale_unique_secondinput) + (dst_negative_scale_unique_secondinput))) + (((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) * S ((dst_negative_code_unique_secondinput) + (dst_negative_scale_unique_secondinput)) + ((dst_negative_scale_unique_secondinput) + (dst_negative_scale_unique_secondinput)))))) /\ (((((exists ff_h_pvs_unique_secondinputpositive. ff_h_pvs_unique_secondinputpositive + S (dst_positive_unique_secondinput) = S ((S (d)) * dst_positive_scale_unique_secondinput)) /\ exists ff_q_pvs_unique_secondinputpositive. dst_positive_code_unique_secondinput = ff_q_pvs_unique_secondinputpositive * S ((S (d)) * dst_positive_scale_unique_secondinput) + (dst_positive_unique_secondinput))) /\ (((((exists ff_h_pvs_unique_secondinputnegative. ff_h_pvs_unique_secondinputnegative + S (dst_negative_unique_secondinput) = S ((S (d)) * dst_negative_scale_unique_secondinput)) /\ exists ff_q_pvs_unique_secondinputnegative. dst_negative_code_unique_secondinput = ff_q_pvs_unique_secondinputnegative * S ((S (d)) * dst_negative_scale_unique_secondinput) + (dst_negative_unique_secondinput))) /\ (exists ge_balance_positive_unique_secondinputvalue ge_balance_negative_unique_secondinputvalue. (((((b) = 2 * (ge_balance_positive_unique_secondinputvalue) /\ (ge_balance_negative_unique_secondinputvalue) = 0) \/ exists ge_signed_half_unique_secondinputvaluedecode. (((b) = 2 * ge_signed_half_unique_secondinputvaluedecode + 1 /\ (ge_balance_positive_unique_secondinputvalue) = 0) /\ (ge_balance_negative_unique_secondinputvalue) = S ge_signed_half_unique_secondinputvaluedecode))) /\ ((dst_positive_unique_secondinput) + ge_balance_negative_unique_secondinputvalue = (dst_negative_unique_secondinput) + ge_balance_positive_unique_secondinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_unique_secondnondivisor. (n) = (d) * pvs_factor_unique_secondnondivisor)) /\ ((b)=0)))) -> a=b

divisor_mask_entry_quotient_input

new owned theorem · read exact theorem evidence

Bundle node 297; exact statement SHA-256 da139e69266fdedc66b06d59cce6e62271c9ed6112411e21fb6b0b94fc537f1f

Exact first-order statement

forall F n d q z. ~(d=0) -> n=d*q -> ((((~((d)=0)) /\ (exists dm_quotient_read_mask. (((n)=(d)*dm_quotient_read_mask) /\ (exists dst_positive_code_read_maskinput dst_positive_scale_read_maskinput dst_negative_code_read_maskinput dst_negative_scale_read_maskinput dst_positive_read_maskinput dst_negative_read_maskinput. (((F) = (((((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) * S ((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) + ((dst_positive_scale_read_maskinput) + (dst_positive_scale_read_maskinput))) + (((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput)))) * S ((((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) * S ((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) + ((dst_positive_scale_read_maskinput) + (dst_positive_scale_read_maskinput))) + (((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput)))) + ((((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput))) + (((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput)))))) /\ (((((exists ff_h_pvs_read_maskinputpositive. ff_h_pvs_read_maskinputpositive + S (dst_positive_read_maskinput) = S ((S (d)) * dst_positive_scale_read_maskinput)) /\ exists ff_q_pvs_read_maskinputpositive. dst_positive_code_read_maskinput = ff_q_pvs_read_maskinputpositive * S ((S (d)) * dst_positive_scale_read_maskinput) + (dst_positive_read_maskinput))) /\ (((((exists ff_h_pvs_read_maskinputnegative. ff_h_pvs_read_maskinputnegative + S (dst_negative_read_maskinput) = S ((S (d)) * dst_negative_scale_read_maskinput)) /\ exists ff_q_pvs_read_maskinputnegative. dst_negative_code_read_maskinput = ff_q_pvs_read_maskinputnegative * S ((S (d)) * dst_negative_scale_read_maskinput) + (dst_negative_read_maskinput))) /\ (exists ge_balance_positive_read_maskinputvalue ge_balance_negative_read_maskinputvalue. (((((z) = 2 * (ge_balance_positive_read_maskinputvalue) /\ (ge_balance_negative_read_maskinputvalue) = 0) \/ exists ge_signed_half_read_maskinputvaluedecode. (((z) = 2 * ge_signed_half_read_maskinputvaluedecode + 1 /\ (ge_balance_positive_read_maskinputvalue) = 0) /\ (ge_balance_negative_read_maskinputvalue) = S ge_signed_half_read_maskinputvaluedecode))) /\ ((dst_positive_read_maskinput) + ge_balance_negative_read_maskinputvalue = (dst_negative_read_maskinput) + ge_balance_positive_read_maskinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_read_masknondivisor. (n) = (d) * pvs_factor_read_masknondivisor)) /\ ((z)=0)))) -> (exists dst_positive_code_read_input dst_positive_scale_read_input dst_negative_code_read_input dst_negative_scale_read_input dst_positive_read_input dst_negative_read_input. (((F) = (((((dst_positive_code_read_input) + (dst_positive_scale_read_input)) * S ((dst_positive_code_read_input) + (dst_positive_scale_read_input)) + ((dst_positive_scale_read_input) + (dst_positive_scale_read_input))) + (((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input)))) * S ((((dst_positive_code_read_input) + (dst_positive_scale_read_input)) * S ((dst_positive_code_read_input) + (dst_positive_scale_read_input)) + ((dst_positive_scale_read_input) + (dst_positive_scale_read_input))) + (((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input)))) + ((((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input))) + (((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input)))))) /\ (((((exists ff_h_pvs_read_inputpositive. ff_h_pvs_read_inputpositive + S (dst_positive_read_input) = S ((S (d)) * dst_positive_scale_read_input)) /\ exists ff_q_pvs_read_inputpositive. dst_positive_code_read_input = ff_q_pvs_read_inputpositive * S ((S (d)) * dst_positive_scale_read_input) + (dst_positive_read_input))) /\ (((((exists ff_h_pvs_read_inputnegative. ff_h_pvs_read_inputnegative + S (dst_negative_read_input) = S ((S (d)) * dst_negative_scale_read_input)) /\ exists ff_q_pvs_read_inputnegative. dst_negative_code_read_input = ff_q_pvs_read_inputnegative * S ((S (d)) * dst_negative_scale_read_input) + (dst_negative_read_input))) /\ (exists ge_balance_positive_read_inputvalue ge_balance_negative_read_inputvalue. (((((z) = 2 * (ge_balance_positive_read_inputvalue) /\ (ge_balance_negative_read_inputvalue) = 0) \/ exists ge_signed_half_read_inputvaluedecode. (((z) = 2 * ge_signed_half_read_inputvaluedecode + 1 /\ (ge_balance_positive_read_inputvalue) = 0) /\ (ge_balance_negative_read_inputvalue) = S ge_signed_half_read_inputvaluedecode))) /\ ((dst_positive_read_input) + ge_balance_negative_read_inputvalue = (dst_negative_read_input) + ge_balance_positive_read_inputvalue)))))))))

divisor_mask_entry_omitted_value

new owned theorem · read exact theorem evidence

Bundle node 298; exact statement SHA-256 0a9a8fad85137bfde14f876f11a985dc42e1f81951718b2c1a297d4d28a94de5

Exact first-order statement

forall F n d z. (d=0 \/ ~(exists pvs_factor_zero_guard. (n) = (d) * pvs_factor_zero_guard)) -> ((((~((d)=0)) /\ (exists dm_quotient_zero_mask. (((n)=(d)*dm_quotient_zero_mask) /\ (exists dst_positive_code_zero_maskinput dst_positive_scale_zero_maskinput dst_negative_code_zero_maskinput dst_negative_scale_zero_maskinput dst_positive_zero_maskinput dst_negative_zero_maskinput. (((F) = (((((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) * S ((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) + ((dst_positive_scale_zero_maskinput) + (dst_positive_scale_zero_maskinput))) + (((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput)))) * S ((((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) * S ((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) + ((dst_positive_scale_zero_maskinput) + (dst_positive_scale_zero_maskinput))) + (((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput)))) + ((((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput))) + (((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput)))))) /\ (((((exists ff_h_pvs_zero_maskinputpositive. ff_h_pvs_zero_maskinputpositive + S (dst_positive_zero_maskinput) = S ((S (d)) * dst_positive_scale_zero_maskinput)) /\ exists ff_q_pvs_zero_maskinputpositive. dst_positive_code_zero_maskinput = ff_q_pvs_zero_maskinputpositive * S ((S (d)) * dst_positive_scale_zero_maskinput) + (dst_positive_zero_maskinput))) /\ (((((exists ff_h_pvs_zero_maskinputnegative. ff_h_pvs_zero_maskinputnegative + S (dst_negative_zero_maskinput) = S ((S (d)) * dst_negative_scale_zero_maskinput)) /\ exists ff_q_pvs_zero_maskinputnegative. dst_negative_code_zero_maskinput = ff_q_pvs_zero_maskinputnegative * S ((S (d)) * dst_negative_scale_zero_maskinput) + (dst_negative_zero_maskinput))) /\ (exists ge_balance_positive_zero_maskinputvalue ge_balance_negative_zero_maskinputvalue. (((((z) = 2 * (ge_balance_positive_zero_maskinputvalue) /\ (ge_balance_negative_zero_maskinputvalue) = 0) \/ exists ge_signed_half_zero_maskinputvaluedecode. (((z) = 2 * ge_signed_half_zero_maskinputvaluedecode + 1 /\ (ge_balance_positive_zero_maskinputvalue) = 0) /\ (ge_balance_negative_zero_maskinputvalue) = S ge_signed_half_zero_maskinputvaluedecode))) /\ ((dst_positive_zero_maskinput) + ge_balance_negative_zero_maskinputvalue = (dst_negative_zero_maskinput) + ge_balance_positive_zero_maskinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_zero_masknondivisor. (n) = (d) * pvs_factor_zero_masknondivisor)) /\ ((z)=0)))) -> z=0

divisor_mask_prefix_zero_constructor

new owned theorem · read exact theorem evidence

Bundle node 299; exact statement SHA-256 a536828bcc4e7cf1c8b02034fceb26f7f0aa720d2db278d6ce7abc71b9c9ef9e

Exact first-order statement

forall F n M. (exists dst_positive_code_base_table dst_positive_scale_base_table dst_negative_code_base_table dst_negative_scale_base_table. (((M) = (((((dst_positive_code_base_table) + (dst_positive_scale_base_table)) * S ((dst_positive_code_base_table) + (dst_positive_scale_base_table)) + ((dst_positive_scale_base_table) + (dst_positive_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))) * S ((((dst_positive_code_base_table) + (dst_positive_scale_base_table)) * S ((dst_positive_code_base_table) + (dst_positive_scale_base_table)) + ((dst_positive_scale_base_table) + (dst_positive_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))) + ((((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))))) /\ (forall dst_index_base_table. (exists pvs_le_gap_base_tabledomain. pvs_le_gap_base_tabledomain + (dst_index_base_table) = (0)) -> exists dst_positive_base_table dst_negative_base_table dst_value_base_table. ((((exists ff_h_pvs_base_tableentrypositive. ff_h_pvs_base_tableentrypositive + S (dst_positive_base_table) = S ((S (dst_index_base_table)) * dst_positive_scale_base_table)) /\ exists ff_q_pvs_base_tableentrypositive. dst_positive_code_base_table = ff_q_pvs_base_tableentrypositive * S ((S (dst_index_base_table)) * dst_positive_scale_base_table) + (dst_positive_base_table))) /\ (((((exists ff_h_pvs_base_tableentrynegative. ff_h_pvs_base_tableentrynegative + S (dst_negative_base_table) = S ((S (dst_index_base_table)) * dst_negative_scale_base_table)) /\ exists ff_q_pvs_base_tableentrynegative. dst_negative_code_base_table = ff_q_pvs_base_tableentrynegative * S ((S (dst_index_base_table)) * dst_negative_scale_base_table) + (dst_negative_base_table))) /\ (exists ge_balance_positive_base_tableentryvalue ge_balance_negative_base_tableentryvalue. (((((dst_value_base_table) = 2 * (ge_balance_positive_base_tableentryvalue) /\ (ge_balance_negative_base_tableentryvalue) = 0) \/ exists ge_signed_half_base_tableentryvaluedecode. (((dst_value_base_table) = 2 * ge_signed_half_base_tableentryvaluedecode + 1 /\ (ge_balance_positive_base_tableentryvalue) = 0) /\ (ge_balance_negative_base_tableentryvalue) = S ge_signed_half_base_tableentryvaluedecode))) /\ ((dst_positive_base_table) + ge_balance_negative_base_tableentryvalue = (dst_negative_base_table) + ge_balance_positive_base_tableentryvalue))))))))) -> (exists dst_positive_code_base_entry dst_positive_scale_base_entry dst_negative_code_base_entry dst_negative_scale_base_entry dst_positive_base_entry dst_negative_base_entry. (((M) = (((((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) * S ((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) + ((dst_positive_scale_base_entry) + (dst_positive_scale_base_entry))) + (((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry)))) * S ((((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) * S ((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) + ((dst_positive_scale_base_entry) + (dst_positive_scale_base_entry))) + (((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry)))) + ((((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry))) + (((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry)))))) /\ (((((exists ff_h_pvs_base_entrypositive. ff_h_pvs_base_entrypositive + S (dst_positive_base_entry) = S ((S (0)) * dst_positive_scale_base_entry)) /\ exists ff_q_pvs_base_entrypositive. dst_positive_code_base_entry = ff_q_pvs_base_entrypositive * S ((S (0)) * dst_positive_scale_base_entry) + (dst_positive_base_entry))) /\ (((((exists ff_h_pvs_base_entrynegative. ff_h_pvs_base_entrynegative + S (dst_negative_base_entry) = S ((S (0)) * dst_negative_scale_base_entry)) /\ exists ff_q_pvs_base_entrynegative. dst_negative_code_base_entry = ff_q_pvs_base_entrynegative * S ((S (0)) * dst_negative_scale_base_entry) + (dst_negative_base_entry))) /\ (exists ge_balance_positive_base_entryvalue ge_balance_negative_base_entryvalue. (((((0) = 2 * (ge_balance_positive_base_entryvalue) /\ (ge_balance_negative_base_entryvalue) = 0) \/ exists ge_signed_half_base_entryvaluedecode. (((0) = 2 * ge_signed_half_base_entryvaluedecode + 1 /\ (ge_balance_positive_base_entryvalue) = 0) /\ (ge_balance_negative_base_entryvalue) = S ge_signed_half_base_entryvaluedecode))) /\ ((dst_positive_base_entry) + ge_balance_negative_base_entryvalue = (dst_negative_base_entry) + ge_balance_positive_base_entryvalue))))))))) -> (((exists dst_positive_code_base_resulttable dst_positive_scale_base_resulttable dst_negative_code_base_resulttable dst_negative_scale_base_resulttable. (((M) = (((((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) * S ((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) + ((dst_positive_scale_base_resulttable) + (dst_positive_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))) * S ((((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) * S ((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) + ((dst_positive_scale_base_resulttable) + (dst_positive_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))) + ((((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))))) /\ (forall dst_index_base_resulttable. (exists pvs_le_gap_base_resulttabledomain. pvs_le_gap_base_resulttabledomain + (dst_index_base_resulttable) = (0)) -> exists dst_positive_base_resulttable dst_negative_base_resulttable dst_value_base_resulttable. ((((exists ff_h_pvs_base_resulttableentrypositive. ff_h_pvs_base_resulttableentrypositive + S (dst_positive_base_resulttable) = S ((S (dst_index_base_resulttable)) * dst_positive_scale_base_resulttable)) /\ exists ff_q_pvs_base_resulttableentrypositive. dst_positive_code_base_resulttable = ff_q_pvs_base_resulttableentrypositive * S ((S (dst_index_base_resulttable)) * dst_positive_scale_base_resulttable) + (dst_positive_base_resulttable))) /\ (((((exists ff_h_pvs_base_resulttableentrynegative. ff_h_pvs_base_resulttableentrynegative + S (dst_negative_base_resulttable) = S ((S (dst_index_base_resulttable)) * dst_negative_scale_base_resulttable)) /\ exists ff_q_pvs_base_resulttableentrynegative. dst_negative_code_base_resulttable = ff_q_pvs_base_resulttableentrynegative * S ((S (dst_index_base_resulttable)) * dst_negative_scale_base_resulttable) + (dst_negative_base_resulttable))) /\ (exists ge_balance_positive_base_resulttableentryvalue ge_balance_negative_base_resulttableentryvalue. (((((dst_value_base_resulttable) = 2 * (ge_balance_positive_base_resulttableentryvalue) /\ (ge_balance_negative_base_resulttableentryvalue) = 0) \/ exists ge_signed_half_base_resulttableentryvaluedecode. (((dst_value_base_resulttable) = 2 * ge_signed_half_base_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_base_resulttableentryvalue) = 0) /\ (ge_balance_negative_base_resulttableentryvalue) = S ge_signed_half_base_resulttableentryvaluedecode))) /\ ((dst_positive_base_resulttable) + ge_balance_negative_base_resulttableentryvalue = (dst_negative_base_resulttable) + ge_balance_positive_base_resulttableentryvalue))))))))) /\ (forall dm_index_base_result dm_value_base_result. (exists pvs_le_gap_base_resultdomain. pvs_le_gap_base_resultdomain + (dm_index_base_result) = (0)) -> (exists dst_positive_code_base_resultlookup dst_positive_scale_base_resultlookup dst_negative_code_base_resultlookup dst_negative_scale_base_resultlookup dst_positive_base_resultlookup dst_negative_base_resultlookup. (((M) = (((((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) * S ((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) + ((dst_positive_scale_base_resultlookup) + (dst_positive_scale_base_resultlookup))) + (((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup)))) * S ((((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) * S ((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) + ((dst_positive_scale_base_resultlookup) + (dst_positive_scale_base_resultlookup))) + (((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup)))) + ((((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup))) + (((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup)))))) /\ (((((exists ff_h_pvs_base_resultlookuppositive. ff_h_pvs_base_resultlookuppositive + S (dst_positive_base_resultlookup) = S ((S (dm_index_base_result)) * dst_positive_scale_base_resultlookup)) /\ exists ff_q_pvs_base_resultlookuppositive. dst_positive_code_base_resultlookup = ff_q_pvs_base_resultlookuppositive * S ((S (dm_index_base_result)) * dst_positive_scale_base_resultlookup) + (dst_positive_base_resultlookup))) /\ (((((exists ff_h_pvs_base_resultlookupnegative. ff_h_pvs_base_resultlookupnegative + S (dst_negative_base_resultlookup) = S ((S (dm_index_base_result)) * dst_negative_scale_base_resultlookup)) /\ exists ff_q_pvs_base_resultlookupnegative. dst_negative_code_base_resultlookup = ff_q_pvs_base_resultlookupnegative * S ((S (dm_index_base_result)) * dst_negative_scale_base_resultlookup) + (dst_negative_base_resultlookup))) /\ (exists ge_balance_positive_base_resultlookupvalue ge_balance_negative_base_resultlookupvalue. (((((dm_value_base_result) = 2 * (ge_balance_positive_base_resultlookupvalue) /\ (ge_balance_negative_base_resultlookupvalue) = 0) \/ exists ge_signed_half_base_resultlookupvaluedecode. (((dm_value_base_result) = 2 * ge_signed_half_base_resultlookupvaluedecode + 1 /\ (ge_balance_positive_base_resultlookupvalue) = 0) /\ (ge_balance_negative_base_resultlookupvalue) = S ge_signed_half_base_resultlookupvaluedecode))) /\ ((dst_positive_base_resultlookup) + ge_balance_negative_base_resultlookupvalue = (dst_negative_base_resultlookup) + ge_balance_positive_base_resultlookupvalue))))))))) -> ((((~((dm_index_base_result)=0)) /\ (exists dm_quotient_base_resultentry. (((n)=(dm_index_base_result)*dm_quotient_base_resultentry) /\ (exists dst_positive_code_base_resultentryinput dst_positive_scale_base_resultentryinput dst_negative_code_base_resultentryinput dst_negative_scale_base_resultentryinput dst_positive_base_resultentryinput dst_negative_base_resultentryinput. (((F) = (((((dst_positive_code_base_resultentryinput) + (dst_positive_scale_base_resultentryinput)) * S ((dst_positive_code_base_resultentryinput) + (dst_positive_scale_base_resultentryinput)) + ((dst_positive_scale_base_resultentryinput) + (dst_positive_scale_base_resultentryinput))) + (((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) * S ((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) + ((dst_negative_scale_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)))) * S ((((dst_positive_code_base_resultentryinput) + (dst_positive_scale_base_resultentryinput)) * S ((dst_positive_code_base_resultentryinput) + (dst_positive_scale_base_resultentryinput)) + ((dst_positive_scale_base_resultentryinput) + (dst_positive_scale_base_resultentryinput))) + (((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) * S ((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) + ((dst_negative_scale_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)))) + ((((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) * S ((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) + ((dst_negative_scale_base_resultentryinput) + (dst_negative_scale_base_resultentryinput))) + (((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) * S ((dst_negative_code_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)) + ((dst_negative_scale_base_resultentryinput) + (dst_negative_scale_base_resultentryinput)))))) /\ (((((exists ff_h_pvs_base_resultentryinputpositive. ff_h_pvs_base_resultentryinputpositive + S (dst_positive_base_resultentryinput) = S ((S (dm_index_base_result)) * dst_positive_scale_base_resultentryinput)) /\ exists ff_q_pvs_base_resultentryinputpositive. dst_positive_code_base_resultentryinput = ff_q_pvs_base_resultentryinputpositive * S ((S (dm_index_base_result)) * dst_positive_scale_base_resultentryinput) + (dst_positive_base_resultentryinput))) /\ (((((exists ff_h_pvs_base_resultentryinputnegative. ff_h_pvs_base_resultentryinputnegative + S (dst_negative_base_resultentryinput) = S ((S (dm_index_base_result)) * dst_negative_scale_base_resultentryinput)) /\ exists ff_q_pvs_base_resultentryinputnegative. dst_negative_code_base_resultentryinput = ff_q_pvs_base_resultentryinputnegative * S ((S (dm_index_base_result)) * dst_negative_scale_base_resultentryinput) + (dst_negative_base_resultentryinput))) /\ (exists ge_balance_positive_base_resultentryinputvalue ge_balance_negative_base_resultentryinputvalue. (((((dm_value_base_result) = 2 * (ge_balance_positive_base_resultentryinputvalue) /\ (ge_balance_negative_base_resultentryinputvalue) = 0) \/ exists ge_signed_half_base_resultentryinputvaluedecode. (((dm_value_base_result) = 2 * ge_signed_half_base_resultentryinputvaluedecode + 1 /\ (ge_balance_positive_base_resultentryinputvalue) = 0) /\ (ge_balance_negative_base_resultentryinputvalue) = S ge_signed_half_base_resultentryinputvaluedecode))) /\ ((dst_positive_base_resultentryinput) + ge_balance_negative_base_resultentryinputvalue = (dst_negative_base_resultentryinput) + ge_balance_positive_base_resultentryinputvalue))))))))))))) \/ ((((dm_index_base_result)=0 \/ ~(exists pvs_factor_base_resultentrynondivisor. (n) = (dm_index_base_result) * pvs_factor_base_resultentrynondivisor)) /\ ((dm_value_base_result)=0)))))))

divisor_mask_prefix_append

new owned theorem · read exact theorem evidence

Bundle node 300; exact statement SHA-256 d7543923b97d26389db0d5554b7dd777f5ebccb3d2e9d605c3c5634ec870d239

Exact first-order statement

forall F n l M z. (((exists dst_positive_code_append_sourcetable dst_positive_scale_append_sourcetable dst_negative_code_append_sourcetable dst_negative_scale_append_sourcetable. (((M) = (((((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) * S ((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) + ((dst_positive_scale_append_sourcetable) + (dst_positive_scale_append_sourcetable))) + (((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable)))) * S ((((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) * S ((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) + ((dst_positive_scale_append_sourcetable) + (dst_positive_scale_append_sourcetable))) + (((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable)))) + ((((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable))) + (((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable)))))) /\ (forall dst_index_append_sourcetable. (exists pvs_le_gap_append_sourcetabledomain. pvs_le_gap_append_sourcetabledomain + (dst_index_append_sourcetable) = (l)) -> exists dst_positive_append_sourcetable dst_negative_append_sourcetable dst_value_append_sourcetable. ((((exists ff_h_pvs_append_sourcetableentrypositive. ff_h_pvs_append_sourcetableentrypositive + S (dst_positive_append_sourcetable) = S ((S (dst_index_append_sourcetable)) * dst_positive_scale_append_sourcetable)) /\ exists ff_q_pvs_append_sourcetableentrypositive. dst_positive_code_append_sourcetable = ff_q_pvs_append_sourcetableentrypositive * S ((S (dst_index_append_sourcetable)) * dst_positive_scale_append_sourcetable) + (dst_positive_append_sourcetable))) /\ (((((exists ff_h_pvs_append_sourcetableentrynegative. ff_h_pvs_append_sourcetableentrynegative + S (dst_negative_append_sourcetable) = S ((S (dst_index_append_sourcetable)) * dst_negative_scale_append_sourcetable)) /\ exists ff_q_pvs_append_sourcetableentrynegative. dst_negative_code_append_sourcetable = ff_q_pvs_append_sourcetableentrynegative * S ((S (dst_index_append_sourcetable)) * dst_negative_scale_append_sourcetable) + (dst_negative_append_sourcetable))) /\ (exists ge_balance_positive_append_sourcetableentryvalue ge_balance_negative_append_sourcetableentryvalue. (((((dst_value_append_sourcetable) = 2 * (ge_balance_positive_append_sourcetableentryvalue) /\ (ge_balance_negative_append_sourcetableentryvalue) = 0) \/ exists ge_signed_half_append_sourcetableentryvaluedecode. (((dst_value_append_sourcetable) = 2 * ge_signed_half_append_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_append_sourcetableentryvalue) = 0) /\ (ge_balance_negative_append_sourcetableentryvalue) = S ge_signed_half_append_sourcetableentryvaluedecode))) /\ ((dst_positive_append_sourcetable) + ge_balance_negative_append_sourcetableentryvalue = (dst_negative_append_sourcetable) + ge_balance_positive_append_sourcetableentryvalue))))))))) /\ (forall dm_index_append_source dm_value_append_source. (exists pvs_le_gap_append_sourcedomain. pvs_le_gap_append_sourcedomain + (dm_index_append_source) = (l)) -> (exists dst_positive_code_append_sourcelookup dst_positive_scale_append_sourcelookup dst_negative_code_append_sourcelookup dst_negative_scale_append_sourcelookup dst_positive_append_sourcelookup dst_negative_append_sourcelookup. (((M) = (((((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) * S ((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) + ((dst_positive_scale_append_sourcelookup) + (dst_positive_scale_append_sourcelookup))) + (((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)))) * S ((((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) * S ((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) + ((dst_positive_scale_append_sourcelookup) + (dst_positive_scale_append_sourcelookup))) + (((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)))) + ((((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup))) + (((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)))))) /\ (((((exists ff_h_pvs_append_sourcelookuppositive. ff_h_pvs_append_sourcelookuppositive + S (dst_positive_append_sourcelookup) = S ((S (dm_index_append_source)) * dst_positive_scale_append_sourcelookup)) /\ exists ff_q_pvs_append_sourcelookuppositive. dst_positive_code_append_sourcelookup = ff_q_pvs_append_sourcelookuppositive * S ((S (dm_index_append_source)) * dst_positive_scale_append_sourcelookup) + (dst_positive_append_sourcelookup))) /\ (((((exists ff_h_pvs_append_sourcelookupnegative. ff_h_pvs_append_sourcelookupnegative + S (dst_negative_append_sourcelookup) = S ((S (dm_index_append_source)) * dst_negative_scale_append_sourcelookup)) /\ exists ff_q_pvs_append_sourcelookupnegative. dst_negative_code_append_sourcelookup = ff_q_pvs_append_sourcelookupnegative * S ((S (dm_index_append_source)) * dst_negative_scale_append_sourcelookup) + (dst_negative_append_sourcelookup))) /\ (exists ge_balance_positive_append_sourcelookupvalue ge_balance_negative_append_sourcelookupvalue. (((((dm_value_append_source) = 2 * (ge_balance_positive_append_sourcelookupvalue) /\ (ge_balance_negative_append_sourcelookupvalue) = 0) \/ exists ge_signed_half_append_sourcelookupvaluedecode. (((dm_value_append_source) = 2 * ge_signed_half_append_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_append_sourcelookupvalue) = 0) /\ (ge_balance_negative_append_sourcelookupvalue) = S ge_signed_half_append_sourcelookupvaluedecode))) /\ ((dst_positive_append_sourcelookup) + ge_balance_negative_append_sourcelookupvalue = (dst_negative_append_sourcelookup) + ge_balance_positive_append_sourcelookupvalue))))))))) -> ((((~((dm_index_append_source)=0)) /\ (exists dm_quotient_append_sourceentry. (((n)=(dm_index_append_source)*dm_quotient_append_sourceentry) /\ (exists dst_positive_code_append_sourceentryinput dst_positive_scale_append_sourceentryinput dst_negative_code_append_sourceentryinput dst_negative_scale_append_sourceentryinput dst_positive_append_sourceentryinput dst_negative_append_sourceentryinput. (((F) = (((((dst_positive_code_append_sourceentryinput) + (dst_positive_scale_append_sourceentryinput)) * S ((dst_positive_code_append_sourceentryinput) + (dst_positive_scale_append_sourceentryinput)) + ((dst_positive_scale_append_sourceentryinput) + (dst_positive_scale_append_sourceentryinput))) + (((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) * S ((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) + ((dst_negative_scale_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)))) * S ((((dst_positive_code_append_sourceentryinput) + (dst_positive_scale_append_sourceentryinput)) * S ((dst_positive_code_append_sourceentryinput) + (dst_positive_scale_append_sourceentryinput)) + ((dst_positive_scale_append_sourceentryinput) + (dst_positive_scale_append_sourceentryinput))) + (((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) * S ((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) + ((dst_negative_scale_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)))) + ((((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) * S ((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) + ((dst_negative_scale_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput))) + (((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) * S ((dst_negative_code_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)) + ((dst_negative_scale_append_sourceentryinput) + (dst_negative_scale_append_sourceentryinput)))))) /\ (((((exists ff_h_pvs_append_sourceentryinputpositive. ff_h_pvs_append_sourceentryinputpositive + S (dst_positive_append_sourceentryinput) = S ((S (dm_index_append_source)) * dst_positive_scale_append_sourceentryinput)) /\ exists ff_q_pvs_append_sourceentryinputpositive. dst_positive_code_append_sourceentryinput = ff_q_pvs_append_sourceentryinputpositive * S ((S (dm_index_append_source)) * dst_positive_scale_append_sourceentryinput) + (dst_positive_append_sourceentryinput))) /\ (((((exists ff_h_pvs_append_sourceentryinputnegative. ff_h_pvs_append_sourceentryinputnegative + S (dst_negative_append_sourceentryinput) = S ((S (dm_index_append_source)) * dst_negative_scale_append_sourceentryinput)) /\ exists ff_q_pvs_append_sourceentryinputnegative. dst_negative_code_append_sourceentryinput = ff_q_pvs_append_sourceentryinputnegative * S ((S (dm_index_append_source)) * dst_negative_scale_append_sourceentryinput) + (dst_negative_append_sourceentryinput))) /\ (exists ge_balance_positive_append_sourceentryinputvalue ge_balance_negative_append_sourceentryinputvalue. (((((dm_value_append_source) = 2 * (ge_balance_positive_append_sourceentryinputvalue) /\ (ge_balance_negative_append_sourceentryinputvalue) = 0) \/ exists ge_signed_half_append_sourceentryinputvaluedecode. (((dm_value_append_source) = 2 * ge_signed_half_append_sourceentryinputvaluedecode + 1 /\ (ge_balance_positive_append_sourceentryinputvalue) = 0) /\ (ge_balance_negative_append_sourceentryinputvalue) = S ge_signed_half_append_sourceentryinputvaluedecode))) /\ ((dst_positive_append_sourceentryinput) + ge_balance_negative_append_sourceentryinputvalue = (dst_negative_append_sourceentryinput) + ge_balance_positive_append_sourceentryinputvalue))))))))))))) \/ ((((dm_index_append_source)=0 \/ ~(exists pvs_factor_append_sourceentrynondivisor. (n) = (dm_index_append_source) * pvs_factor_append_sourceentrynondivisor)) /\ ((dm_value_append_source)=0))))))) -> ((((~((S l)=0)) /\ (exists dm_quotient_append_last. (((n)=(S l)*dm_quotient_append_last) /\ (exists dst_positive_code_append_lastinput dst_positive_scale_append_lastinput dst_negative_code_append_lastinput dst_negative_scale_append_lastinput dst_positive_append_lastinput dst_negative_append_lastinput. (((F) = (((((dst_positive_code_append_lastinput) + (dst_positive_scale_append_lastinput)) * S ((dst_positive_code_append_lastinput) + (dst_positive_scale_append_lastinput)) + ((dst_positive_scale_append_lastinput) + (dst_positive_scale_append_lastinput))) + (((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) * S ((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) + ((dst_negative_scale_append_lastinput) + (dst_negative_scale_append_lastinput)))) * S ((((dst_positive_code_append_lastinput) + (dst_positive_scale_append_lastinput)) * S ((dst_positive_code_append_lastinput) + (dst_positive_scale_append_lastinput)) + ((dst_positive_scale_append_lastinput) + (dst_positive_scale_append_lastinput))) + (((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) * S ((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) + ((dst_negative_scale_append_lastinput) + (dst_negative_scale_append_lastinput)))) + ((((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) * S ((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) + ((dst_negative_scale_append_lastinput) + (dst_negative_scale_append_lastinput))) + (((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) * S ((dst_negative_code_append_lastinput) + (dst_negative_scale_append_lastinput)) + ((dst_negative_scale_append_lastinput) + (dst_negative_scale_append_lastinput)))))) /\ (((((exists ff_h_pvs_append_lastinputpositive. ff_h_pvs_append_lastinputpositive + S (dst_positive_append_lastinput) = S ((S (S l)) * dst_positive_scale_append_lastinput)) /\ exists ff_q_pvs_append_lastinputpositive. dst_positive_code_append_lastinput = ff_q_pvs_append_lastinputpositive * S ((S (S l)) * dst_positive_scale_append_lastinput) + (dst_positive_append_lastinput))) /\ (((((exists ff_h_pvs_append_lastinputnegative. ff_h_pvs_append_lastinputnegative + S (dst_negative_append_lastinput) = S ((S (S l)) * dst_negative_scale_append_lastinput)) /\ exists ff_q_pvs_append_lastinputnegative. dst_negative_code_append_lastinput = ff_q_pvs_append_lastinputnegative * S ((S (S l)) * dst_negative_scale_append_lastinput) + (dst_negative_append_lastinput))) /\ (exists ge_balance_positive_append_lastinputvalue ge_balance_negative_append_lastinputvalue. (((((z) = 2 * (ge_balance_positive_append_lastinputvalue) /\ (ge_balance_negative_append_lastinputvalue) = 0) \/ exists ge_signed_half_append_lastinputvaluedecode. (((z) = 2 * ge_signed_half_append_lastinputvaluedecode + 1 /\ (ge_balance_positive_append_lastinputvalue) = 0) /\ (ge_balance_negative_append_lastinputvalue) = S ge_signed_half_append_lastinputvaluedecode))) /\ ((dst_positive_append_lastinput) + ge_balance_negative_append_lastinputvalue = (dst_negative_append_lastinput) + ge_balance_positive_append_lastinputvalue))))))))))))) \/ ((((S l)=0 \/ ~(exists pvs_factor_append_lastnondivisor. (n) = (S l) * pvs_factor_append_lastnondivisor)) /\ ((z)=0)))) -> exists G. (((exists dst_positive_code_append_resulttable dst_positive_scale_append_resulttable dst_negative_code_append_resulttable dst_negative_scale_append_resulttable. (((G) = (((((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) * S ((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) + ((dst_positive_scale_append_resulttable) + (dst_positive_scale_append_resulttable))) + (((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable)))) * S ((((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) * S ((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) + ((dst_positive_scale_append_resulttable) + (dst_positive_scale_append_resulttable))) + (((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable)))) + ((((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable))) + (((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable)))))) /\ (forall dst_index_append_resulttable. (exists pvs_le_gap_append_resulttabledomain. pvs_le_gap_append_resulttabledomain + (dst_index_append_resulttable) = (S l)) -> exists dst_positive_append_resulttable dst_negative_append_resulttable dst_value_append_resulttable. ((((exists ff_h_pvs_append_resulttableentrypositive. ff_h_pvs_append_resulttableentrypositive + S (dst_positive_append_resulttable) = S ((S (dst_index_append_resulttable)) * dst_positive_scale_append_resulttable)) /\ exists ff_q_pvs_append_resulttableentrypositive. dst_positive_code_append_resulttable = ff_q_pvs_append_resulttableentrypositive * S ((S (dst_index_append_resulttable)) * dst_positive_scale_append_resulttable) + (dst_positive_append_resulttable))) /\ (((((exists ff_h_pvs_append_resulttableentrynegative. ff_h_pvs_append_resulttableentrynegative + S (dst_negative_append_resulttable) = S ((S (dst_index_append_resulttable)) * dst_negative_scale_append_resulttable)) /\ exists ff_q_pvs_append_resulttableentrynegative. dst_negative_code_append_resulttable = ff_q_pvs_append_resulttableentrynegative * S ((S (dst_index_append_resulttable)) * dst_negative_scale_append_resulttable) + (dst_negative_append_resulttable))) /\ (exists ge_balance_positive_append_resulttableentryvalue ge_balance_negative_append_resulttableentryvalue. (((((dst_value_append_resulttable) = 2 * (ge_balance_positive_append_resulttableentryvalue) /\ (ge_balance_negative_append_resulttableentryvalue) = 0) \/ exists ge_signed_half_append_resulttableentryvaluedecode. (((dst_value_append_resulttable) = 2 * ge_signed_half_append_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_append_resulttableentryvalue) = 0) /\ (ge_balance_negative_append_resulttableentryvalue) = S ge_signed_half_append_resulttableentryvaluedecode))) /\ ((dst_positive_append_resulttable) + ge_balance_negative_append_resulttableentryvalue = (dst_negative_append_resulttable) + ge_balance_positive_append_resulttableentryvalue))))))))) /\ (forall dm_index_append_result dm_value_append_result. (exists pvs_le_gap_append_resultdomain. pvs_le_gap_append_resultdomain + (dm_index_append_result) = (S l)) -> (exists dst_positive_code_append_resultlookup dst_positive_scale_append_resultlookup dst_negative_code_append_resultlookup dst_negative_scale_append_resultlookup dst_positive_append_resultlookup dst_negative_append_resultlookup. (((G) = (((((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) * S ((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) + ((dst_positive_scale_append_resultlookup) + (dst_positive_scale_append_resultlookup))) + (((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup)))) * S ((((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) * S ((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) + ((dst_positive_scale_append_resultlookup) + (dst_positive_scale_append_resultlookup))) + (((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup)))) + ((((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup))) + (((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup)))))) /\ (((((exists ff_h_pvs_append_resultlookuppositive. ff_h_pvs_append_resultlookuppositive + S (dst_positive_append_resultlookup) = S ((S (dm_index_append_result)) * dst_positive_scale_append_resultlookup)) /\ exists ff_q_pvs_append_resultlookuppositive. dst_positive_code_append_resultlookup = ff_q_pvs_append_resultlookuppositive * S ((S (dm_index_append_result)) * dst_positive_scale_append_resultlookup) + (dst_positive_append_resultlookup))) /\ (((((exists ff_h_pvs_append_resultlookupnegative. ff_h_pvs_append_resultlookupnegative + S (dst_negative_append_resultlookup) = S ((S (dm_index_append_result)) * dst_negative_scale_append_resultlookup)) /\ exists ff_q_pvs_append_resultlookupnegative. dst_negative_code_append_resultlookup = ff_q_pvs_append_resultlookupnegative * S ((S (dm_index_append_result)) * dst_negative_scale_append_resultlookup) + (dst_negative_append_resultlookup))) /\ (exists ge_balance_positive_append_resultlookupvalue ge_balance_negative_append_resultlookupvalue. (((((dm_value_append_result) = 2 * (ge_balance_positive_append_resultlookupvalue) /\ (ge_balance_negative_append_resultlookupvalue) = 0) \/ exists ge_signed_half_append_resultlookupvaluedecode. (((dm_value_append_result) = 2 * ge_signed_half_append_resultlookupvaluedecode + 1 /\ (ge_balance_positive_append_resultlookupvalue) = 0) /\ (ge_balance_negative_append_resultlookupvalue) = S ge_signed_half_append_resultlookupvaluedecode))) /\ ((dst_positive_append_resultlookup) + ge_balance_negative_append_resultlookupvalue = (dst_negative_append_resultlookup) + ge_balance_positive_append_resultlookupvalue))))))))) -> ((((~((dm_index_append_result)=0)) /\ (exists dm_quotient_append_resultentry. (((n)=(dm_index_append_result)*dm_quotient_append_resultentry) /\ (exists dst_positive_code_append_resultentryinput dst_positive_scale_append_resultentryinput dst_negative_code_append_resultentryinput dst_negative_scale_append_resultentryinput dst_positive_append_resultentryinput dst_negative_append_resultentryinput. (((F) = (((((dst_positive_code_append_resultentryinput) + (dst_positive_scale_append_resultentryinput)) * S ((dst_positive_code_append_resultentryinput) + (dst_positive_scale_append_resultentryinput)) + ((dst_positive_scale_append_resultentryinput) + (dst_positive_scale_append_resultentryinput))) + (((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) * S ((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) + ((dst_negative_scale_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)))) * S ((((dst_positive_code_append_resultentryinput) + (dst_positive_scale_append_resultentryinput)) * S ((dst_positive_code_append_resultentryinput) + (dst_positive_scale_append_resultentryinput)) + ((dst_positive_scale_append_resultentryinput) + (dst_positive_scale_append_resultentryinput))) + (((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) * S ((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) + ((dst_negative_scale_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)))) + ((((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) * S ((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) + ((dst_negative_scale_append_resultentryinput) + (dst_negative_scale_append_resultentryinput))) + (((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) * S ((dst_negative_code_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)) + ((dst_negative_scale_append_resultentryinput) + (dst_negative_scale_append_resultentryinput)))))) /\ (((((exists ff_h_pvs_append_resultentryinputpositive. ff_h_pvs_append_resultentryinputpositive + S (dst_positive_append_resultentryinput) = S ((S (dm_index_append_result)) * dst_positive_scale_append_resultentryinput)) /\ exists ff_q_pvs_append_resultentryinputpositive. dst_positive_code_append_resultentryinput = ff_q_pvs_append_resultentryinputpositive * S ((S (dm_index_append_result)) * dst_positive_scale_append_resultentryinput) + (dst_positive_append_resultentryinput))) /\ (((((exists ff_h_pvs_append_resultentryinputnegative. ff_h_pvs_append_resultentryinputnegative + S (dst_negative_append_resultentryinput) = S ((S (dm_index_append_result)) * dst_negative_scale_append_resultentryinput)) /\ exists ff_q_pvs_append_resultentryinputnegative. dst_negative_code_append_resultentryinput = ff_q_pvs_append_resultentryinputnegative * S ((S (dm_index_append_result)) * dst_negative_scale_append_resultentryinput) + (dst_negative_append_resultentryinput))) /\ (exists ge_balance_positive_append_resultentryinputvalue ge_balance_negative_append_resultentryinputvalue. (((((dm_value_append_result) = 2 * (ge_balance_positive_append_resultentryinputvalue) /\ (ge_balance_negative_append_resultentryinputvalue) = 0) \/ exists ge_signed_half_append_resultentryinputvaluedecode. (((dm_value_append_result) = 2 * ge_signed_half_append_resultentryinputvaluedecode + 1 /\ (ge_balance_positive_append_resultentryinputvalue) = 0) /\ (ge_balance_negative_append_resultentryinputvalue) = S ge_signed_half_append_resultentryinputvaluedecode))) /\ ((dst_positive_append_resultentryinput) + ge_balance_negative_append_resultentryinputvalue = (dst_negative_append_resultentryinput) + ge_balance_positive_append_resultentryinputvalue))))))))))))) \/ ((((dm_index_append_result)=0 \/ ~(exists pvs_factor_append_resultentrynondivisor. (n) = (dm_index_append_result) * pvs_factor_append_resultentrynondivisor)) /\ ((dm_value_append_result)=0))))))) /\ (forall dst_index_append_equal dst_first_append_equal dst_second_append_equal. (exists pvs_gap_append_equalbound. pvs_gap_append_equalbound + S (dst_index_append_equal) = (S l)) -> (exists dst_positive_code_append_equalfirst dst_positive_scale_append_equalfirst dst_negative_code_append_equalfirst dst_negative_scale_append_equalfirst dst_positive_append_equalfirst dst_negative_append_equalfirst. (((M) = (((((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) * S ((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) + ((dst_positive_scale_append_equalfirst) + (dst_positive_scale_append_equalfirst))) + (((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst)))) * S ((((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) * S ((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) + ((dst_positive_scale_append_equalfirst) + (dst_positive_scale_append_equalfirst))) + (((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst)))) + ((((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst))) + (((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst)))))) /\ (((((exists ff_h_pvs_append_equalfirstpositive. ff_h_pvs_append_equalfirstpositive + S (dst_positive_append_equalfirst) = S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalfirst)) /\ exists ff_q_pvs_append_equalfirstpositive. dst_positive_code_append_equalfirst = ff_q_pvs_append_equalfirstpositive * S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalfirst) + (dst_positive_append_equalfirst))) /\ (((((exists ff_h_pvs_append_equalfirstnegative. ff_h_pvs_append_equalfirstnegative + S (dst_negative_append_equalfirst) = S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalfirst)) /\ exists ff_q_pvs_append_equalfirstnegative. dst_negative_code_append_equalfirst = ff_q_pvs_append_equalfirstnegative * S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalfirst) + (dst_negative_append_equalfirst))) /\ (exists ge_balance_positive_append_equalfirstvalue ge_balance_negative_append_equalfirstvalue. (((((dst_first_append_equal) = 2 * (ge_balance_positive_append_equalfirstvalue) /\ (ge_balance_negative_append_equalfirstvalue) = 0) \/ exists ge_signed_half_append_equalfirstvaluedecode. (((dst_first_append_equal) = 2 * ge_signed_half_append_equalfirstvaluedecode + 1 /\ (ge_balance_positive_append_equalfirstvalue) = 0) /\ (ge_balance_negative_append_equalfirstvalue) = S ge_signed_half_append_equalfirstvaluedecode))) /\ ((dst_positive_append_equalfirst) + ge_balance_negative_append_equalfirstvalue = (dst_negative_append_equalfirst) + ge_balance_positive_append_equalfirstvalue))))))))) -> (exists dst_positive_code_append_equalsecond dst_positive_scale_append_equalsecond dst_negative_code_append_equalsecond dst_negative_scale_append_equalsecond dst_positive_append_equalsecond dst_negative_append_equalsecond. (((G) = (((((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) * S ((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) + ((dst_positive_scale_append_equalsecond) + (dst_positive_scale_append_equalsecond))) + (((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond)))) * S ((((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) * S ((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) + ((dst_positive_scale_append_equalsecond) + (dst_positive_scale_append_equalsecond))) + (((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond)))) + ((((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond))) + (((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond)))))) /\ (((((exists ff_h_pvs_append_equalsecondpositive. ff_h_pvs_append_equalsecondpositive + S (dst_positive_append_equalsecond) = S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalsecond)) /\ exists ff_q_pvs_append_equalsecondpositive. dst_positive_code_append_equalsecond = ff_q_pvs_append_equalsecondpositive * S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalsecond) + (dst_positive_append_equalsecond))) /\ (((((exists ff_h_pvs_append_equalsecondnegative. ff_h_pvs_append_equalsecondnegative + S (dst_negative_append_equalsecond) = S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalsecond)) /\ exists ff_q_pvs_append_equalsecondnegative. dst_negative_code_append_equalsecond = ff_q_pvs_append_equalsecondnegative * S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalsecond) + (dst_negative_append_equalsecond))) /\ (exists ge_balance_positive_append_equalsecondvalue ge_balance_negative_append_equalsecondvalue. (((((dst_second_append_equal) = 2 * (ge_balance_positive_append_equalsecondvalue) /\ (ge_balance_negative_append_equalsecondvalue) = 0) \/ exists ge_signed_half_append_equalsecondvaluedecode. (((dst_second_append_equal) = 2 * ge_signed_half_append_equalsecondvaluedecode + 1 /\ (ge_balance_positive_append_equalsecondvalue) = 0) /\ (ge_balance_negative_append_equalsecondvalue) = S ge_signed_half_append_equalsecondvaluedecode))) /\ ((dst_positive_append_equalsecond) + ge_balance_negative_append_equalsecondvalue = (dst_negative_append_equalsecond) + ge_balance_positive_append_equalsecondvalue))))))))) -> dst_first_append_equal = dst_second_append_equal)

divisor_mask_prefix_exists

new owned theorem · read exact theorem evidence

Bundle node 301; exact statement SHA-256 f99a5b3c20eeffe48ac81ab98325b71f26b31ef460d755548f4a8b3fa70e54f7

Exact first-order statement

forall N F n l. (exists dst_positive_code_exists_input dst_positive_scale_exists_input dst_negative_code_exists_input dst_negative_scale_exists_input. (((F) = (((((dst_positive_code_exists_input) + (dst_positive_scale_exists_input)) * S ((dst_positive_code_exists_input) + (dst_positive_scale_exists_input)) + ((dst_positive_scale_exists_input) + (dst_positive_scale_exists_input))) + (((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) * S ((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) + ((dst_negative_scale_exists_input) + (dst_negative_scale_exists_input)))) * S ((((dst_positive_code_exists_input) + (dst_positive_scale_exists_input)) * S ((dst_positive_code_exists_input) + (dst_positive_scale_exists_input)) + ((dst_positive_scale_exists_input) + (dst_positive_scale_exists_input))) + (((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) * S ((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) + ((dst_negative_scale_exists_input) + (dst_negative_scale_exists_input)))) + ((((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) * S ((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) + ((dst_negative_scale_exists_input) + (dst_negative_scale_exists_input))) + (((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) * S ((dst_negative_code_exists_input) + (dst_negative_scale_exists_input)) + ((dst_negative_scale_exists_input) + (dst_negative_scale_exists_input)))))) /\ (forall dst_index_exists_input. (exists pvs_le_gap_exists_inputdomain. pvs_le_gap_exists_inputdomain + (dst_index_exists_input) = (N)) -> exists dst_positive_exists_input dst_negative_exists_input dst_value_exists_input. ((((exists ff_h_pvs_exists_inputentrypositive. ff_h_pvs_exists_inputentrypositive + S (dst_positive_exists_input) = S ((S (dst_index_exists_input)) * dst_positive_scale_exists_input)) /\ exists ff_q_pvs_exists_inputentrypositive. dst_positive_code_exists_input = ff_q_pvs_exists_inputentrypositive * S ((S (dst_index_exists_input)) * dst_positive_scale_exists_input) + (dst_positive_exists_input))) /\ (((((exists ff_h_pvs_exists_inputentrynegative. ff_h_pvs_exists_inputentrynegative + S (dst_negative_exists_input) = S ((S (dst_index_exists_input)) * dst_negative_scale_exists_input)) /\ exists ff_q_pvs_exists_inputentrynegative. dst_negative_code_exists_input = ff_q_pvs_exists_inputentrynegative * S ((S (dst_index_exists_input)) * dst_negative_scale_exists_input) + (dst_negative_exists_input))) /\ (exists ge_balance_positive_exists_inputentryvalue ge_balance_negative_exists_inputentryvalue. (((((dst_value_exists_input) = 2 * (ge_balance_positive_exists_inputentryvalue) /\ (ge_balance_negative_exists_inputentryvalue) = 0) \/ exists ge_signed_half_exists_inputentryvaluedecode. (((dst_value_exists_input) = 2 * ge_signed_half_exists_inputentryvaluedecode + 1 /\ (ge_balance_positive_exists_inputentryvalue) = 0) /\ (ge_balance_negative_exists_inputentryvalue) = S ge_signed_half_exists_inputentryvaluedecode))) /\ ((dst_positive_exists_input) + ge_balance_negative_exists_inputentryvalue = (dst_negative_exists_input) + ge_balance_positive_exists_inputentryvalue))))))))) -> (exists pvs_le_gap_exists_bound. pvs_le_gap_exists_bound + (l) = (N)) -> exists M. (((exists dst_positive_code_exists_masktable dst_positive_scale_exists_masktable dst_negative_code_exists_masktable dst_negative_scale_exists_masktable. (((M) = (((((dst_positive_code_exists_masktable) + (dst_positive_scale_exists_masktable)) * S ((dst_positive_code_exists_masktable) + (dst_positive_scale_exists_masktable)) + ((dst_positive_scale_exists_masktable) + (dst_positive_scale_exists_masktable))) + (((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) * S ((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) + ((dst_negative_scale_exists_masktable) + (dst_negative_scale_exists_masktable)))) * S ((((dst_positive_code_exists_masktable) + (dst_positive_scale_exists_masktable)) * S ((dst_positive_code_exists_masktable) + (dst_positive_scale_exists_masktable)) + ((dst_positive_scale_exists_masktable) + (dst_positive_scale_exists_masktable))) + (((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) * S ((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) + ((dst_negative_scale_exists_masktable) + (dst_negative_scale_exists_masktable)))) + ((((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) * S ((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) + ((dst_negative_scale_exists_masktable) + (dst_negative_scale_exists_masktable))) + (((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) * S ((dst_negative_code_exists_masktable) + (dst_negative_scale_exists_masktable)) + ((dst_negative_scale_exists_masktable) + (dst_negative_scale_exists_masktable)))))) /\ (forall dst_index_exists_masktable. (exists pvs_le_gap_exists_masktabledomain. pvs_le_gap_exists_masktabledomain + (dst_index_exists_masktable) = (l)) -> exists dst_positive_exists_masktable dst_negative_exists_masktable dst_value_exists_masktable. ((((exists ff_h_pvs_exists_masktableentrypositive. ff_h_pvs_exists_masktableentrypositive + S (dst_positive_exists_masktable) = S ((S (dst_index_exists_masktable)) * dst_positive_scale_exists_masktable)) /\ exists ff_q_pvs_exists_masktableentrypositive. dst_positive_code_exists_masktable = ff_q_pvs_exists_masktableentrypositive * S ((S (dst_index_exists_masktable)) * dst_positive_scale_exists_masktable) + (dst_positive_exists_masktable))) /\ (((((exists ff_h_pvs_exists_masktableentrynegative. ff_h_pvs_exists_masktableentrynegative + S (dst_negative_exists_masktable) = S ((S (dst_index_exists_masktable)) * dst_negative_scale_exists_masktable)) /\ exists ff_q_pvs_exists_masktableentrynegative. dst_negative_code_exists_masktable = ff_q_pvs_exists_masktableentrynegative * S ((S (dst_index_exists_masktable)) * dst_negative_scale_exists_masktable) + (dst_negative_exists_masktable))) /\ (exists ge_balance_positive_exists_masktableentryvalue ge_balance_negative_exists_masktableentryvalue. (((((dst_value_exists_masktable) = 2 * (ge_balance_positive_exists_masktableentryvalue) /\ (ge_balance_negative_exists_masktableentryvalue) = 0) \/ exists ge_signed_half_exists_masktableentryvaluedecode. (((dst_value_exists_masktable) = 2 * ge_signed_half_exists_masktableentryvaluedecode + 1 /\ (ge_balance_positive_exists_masktableentryvalue) = 0) /\ (ge_balance_negative_exists_masktableentryvalue) = S ge_signed_half_exists_masktableentryvaluedecode))) /\ ((dst_positive_exists_masktable) + ge_balance_negative_exists_masktableentryvalue = (dst_negative_exists_masktable) + ge_balance_positive_exists_masktableentryvalue))))))))) /\ (forall dm_index_exists_mask dm_value_exists_mask. (exists pvs_le_gap_exists_maskdomain. pvs_le_gap_exists_maskdomain + (dm_index_exists_mask) = (l)) -> (exists dst_positive_code_exists_masklookup dst_positive_scale_exists_masklookup dst_negative_code_exists_masklookup dst_negative_scale_exists_masklookup dst_positive_exists_masklookup dst_negative_exists_masklookup. (((M) = (((((dst_positive_code_exists_masklookup) + (dst_positive_scale_exists_masklookup)) * S ((dst_positive_code_exists_masklookup) + (dst_positive_scale_exists_masklookup)) + ((dst_positive_scale_exists_masklookup) + (dst_positive_scale_exists_masklookup))) + (((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) * S ((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) + ((dst_negative_scale_exists_masklookup) + (dst_negative_scale_exists_masklookup)))) * S ((((dst_positive_code_exists_masklookup) + (dst_positive_scale_exists_masklookup)) * S ((dst_positive_code_exists_masklookup) + (dst_positive_scale_exists_masklookup)) + ((dst_positive_scale_exists_masklookup) + (dst_positive_scale_exists_masklookup))) + (((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) * S ((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) + ((dst_negative_scale_exists_masklookup) + (dst_negative_scale_exists_masklookup)))) + ((((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) * S ((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) + ((dst_negative_scale_exists_masklookup) + (dst_negative_scale_exists_masklookup))) + (((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) * S ((dst_negative_code_exists_masklookup) + (dst_negative_scale_exists_masklookup)) + ((dst_negative_scale_exists_masklookup) + (dst_negative_scale_exists_masklookup)))))) /\ (((((exists ff_h_pvs_exists_masklookuppositive. ff_h_pvs_exists_masklookuppositive + S (dst_positive_exists_masklookup) = S ((S (dm_index_exists_mask)) * dst_positive_scale_exists_masklookup)) /\ exists ff_q_pvs_exists_masklookuppositive. dst_positive_code_exists_masklookup = ff_q_pvs_exists_masklookuppositive * S ((S (dm_index_exists_mask)) * dst_positive_scale_exists_masklookup) + (dst_positive_exists_masklookup))) /\ (((((exists ff_h_pvs_exists_masklookupnegative. ff_h_pvs_exists_masklookupnegative + S (dst_negative_exists_masklookup) = S ((S (dm_index_exists_mask)) * dst_negative_scale_exists_masklookup)) /\ exists ff_q_pvs_exists_masklookupnegative. dst_negative_code_exists_masklookup = ff_q_pvs_exists_masklookupnegative * S ((S (dm_index_exists_mask)) * dst_negative_scale_exists_masklookup) + (dst_negative_exists_masklookup))) /\ (exists ge_balance_positive_exists_masklookupvalue ge_balance_negative_exists_masklookupvalue. (((((dm_value_exists_mask) = 2 * (ge_balance_positive_exists_masklookupvalue) /\ (ge_balance_negative_exists_masklookupvalue) = 0) \/ exists ge_signed_half_exists_masklookupvaluedecode. (((dm_value_exists_mask) = 2 * ge_signed_half_exists_masklookupvaluedecode + 1 /\ (ge_balance_positive_exists_masklookupvalue) = 0) /\ (ge_balance_negative_exists_masklookupvalue) = S ge_signed_half_exists_masklookupvaluedecode))) /\ ((dst_positive_exists_masklookup) + ge_balance_negative_exists_masklookupvalue = (dst_negative_exists_masklookup) + ge_balance_positive_exists_masklookupvalue))))))))) -> ((((~((dm_index_exists_mask)=0)) /\ (exists dm_quotient_exists_maskentry. (((n)=(dm_index_exists_mask)*dm_quotient_exists_maskentry) /\ (exists dst_positive_code_exists_maskentryinput dst_positive_scale_exists_maskentryinput dst_negative_code_exists_maskentryinput dst_negative_scale_exists_maskentryinput dst_positive_exists_maskentryinput dst_negative_exists_maskentryinput. (((F) = (((((dst_positive_code_exists_maskentryinput) + (dst_positive_scale_exists_maskentryinput)) * S ((dst_positive_code_exists_maskentryinput) + (dst_positive_scale_exists_maskentryinput)) + ((dst_positive_scale_exists_maskentryinput) + (dst_positive_scale_exists_maskentryinput))) + (((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) * S ((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) + ((dst_negative_scale_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)))) * S ((((dst_positive_code_exists_maskentryinput) + (dst_positive_scale_exists_maskentryinput)) * S ((dst_positive_code_exists_maskentryinput) + (dst_positive_scale_exists_maskentryinput)) + ((dst_positive_scale_exists_maskentryinput) + (dst_positive_scale_exists_maskentryinput))) + (((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) * S ((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) + ((dst_negative_scale_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)))) + ((((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) * S ((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) + ((dst_negative_scale_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput))) + (((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) * S ((dst_negative_code_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)) + ((dst_negative_scale_exists_maskentryinput) + (dst_negative_scale_exists_maskentryinput)))))) /\ (((((exists ff_h_pvs_exists_maskentryinputpositive. ff_h_pvs_exists_maskentryinputpositive + S (dst_positive_exists_maskentryinput) = S ((S (dm_index_exists_mask)) * dst_positive_scale_exists_maskentryinput)) /\ exists ff_q_pvs_exists_maskentryinputpositive. dst_positive_code_exists_maskentryinput = ff_q_pvs_exists_maskentryinputpositive * S ((S (dm_index_exists_mask)) * dst_positive_scale_exists_maskentryinput) + (dst_positive_exists_maskentryinput))) /\ (((((exists ff_h_pvs_exists_maskentryinputnegative. ff_h_pvs_exists_maskentryinputnegative + S (dst_negative_exists_maskentryinput) = S ((S (dm_index_exists_mask)) * dst_negative_scale_exists_maskentryinput)) /\ exists ff_q_pvs_exists_maskentryinputnegative. dst_negative_code_exists_maskentryinput = ff_q_pvs_exists_maskentryinputnegative * S ((S (dm_index_exists_mask)) * dst_negative_scale_exists_maskentryinput) + (dst_negative_exists_maskentryinput))) /\ (exists ge_balance_positive_exists_maskentryinputvalue ge_balance_negative_exists_maskentryinputvalue. (((((dm_value_exists_mask) = 2 * (ge_balance_positive_exists_maskentryinputvalue) /\ (ge_balance_negative_exists_maskentryinputvalue) = 0) \/ exists ge_signed_half_exists_maskentryinputvaluedecode. (((dm_value_exists_mask) = 2 * ge_signed_half_exists_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_exists_maskentryinputvalue) = 0) /\ (ge_balance_negative_exists_maskentryinputvalue) = S ge_signed_half_exists_maskentryinputvaluedecode))) /\ ((dst_positive_exists_maskentryinput) + ge_balance_negative_exists_maskentryinputvalue = (dst_negative_exists_maskentryinput) + ge_balance_positive_exists_maskentryinputvalue))))))))))))) \/ ((((dm_index_exists_mask)=0 \/ ~(exists pvs_factor_exists_maskentrynondivisor. (n) = (dm_index_exists_mask) * pvs_factor_exists_maskentrynondivisor)) /\ ((dm_value_exists_mask)=0)))))))

divisor_mask_prefix_extensional

new owned theorem · read exact theorem evidence

Bundle node 302; exact statement SHA-256 a66c126f6e1a95f8dc7f9b20f87d965da7ddf1c765e0cef33da9a3060ac6f319

Exact first-order statement

forall F n l M K. (((exists dst_positive_code_unique_first_masktable dst_positive_scale_unique_first_masktable dst_negative_code_unique_first_masktable dst_negative_scale_unique_first_masktable. (((M) = (((((dst_positive_code_unique_first_masktable) + (dst_positive_scale_unique_first_masktable)) * S ((dst_positive_code_unique_first_masktable) + (dst_positive_scale_unique_first_masktable)) + ((dst_positive_scale_unique_first_masktable) + (dst_positive_scale_unique_first_masktable))) + (((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) * S ((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) + ((dst_negative_scale_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)))) * S ((((dst_positive_code_unique_first_masktable) + (dst_positive_scale_unique_first_masktable)) * S ((dst_positive_code_unique_first_masktable) + (dst_positive_scale_unique_first_masktable)) + ((dst_positive_scale_unique_first_masktable) + (dst_positive_scale_unique_first_masktable))) + (((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) * S ((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) + ((dst_negative_scale_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)))) + ((((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) * S ((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) + ((dst_negative_scale_unique_first_masktable) + (dst_negative_scale_unique_first_masktable))) + (((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) * S ((dst_negative_code_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)) + ((dst_negative_scale_unique_first_masktable) + (dst_negative_scale_unique_first_masktable)))))) /\ (forall dst_index_unique_first_masktable. (exists pvs_le_gap_unique_first_masktabledomain. pvs_le_gap_unique_first_masktabledomain + (dst_index_unique_first_masktable) = (l)) -> exists dst_positive_unique_first_masktable dst_negative_unique_first_masktable dst_value_unique_first_masktable. ((((exists ff_h_pvs_unique_first_masktableentrypositive. ff_h_pvs_unique_first_masktableentrypositive + S (dst_positive_unique_first_masktable) = S ((S (dst_index_unique_first_masktable)) * dst_positive_scale_unique_first_masktable)) /\ exists ff_q_pvs_unique_first_masktableentrypositive. dst_positive_code_unique_first_masktable = ff_q_pvs_unique_first_masktableentrypositive * S ((S (dst_index_unique_first_masktable)) * dst_positive_scale_unique_first_masktable) + (dst_positive_unique_first_masktable))) /\ (((((exists ff_h_pvs_unique_first_masktableentrynegative. ff_h_pvs_unique_first_masktableentrynegative + S (dst_negative_unique_first_masktable) = S ((S (dst_index_unique_first_masktable)) * dst_negative_scale_unique_first_masktable)) /\ exists ff_q_pvs_unique_first_masktableentrynegative. dst_negative_code_unique_first_masktable = ff_q_pvs_unique_first_masktableentrynegative * S ((S (dst_index_unique_first_masktable)) * dst_negative_scale_unique_first_masktable) + (dst_negative_unique_first_masktable))) /\ (exists ge_balance_positive_unique_first_masktableentryvalue ge_balance_negative_unique_first_masktableentryvalue. (((((dst_value_unique_first_masktable) = 2 * (ge_balance_positive_unique_first_masktableentryvalue) /\ (ge_balance_negative_unique_first_masktableentryvalue) = 0) \/ exists ge_signed_half_unique_first_masktableentryvaluedecode. (((dst_value_unique_first_masktable) = 2 * ge_signed_half_unique_first_masktableentryvaluedecode + 1 /\ (ge_balance_positive_unique_first_masktableentryvalue) = 0) /\ (ge_balance_negative_unique_first_masktableentryvalue) = S ge_signed_half_unique_first_masktableentryvaluedecode))) /\ ((dst_positive_unique_first_masktable) + ge_balance_negative_unique_first_masktableentryvalue = (dst_negative_unique_first_masktable) + ge_balance_positive_unique_first_masktableentryvalue))))))))) /\ (forall dm_index_unique_first_mask dm_value_unique_first_mask. (exists pvs_le_gap_unique_first_maskdomain. pvs_le_gap_unique_first_maskdomain + (dm_index_unique_first_mask) = (l)) -> (exists dst_positive_code_unique_first_masklookup dst_positive_scale_unique_first_masklookup dst_negative_code_unique_first_masklookup dst_negative_scale_unique_first_masklookup dst_positive_unique_first_masklookup dst_negative_unique_first_masklookup. (((M) = (((((dst_positive_code_unique_first_masklookup) + (dst_positive_scale_unique_first_masklookup)) * S ((dst_positive_code_unique_first_masklookup) + (dst_positive_scale_unique_first_masklookup)) + ((dst_positive_scale_unique_first_masklookup) + (dst_positive_scale_unique_first_masklookup))) + (((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) * S ((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) + ((dst_negative_scale_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)))) * S ((((dst_positive_code_unique_first_masklookup) + (dst_positive_scale_unique_first_masklookup)) * S ((dst_positive_code_unique_first_masklookup) + (dst_positive_scale_unique_first_masklookup)) + ((dst_positive_scale_unique_first_masklookup) + (dst_positive_scale_unique_first_masklookup))) + (((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) * S ((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) + ((dst_negative_scale_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)))) + ((((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) * S ((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) + ((dst_negative_scale_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup))) + (((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) * S ((dst_negative_code_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)) + ((dst_negative_scale_unique_first_masklookup) + (dst_negative_scale_unique_first_masklookup)))))) /\ (((((exists ff_h_pvs_unique_first_masklookuppositive. ff_h_pvs_unique_first_masklookuppositive + S (dst_positive_unique_first_masklookup) = S ((S (dm_index_unique_first_mask)) * dst_positive_scale_unique_first_masklookup)) /\ exists ff_q_pvs_unique_first_masklookuppositive. dst_positive_code_unique_first_masklookup = ff_q_pvs_unique_first_masklookuppositive * S ((S (dm_index_unique_first_mask)) * dst_positive_scale_unique_first_masklookup) + (dst_positive_unique_first_masklookup))) /\ (((((exists ff_h_pvs_unique_first_masklookupnegative. ff_h_pvs_unique_first_masklookupnegative + S (dst_negative_unique_first_masklookup) = S ((S (dm_index_unique_first_mask)) * dst_negative_scale_unique_first_masklookup)) /\ exists ff_q_pvs_unique_first_masklookupnegative. dst_negative_code_unique_first_masklookup = ff_q_pvs_unique_first_masklookupnegative * S ((S (dm_index_unique_first_mask)) * dst_negative_scale_unique_first_masklookup) + (dst_negative_unique_first_masklookup))) /\ (exists ge_balance_positive_unique_first_masklookupvalue ge_balance_negative_unique_first_masklookupvalue. (((((dm_value_unique_first_mask) = 2 * (ge_balance_positive_unique_first_masklookupvalue) /\ (ge_balance_negative_unique_first_masklookupvalue) = 0) \/ exists ge_signed_half_unique_first_masklookupvaluedecode. (((dm_value_unique_first_mask) = 2 * ge_signed_half_unique_first_masklookupvaluedecode + 1 /\ (ge_balance_positive_unique_first_masklookupvalue) = 0) /\ (ge_balance_negative_unique_first_masklookupvalue) = S ge_signed_half_unique_first_masklookupvaluedecode))) /\ ((dst_positive_unique_first_masklookup) + ge_balance_negative_unique_first_masklookupvalue = (dst_negative_unique_first_masklookup) + ge_balance_positive_unique_first_masklookupvalue))))))))) -> ((((~((dm_index_unique_first_mask)=0)) /\ (exists dm_quotient_unique_first_maskentry. (((n)=(dm_index_unique_first_mask)*dm_quotient_unique_first_maskentry) /\ (exists dst_positive_code_unique_first_maskentryinput dst_positive_scale_unique_first_maskentryinput dst_negative_code_unique_first_maskentryinput dst_negative_scale_unique_first_maskentryinput dst_positive_unique_first_maskentryinput dst_negative_unique_first_maskentryinput. (((F) = (((((dst_positive_code_unique_first_maskentryinput) + (dst_positive_scale_unique_first_maskentryinput)) * S ((dst_positive_code_unique_first_maskentryinput) + (dst_positive_scale_unique_first_maskentryinput)) + ((dst_positive_scale_unique_first_maskentryinput) + (dst_positive_scale_unique_first_maskentryinput))) + (((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) * S ((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) + ((dst_negative_scale_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)))) * S ((((dst_positive_code_unique_first_maskentryinput) + (dst_positive_scale_unique_first_maskentryinput)) * S ((dst_positive_code_unique_first_maskentryinput) + (dst_positive_scale_unique_first_maskentryinput)) + ((dst_positive_scale_unique_first_maskentryinput) + (dst_positive_scale_unique_first_maskentryinput))) + (((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) * S ((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) + ((dst_negative_scale_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)))) + ((((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) * S ((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) + ((dst_negative_scale_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput))) + (((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) * S ((dst_negative_code_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)) + ((dst_negative_scale_unique_first_maskentryinput) + (dst_negative_scale_unique_first_maskentryinput)))))) /\ (((((exists ff_h_pvs_unique_first_maskentryinputpositive. ff_h_pvs_unique_first_maskentryinputpositive + S (dst_positive_unique_first_maskentryinput) = S ((S (dm_index_unique_first_mask)) * dst_positive_scale_unique_first_maskentryinput)) /\ exists ff_q_pvs_unique_first_maskentryinputpositive. dst_positive_code_unique_first_maskentryinput = ff_q_pvs_unique_first_maskentryinputpositive * S ((S (dm_index_unique_first_mask)) * dst_positive_scale_unique_first_maskentryinput) + (dst_positive_unique_first_maskentryinput))) /\ (((((exists ff_h_pvs_unique_first_maskentryinputnegative. ff_h_pvs_unique_first_maskentryinputnegative + S (dst_negative_unique_first_maskentryinput) = S ((S (dm_index_unique_first_mask)) * dst_negative_scale_unique_first_maskentryinput)) /\ exists ff_q_pvs_unique_first_maskentryinputnegative. dst_negative_code_unique_first_maskentryinput = ff_q_pvs_unique_first_maskentryinputnegative * S ((S (dm_index_unique_first_mask)) * dst_negative_scale_unique_first_maskentryinput) + (dst_negative_unique_first_maskentryinput))) /\ (exists ge_balance_positive_unique_first_maskentryinputvalue ge_balance_negative_unique_first_maskentryinputvalue. (((((dm_value_unique_first_mask) = 2 * (ge_balance_positive_unique_first_maskentryinputvalue) /\ (ge_balance_negative_unique_first_maskentryinputvalue) = 0) \/ exists ge_signed_half_unique_first_maskentryinputvaluedecode. (((dm_value_unique_first_mask) = 2 * ge_signed_half_unique_first_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_unique_first_maskentryinputvalue) = 0) /\ (ge_balance_negative_unique_first_maskentryinputvalue) = S ge_signed_half_unique_first_maskentryinputvaluedecode))) /\ ((dst_positive_unique_first_maskentryinput) + ge_balance_negative_unique_first_maskentryinputvalue = (dst_negative_unique_first_maskentryinput) + ge_balance_positive_unique_first_maskentryinputvalue))))))))))))) \/ ((((dm_index_unique_first_mask)=0 \/ ~(exists pvs_factor_unique_first_maskentrynondivisor. (n) = (dm_index_unique_first_mask) * pvs_factor_unique_first_maskentrynondivisor)) /\ ((dm_value_unique_first_mask)=0))))))) -> (((exists dst_positive_code_unique_second_masktable dst_positive_scale_unique_second_masktable dst_negative_code_unique_second_masktable dst_negative_scale_unique_second_masktable. (((K) = (((((dst_positive_code_unique_second_masktable) + (dst_positive_scale_unique_second_masktable)) * S ((dst_positive_code_unique_second_masktable) + (dst_positive_scale_unique_second_masktable)) + ((dst_positive_scale_unique_second_masktable) + (dst_positive_scale_unique_second_masktable))) + (((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) * S ((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) + ((dst_negative_scale_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)))) * S ((((dst_positive_code_unique_second_masktable) + (dst_positive_scale_unique_second_masktable)) * S ((dst_positive_code_unique_second_masktable) + (dst_positive_scale_unique_second_masktable)) + ((dst_positive_scale_unique_second_masktable) + (dst_positive_scale_unique_second_masktable))) + (((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) * S ((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) + ((dst_negative_scale_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)))) + ((((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) * S ((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) + ((dst_negative_scale_unique_second_masktable) + (dst_negative_scale_unique_second_masktable))) + (((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) * S ((dst_negative_code_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)) + ((dst_negative_scale_unique_second_masktable) + (dst_negative_scale_unique_second_masktable)))))) /\ (forall dst_index_unique_second_masktable. (exists pvs_le_gap_unique_second_masktabledomain. pvs_le_gap_unique_second_masktabledomain + (dst_index_unique_second_masktable) = (l)) -> exists dst_positive_unique_second_masktable dst_negative_unique_second_masktable dst_value_unique_second_masktable. ((((exists ff_h_pvs_unique_second_masktableentrypositive. ff_h_pvs_unique_second_masktableentrypositive + S (dst_positive_unique_second_masktable) = S ((S (dst_index_unique_second_masktable)) * dst_positive_scale_unique_second_masktable)) /\ exists ff_q_pvs_unique_second_masktableentrypositive. dst_positive_code_unique_second_masktable = ff_q_pvs_unique_second_masktableentrypositive * S ((S (dst_index_unique_second_masktable)) * dst_positive_scale_unique_second_masktable) + (dst_positive_unique_second_masktable))) /\ (((((exists ff_h_pvs_unique_second_masktableentrynegative. ff_h_pvs_unique_second_masktableentrynegative + S (dst_negative_unique_second_masktable) = S ((S (dst_index_unique_second_masktable)) * dst_negative_scale_unique_second_masktable)) /\ exists ff_q_pvs_unique_second_masktableentrynegative. dst_negative_code_unique_second_masktable = ff_q_pvs_unique_second_masktableentrynegative * S ((S (dst_index_unique_second_masktable)) * dst_negative_scale_unique_second_masktable) + (dst_negative_unique_second_masktable))) /\ (exists ge_balance_positive_unique_second_masktableentryvalue ge_balance_negative_unique_second_masktableentryvalue. (((((dst_value_unique_second_masktable) = 2 * (ge_balance_positive_unique_second_masktableentryvalue) /\ (ge_balance_negative_unique_second_masktableentryvalue) = 0) \/ exists ge_signed_half_unique_second_masktableentryvaluedecode. (((dst_value_unique_second_masktable) = 2 * ge_signed_half_unique_second_masktableentryvaluedecode + 1 /\ (ge_balance_positive_unique_second_masktableentryvalue) = 0) /\ (ge_balance_negative_unique_second_masktableentryvalue) = S ge_signed_half_unique_second_masktableentryvaluedecode))) /\ ((dst_positive_unique_second_masktable) + ge_balance_negative_unique_second_masktableentryvalue = (dst_negative_unique_second_masktable) + ge_balance_positive_unique_second_masktableentryvalue))))))))) /\ (forall dm_index_unique_second_mask dm_value_unique_second_mask. (exists pvs_le_gap_unique_second_maskdomain. pvs_le_gap_unique_second_maskdomain + (dm_index_unique_second_mask) = (l)) -> (exists dst_positive_code_unique_second_masklookup dst_positive_scale_unique_second_masklookup dst_negative_code_unique_second_masklookup dst_negative_scale_unique_second_masklookup dst_positive_unique_second_masklookup dst_negative_unique_second_masklookup. (((K) = (((((dst_positive_code_unique_second_masklookup) + (dst_positive_scale_unique_second_masklookup)) * S ((dst_positive_code_unique_second_masklookup) + (dst_positive_scale_unique_second_masklookup)) + ((dst_positive_scale_unique_second_masklookup) + (dst_positive_scale_unique_second_masklookup))) + (((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) * S ((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) + ((dst_negative_scale_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)))) * S ((((dst_positive_code_unique_second_masklookup) + (dst_positive_scale_unique_second_masklookup)) * S ((dst_positive_code_unique_second_masklookup) + (dst_positive_scale_unique_second_masklookup)) + ((dst_positive_scale_unique_second_masklookup) + (dst_positive_scale_unique_second_masklookup))) + (((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) * S ((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) + ((dst_negative_scale_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)))) + ((((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) * S ((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) + ((dst_negative_scale_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup))) + (((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) * S ((dst_negative_code_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)) + ((dst_negative_scale_unique_second_masklookup) + (dst_negative_scale_unique_second_masklookup)))))) /\ (((((exists ff_h_pvs_unique_second_masklookuppositive. ff_h_pvs_unique_second_masklookuppositive + S (dst_positive_unique_second_masklookup) = S ((S (dm_index_unique_second_mask)) * dst_positive_scale_unique_second_masklookup)) /\ exists ff_q_pvs_unique_second_masklookuppositive. dst_positive_code_unique_second_masklookup = ff_q_pvs_unique_second_masklookuppositive * S ((S (dm_index_unique_second_mask)) * dst_positive_scale_unique_second_masklookup) + (dst_positive_unique_second_masklookup))) /\ (((((exists ff_h_pvs_unique_second_masklookupnegative. ff_h_pvs_unique_second_masklookupnegative + S (dst_negative_unique_second_masklookup) = S ((S (dm_index_unique_second_mask)) * dst_negative_scale_unique_second_masklookup)) /\ exists ff_q_pvs_unique_second_masklookupnegative. dst_negative_code_unique_second_masklookup = ff_q_pvs_unique_second_masklookupnegative * S ((S (dm_index_unique_second_mask)) * dst_negative_scale_unique_second_masklookup) + (dst_negative_unique_second_masklookup))) /\ (exists ge_balance_positive_unique_second_masklookupvalue ge_balance_negative_unique_second_masklookupvalue. (((((dm_value_unique_second_mask) = 2 * (ge_balance_positive_unique_second_masklookupvalue) /\ (ge_balance_negative_unique_second_masklookupvalue) = 0) \/ exists ge_signed_half_unique_second_masklookupvaluedecode. (((dm_value_unique_second_mask) = 2 * ge_signed_half_unique_second_masklookupvaluedecode + 1 /\ (ge_balance_positive_unique_second_masklookupvalue) = 0) /\ (ge_balance_negative_unique_second_masklookupvalue) = S ge_signed_half_unique_second_masklookupvaluedecode))) /\ ((dst_positive_unique_second_masklookup) + ge_balance_negative_unique_second_masklookupvalue = (dst_negative_unique_second_masklookup) + ge_balance_positive_unique_second_masklookupvalue))))))))) -> ((((~((dm_index_unique_second_mask)=0)) /\ (exists dm_quotient_unique_second_maskentry. (((n)=(dm_index_unique_second_mask)*dm_quotient_unique_second_maskentry) /\ (exists dst_positive_code_unique_second_maskentryinput dst_positive_scale_unique_second_maskentryinput dst_negative_code_unique_second_maskentryinput dst_negative_scale_unique_second_maskentryinput dst_positive_unique_second_maskentryinput dst_negative_unique_second_maskentryinput. (((F) = (((((dst_positive_code_unique_second_maskentryinput) + (dst_positive_scale_unique_second_maskentryinput)) * S ((dst_positive_code_unique_second_maskentryinput) + (dst_positive_scale_unique_second_maskentryinput)) + ((dst_positive_scale_unique_second_maskentryinput) + (dst_positive_scale_unique_second_maskentryinput))) + (((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) * S ((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) + ((dst_negative_scale_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)))) * S ((((dst_positive_code_unique_second_maskentryinput) + (dst_positive_scale_unique_second_maskentryinput)) * S ((dst_positive_code_unique_second_maskentryinput) + (dst_positive_scale_unique_second_maskentryinput)) + ((dst_positive_scale_unique_second_maskentryinput) + (dst_positive_scale_unique_second_maskentryinput))) + (((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) * S ((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) + ((dst_negative_scale_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)))) + ((((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) * S ((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) + ((dst_negative_scale_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput))) + (((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) * S ((dst_negative_code_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)) + ((dst_negative_scale_unique_second_maskentryinput) + (dst_negative_scale_unique_second_maskentryinput)))))) /\ (((((exists ff_h_pvs_unique_second_maskentryinputpositive. ff_h_pvs_unique_second_maskentryinputpositive + S (dst_positive_unique_second_maskentryinput) = S ((S (dm_index_unique_second_mask)) * dst_positive_scale_unique_second_maskentryinput)) /\ exists ff_q_pvs_unique_second_maskentryinputpositive. dst_positive_code_unique_second_maskentryinput = ff_q_pvs_unique_second_maskentryinputpositive * S ((S (dm_index_unique_second_mask)) * dst_positive_scale_unique_second_maskentryinput) + (dst_positive_unique_second_maskentryinput))) /\ (((((exists ff_h_pvs_unique_second_maskentryinputnegative. ff_h_pvs_unique_second_maskentryinputnegative + S (dst_negative_unique_second_maskentryinput) = S ((S (dm_index_unique_second_mask)) * dst_negative_scale_unique_second_maskentryinput)) /\ exists ff_q_pvs_unique_second_maskentryinputnegative. dst_negative_code_unique_second_maskentryinput = ff_q_pvs_unique_second_maskentryinputnegative * S ((S (dm_index_unique_second_mask)) * dst_negative_scale_unique_second_maskentryinput) + (dst_negative_unique_second_maskentryinput))) /\ (exists ge_balance_positive_unique_second_maskentryinputvalue ge_balance_negative_unique_second_maskentryinputvalue. (((((dm_value_unique_second_mask) = 2 * (ge_balance_positive_unique_second_maskentryinputvalue) /\ (ge_balance_negative_unique_second_maskentryinputvalue) = 0) \/ exists ge_signed_half_unique_second_maskentryinputvaluedecode. (((dm_value_unique_second_mask) = 2 * ge_signed_half_unique_second_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_unique_second_maskentryinputvalue) = 0) /\ (ge_balance_negative_unique_second_maskentryinputvalue) = S ge_signed_half_unique_second_maskentryinputvaluedecode))) /\ ((dst_positive_unique_second_maskentryinput) + ge_balance_negative_unique_second_maskentryinputvalue = (dst_negative_unique_second_maskentryinput) + ge_balance_positive_unique_second_maskentryinputvalue))))))))))))) \/ ((((dm_index_unique_second_mask)=0 \/ ~(exists pvs_factor_unique_second_maskentrynondivisor. (n) = (dm_index_unique_second_mask) * pvs_factor_unique_second_maskentrynondivisor)) /\ ((dm_value_unique_second_mask)=0))))))) -> (forall dst_index_unique_mask_values dst_first_unique_mask_values dst_second_unique_mask_values. (exists pvs_gap_unique_mask_valuesbound. pvs_gap_unique_mask_valuesbound + S (dst_index_unique_mask_values) = (S l)) -> (exists dst_positive_code_unique_mask_valuesfirst dst_positive_scale_unique_mask_valuesfirst dst_negative_code_unique_mask_valuesfirst dst_negative_scale_unique_mask_valuesfirst dst_positive_unique_mask_valuesfirst dst_negative_unique_mask_valuesfirst. (((M) = (((((dst_positive_code_unique_mask_valuesfirst) + (dst_positive_scale_unique_mask_valuesfirst)) * S ((dst_positive_code_unique_mask_valuesfirst) + (dst_positive_scale_unique_mask_valuesfirst)) + ((dst_positive_scale_unique_mask_valuesfirst) + (dst_positive_scale_unique_mask_valuesfirst))) + (((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) * S ((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) + ((dst_negative_scale_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)))) * S ((((dst_positive_code_unique_mask_valuesfirst) + (dst_positive_scale_unique_mask_valuesfirst)) * S ((dst_positive_code_unique_mask_valuesfirst) + (dst_positive_scale_unique_mask_valuesfirst)) + ((dst_positive_scale_unique_mask_valuesfirst) + (dst_positive_scale_unique_mask_valuesfirst))) + (((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) * S ((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) + ((dst_negative_scale_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)))) + ((((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) * S ((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) + ((dst_negative_scale_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst))) + (((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) * S ((dst_negative_code_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)) + ((dst_negative_scale_unique_mask_valuesfirst) + (dst_negative_scale_unique_mask_valuesfirst)))))) /\ (((((exists ff_h_pvs_unique_mask_valuesfirstpositive. ff_h_pvs_unique_mask_valuesfirstpositive + S (dst_positive_unique_mask_valuesfirst) = S ((S (dst_index_unique_mask_values)) * dst_positive_scale_unique_mask_valuesfirst)) /\ exists ff_q_pvs_unique_mask_valuesfirstpositive. dst_positive_code_unique_mask_valuesfirst = ff_q_pvs_unique_mask_valuesfirstpositive * S ((S (dst_index_unique_mask_values)) * dst_positive_scale_unique_mask_valuesfirst) + (dst_positive_unique_mask_valuesfirst))) /\ (((((exists ff_h_pvs_unique_mask_valuesfirstnegative. ff_h_pvs_unique_mask_valuesfirstnegative + S (dst_negative_unique_mask_valuesfirst) = S ((S (dst_index_unique_mask_values)) * dst_negative_scale_unique_mask_valuesfirst)) /\ exists ff_q_pvs_unique_mask_valuesfirstnegative. dst_negative_code_unique_mask_valuesfirst = ff_q_pvs_unique_mask_valuesfirstnegative * S ((S (dst_index_unique_mask_values)) * dst_negative_scale_unique_mask_valuesfirst) + (dst_negative_unique_mask_valuesfirst))) /\ (exists ge_balance_positive_unique_mask_valuesfirstvalue ge_balance_negative_unique_mask_valuesfirstvalue. (((((dst_first_unique_mask_values) = 2 * (ge_balance_positive_unique_mask_valuesfirstvalue) /\ (ge_balance_negative_unique_mask_valuesfirstvalue) = 0) \/ exists ge_signed_half_unique_mask_valuesfirstvaluedecode. (((dst_first_unique_mask_values) = 2 * ge_signed_half_unique_mask_valuesfirstvaluedecode + 1 /\ (ge_balance_positive_unique_mask_valuesfirstvalue) = 0) /\ (ge_balance_negative_unique_mask_valuesfirstvalue) = S ge_signed_half_unique_mask_valuesfirstvaluedecode))) /\ ((dst_positive_unique_mask_valuesfirst) + ge_balance_negative_unique_mask_valuesfirstvalue = (dst_negative_unique_mask_valuesfirst) + ge_balance_positive_unique_mask_valuesfirstvalue))))))))) -> (exists dst_positive_code_unique_mask_valuessecond dst_positive_scale_unique_mask_valuessecond dst_negative_code_unique_mask_valuessecond dst_negative_scale_unique_mask_valuessecond dst_positive_unique_mask_valuessecond dst_negative_unique_mask_valuessecond. (((K) = (((((dst_positive_code_unique_mask_valuessecond) + (dst_positive_scale_unique_mask_valuessecond)) * S ((dst_positive_code_unique_mask_valuessecond) + (dst_positive_scale_unique_mask_valuessecond)) + ((dst_positive_scale_unique_mask_valuessecond) + (dst_positive_scale_unique_mask_valuessecond))) + (((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) * S ((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) + ((dst_negative_scale_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)))) * S ((((dst_positive_code_unique_mask_valuessecond) + (dst_positive_scale_unique_mask_valuessecond)) * S ((dst_positive_code_unique_mask_valuessecond) + (dst_positive_scale_unique_mask_valuessecond)) + ((dst_positive_scale_unique_mask_valuessecond) + (dst_positive_scale_unique_mask_valuessecond))) + (((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) * S ((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) + ((dst_negative_scale_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)))) + ((((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) * S ((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) + ((dst_negative_scale_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond))) + (((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) * S ((dst_negative_code_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)) + ((dst_negative_scale_unique_mask_valuessecond) + (dst_negative_scale_unique_mask_valuessecond)))))) /\ (((((exists ff_h_pvs_unique_mask_valuessecondpositive. ff_h_pvs_unique_mask_valuessecondpositive + S (dst_positive_unique_mask_valuessecond) = S ((S (dst_index_unique_mask_values)) * dst_positive_scale_unique_mask_valuessecond)) /\ exists ff_q_pvs_unique_mask_valuessecondpositive. dst_positive_code_unique_mask_valuessecond = ff_q_pvs_unique_mask_valuessecondpositive * S ((S (dst_index_unique_mask_values)) * dst_positive_scale_unique_mask_valuessecond) + (dst_positive_unique_mask_valuessecond))) /\ (((((exists ff_h_pvs_unique_mask_valuessecondnegative. ff_h_pvs_unique_mask_valuessecondnegative + S (dst_negative_unique_mask_valuessecond) = S ((S (dst_index_unique_mask_values)) * dst_negative_scale_unique_mask_valuessecond)) /\ exists ff_q_pvs_unique_mask_valuessecondnegative. dst_negative_code_unique_mask_valuessecond = ff_q_pvs_unique_mask_valuessecondnegative * S ((S (dst_index_unique_mask_values)) * dst_negative_scale_unique_mask_valuessecond) + (dst_negative_unique_mask_valuessecond))) /\ (exists ge_balance_positive_unique_mask_valuessecondvalue ge_balance_negative_unique_mask_valuessecondvalue. (((((dst_second_unique_mask_values) = 2 * (ge_balance_positive_unique_mask_valuessecondvalue) /\ (ge_balance_negative_unique_mask_valuessecondvalue) = 0) \/ exists ge_signed_half_unique_mask_valuessecondvaluedecode. (((dst_second_unique_mask_values) = 2 * ge_signed_half_unique_mask_valuessecondvaluedecode + 1 /\ (ge_balance_positive_unique_mask_valuessecondvalue) = 0) /\ (ge_balance_negative_unique_mask_valuessecondvalue) = S ge_signed_half_unique_mask_valuessecondvaluedecode))) /\ ((dst_positive_unique_mask_valuessecond) + ge_balance_negative_unique_mask_valuessecondvalue = (dst_negative_unique_mask_valuessecond) + ge_balance_positive_unique_mask_valuessecondvalue))))))))) -> dst_first_unique_mask_values = dst_second_unique_mask_values)

divisor_mask_prefix_restrict

new owned theorem · read exact theorem evidence

Bundle node 303; exact statement SHA-256 7975bc878c46f0676d938ef415531c8f8eaf123cb8d7ddccd414fa3130fdc95b

Exact first-order statement

forall F n l k M. (((exists dst_positive_code_restrict_masktable dst_positive_scale_restrict_masktable dst_negative_code_restrict_masktable dst_negative_scale_restrict_masktable. (((M) = (((((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) * S ((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) + ((dst_positive_scale_restrict_masktable) + (dst_positive_scale_restrict_masktable))) + (((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable)))) * S ((((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) * S ((dst_positive_code_restrict_masktable) + (dst_positive_scale_restrict_masktable)) + ((dst_positive_scale_restrict_masktable) + (dst_positive_scale_restrict_masktable))) + (((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable)))) + ((((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable))) + (((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) * S ((dst_negative_code_restrict_masktable) + (dst_negative_scale_restrict_masktable)) + ((dst_negative_scale_restrict_masktable) + (dst_negative_scale_restrict_masktable)))))) /\ (forall dst_index_restrict_masktable. (exists pvs_le_gap_restrict_masktabledomain. pvs_le_gap_restrict_masktabledomain + (dst_index_restrict_masktable) = (l)) -> exists dst_positive_restrict_masktable dst_negative_restrict_masktable dst_value_restrict_masktable. ((((exists ff_h_pvs_restrict_masktableentrypositive. ff_h_pvs_restrict_masktableentrypositive + S (dst_positive_restrict_masktable) = S ((S (dst_index_restrict_masktable)) * dst_positive_scale_restrict_masktable)) /\ exists ff_q_pvs_restrict_masktableentrypositive. dst_positive_code_restrict_masktable = ff_q_pvs_restrict_masktableentrypositive * S ((S (dst_index_restrict_masktable)) * dst_positive_scale_restrict_masktable) + (dst_positive_restrict_masktable))) /\ (((((exists ff_h_pvs_restrict_masktableentrynegative. ff_h_pvs_restrict_masktableentrynegative + S (dst_negative_restrict_masktable) = S ((S (dst_index_restrict_masktable)) * dst_negative_scale_restrict_masktable)) /\ exists ff_q_pvs_restrict_masktableentrynegative. dst_negative_code_restrict_masktable = ff_q_pvs_restrict_masktableentrynegative * S ((S (dst_index_restrict_masktable)) * dst_negative_scale_restrict_masktable) + (dst_negative_restrict_masktable))) /\ (exists ge_balance_positive_restrict_masktableentryvalue ge_balance_negative_restrict_masktableentryvalue. (((((dst_value_restrict_masktable) = 2 * (ge_balance_positive_restrict_masktableentryvalue) /\ (ge_balance_negative_restrict_masktableentryvalue) = 0) \/ exists ge_signed_half_restrict_masktableentryvaluedecode. (((dst_value_restrict_masktable) = 2 * ge_signed_half_restrict_masktableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_masktableentryvalue) = 0) /\ (ge_balance_negative_restrict_masktableentryvalue) = S ge_signed_half_restrict_masktableentryvaluedecode))) /\ ((dst_positive_restrict_masktable) + ge_balance_negative_restrict_masktableentryvalue = (dst_negative_restrict_masktable) + ge_balance_positive_restrict_masktableentryvalue))))))))) /\ (forall dm_index_restrict_mask dm_value_restrict_mask. (exists pvs_le_gap_restrict_maskdomain. pvs_le_gap_restrict_maskdomain + (dm_index_restrict_mask) = (l)) -> (exists dst_positive_code_restrict_masklookup dst_positive_scale_restrict_masklookup dst_negative_code_restrict_masklookup dst_negative_scale_restrict_masklookup dst_positive_restrict_masklookup dst_negative_restrict_masklookup. (((M) = (((((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) * S ((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) + ((dst_positive_scale_restrict_masklookup) + (dst_positive_scale_restrict_masklookup))) + (((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)))) * S ((((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) * S ((dst_positive_code_restrict_masklookup) + (dst_positive_scale_restrict_masklookup)) + ((dst_positive_scale_restrict_masklookup) + (dst_positive_scale_restrict_masklookup))) + (((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)))) + ((((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup))) + (((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) * S ((dst_negative_code_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)) + ((dst_negative_scale_restrict_masklookup) + (dst_negative_scale_restrict_masklookup)))))) /\ (((((exists ff_h_pvs_restrict_masklookuppositive. ff_h_pvs_restrict_masklookuppositive + S (dst_positive_restrict_masklookup) = S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_masklookup)) /\ exists ff_q_pvs_restrict_masklookuppositive. dst_positive_code_restrict_masklookup = ff_q_pvs_restrict_masklookuppositive * S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_masklookup) + (dst_positive_restrict_masklookup))) /\ (((((exists ff_h_pvs_restrict_masklookupnegative. ff_h_pvs_restrict_masklookupnegative + S (dst_negative_restrict_masklookup) = S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_masklookup)) /\ exists ff_q_pvs_restrict_masklookupnegative. dst_negative_code_restrict_masklookup = ff_q_pvs_restrict_masklookupnegative * S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_masklookup) + (dst_negative_restrict_masklookup))) /\ (exists ge_balance_positive_restrict_masklookupvalue ge_balance_negative_restrict_masklookupvalue. (((((dm_value_restrict_mask) = 2 * (ge_balance_positive_restrict_masklookupvalue) /\ (ge_balance_negative_restrict_masklookupvalue) = 0) \/ exists ge_signed_half_restrict_masklookupvaluedecode. (((dm_value_restrict_mask) = 2 * ge_signed_half_restrict_masklookupvaluedecode + 1 /\ (ge_balance_positive_restrict_masklookupvalue) = 0) /\ (ge_balance_negative_restrict_masklookupvalue) = S ge_signed_half_restrict_masklookupvaluedecode))) /\ ((dst_positive_restrict_masklookup) + ge_balance_negative_restrict_masklookupvalue = (dst_negative_restrict_masklookup) + ge_balance_positive_restrict_masklookupvalue))))))))) -> ((((~((dm_index_restrict_mask)=0)) /\ (exists dm_quotient_restrict_maskentry. (((n)=(dm_index_restrict_mask)*dm_quotient_restrict_maskentry) /\ (exists dst_positive_code_restrict_maskentryinput dst_positive_scale_restrict_maskentryinput dst_negative_code_restrict_maskentryinput dst_negative_scale_restrict_maskentryinput dst_positive_restrict_maskentryinput dst_negative_restrict_maskentryinput. (((F) = (((((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) * S ((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) + ((dst_positive_scale_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput))) + (((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)))) * S ((((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) * S ((dst_positive_code_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput)) + ((dst_positive_scale_restrict_maskentryinput) + (dst_positive_scale_restrict_maskentryinput))) + (((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)))) + ((((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput))) + (((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) * S ((dst_negative_code_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)) + ((dst_negative_scale_restrict_maskentryinput) + (dst_negative_scale_restrict_maskentryinput)))))) /\ (((((exists ff_h_pvs_restrict_maskentryinputpositive. ff_h_pvs_restrict_maskentryinputpositive + S (dst_positive_restrict_maskentryinput) = S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_maskentryinput)) /\ exists ff_q_pvs_restrict_maskentryinputpositive. dst_positive_code_restrict_maskentryinput = ff_q_pvs_restrict_maskentryinputpositive * S ((S (dm_index_restrict_mask)) * dst_positive_scale_restrict_maskentryinput) + (dst_positive_restrict_maskentryinput))) /\ (((((exists ff_h_pvs_restrict_maskentryinputnegative. ff_h_pvs_restrict_maskentryinputnegative + S (dst_negative_restrict_maskentryinput) = S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_maskentryinput)) /\ exists ff_q_pvs_restrict_maskentryinputnegative. dst_negative_code_restrict_maskentryinput = ff_q_pvs_restrict_maskentryinputnegative * S ((S (dm_index_restrict_mask)) * dst_negative_scale_restrict_maskentryinput) + (dst_negative_restrict_maskentryinput))) /\ (exists ge_balance_positive_restrict_maskentryinputvalue ge_balance_negative_restrict_maskentryinputvalue. (((((dm_value_restrict_mask) = 2 * (ge_balance_positive_restrict_maskentryinputvalue) /\ (ge_balance_negative_restrict_maskentryinputvalue) = 0) \/ exists ge_signed_half_restrict_maskentryinputvaluedecode. (((dm_value_restrict_mask) = 2 * ge_signed_half_restrict_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_restrict_maskentryinputvalue) = 0) /\ (ge_balance_negative_restrict_maskentryinputvalue) = S ge_signed_half_restrict_maskentryinputvaluedecode))) /\ ((dst_positive_restrict_maskentryinput) + ge_balance_negative_restrict_maskentryinputvalue = (dst_negative_restrict_maskentryinput) + ge_balance_positive_restrict_maskentryinputvalue))))))))))))) \/ ((((dm_index_restrict_mask)=0 \/ ~(exists pvs_factor_restrict_maskentrynondivisor. (n) = (dm_index_restrict_mask) * pvs_factor_restrict_maskentrynondivisor)) /\ ((dm_value_restrict_mask)=0))))))) -> (exists pvs_le_gap_restrict_bound. pvs_le_gap_restrict_bound + (k) = (l)) -> (((exists dst_positive_code_restrict_resulttable dst_positive_scale_restrict_resulttable dst_negative_code_restrict_resulttable dst_negative_scale_restrict_resulttable. (((M) = (((((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) * S ((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) + ((dst_positive_scale_restrict_resulttable) + (dst_positive_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))) * S ((((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) * S ((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) + ((dst_positive_scale_restrict_resulttable) + (dst_positive_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))) + ((((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))))) /\ (forall dst_index_restrict_resulttable. (exists pvs_le_gap_restrict_resulttabledomain. pvs_le_gap_restrict_resulttabledomain + (dst_index_restrict_resulttable) = (k)) -> exists dst_positive_restrict_resulttable dst_negative_restrict_resulttable dst_value_restrict_resulttable. ((((exists ff_h_pvs_restrict_resulttableentrypositive. ff_h_pvs_restrict_resulttableentrypositive + S (dst_positive_restrict_resulttable) = S ((S (dst_index_restrict_resulttable)) * dst_positive_scale_restrict_resulttable)) /\ exists ff_q_pvs_restrict_resulttableentrypositive. dst_positive_code_restrict_resulttable = ff_q_pvs_restrict_resulttableentrypositive * S ((S (dst_index_restrict_resulttable)) * dst_positive_scale_restrict_resulttable) + (dst_positive_restrict_resulttable))) /\ (((((exists ff_h_pvs_restrict_resulttableentrynegative. ff_h_pvs_restrict_resulttableentrynegative + S (dst_negative_restrict_resulttable) = S ((S (dst_index_restrict_resulttable)) * dst_negative_scale_restrict_resulttable)) /\ exists ff_q_pvs_restrict_resulttableentrynegative. dst_negative_code_restrict_resulttable = ff_q_pvs_restrict_resulttableentrynegative * S ((S (dst_index_restrict_resulttable)) * dst_negative_scale_restrict_resulttable) + (dst_negative_restrict_resulttable))) /\ (exists ge_balance_positive_restrict_resulttableentryvalue ge_balance_negative_restrict_resulttableentryvalue. (((((dst_value_restrict_resulttable) = 2 * (ge_balance_positive_restrict_resulttableentryvalue) /\ (ge_balance_negative_restrict_resulttableentryvalue) = 0) \/ exists ge_signed_half_restrict_resulttableentryvaluedecode. (((dst_value_restrict_resulttable) = 2 * ge_signed_half_restrict_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resulttableentryvalue) = 0) /\ (ge_balance_negative_restrict_resulttableentryvalue) = S ge_signed_half_restrict_resulttableentryvaluedecode))) /\ ((dst_positive_restrict_resulttable) + ge_balance_negative_restrict_resulttableentryvalue = (dst_negative_restrict_resulttable) + ge_balance_positive_restrict_resulttableentryvalue))))))))) /\ (forall dm_index_restrict_result dm_value_restrict_result. (exists pvs_le_gap_restrict_resultdomain. pvs_le_gap_restrict_resultdomain + (dm_index_restrict_result) = (k)) -> (exists dst_positive_code_restrict_resultlookup dst_positive_scale_restrict_resultlookup dst_negative_code_restrict_resultlookup dst_negative_scale_restrict_resultlookup dst_positive_restrict_resultlookup dst_negative_restrict_resultlookup. (((M) = (((((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) * S ((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) + ((dst_positive_scale_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))) * S ((((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) * S ((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) + ((dst_positive_scale_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))) + ((((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))))) /\ (((((exists ff_h_pvs_restrict_resultlookuppositive. ff_h_pvs_restrict_resultlookuppositive + S (dst_positive_restrict_resultlookup) = S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultlookup)) /\ exists ff_q_pvs_restrict_resultlookuppositive. dst_positive_code_restrict_resultlookup = ff_q_pvs_restrict_resultlookuppositive * S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultlookup) + (dst_positive_restrict_resultlookup))) /\ (((((exists ff_h_pvs_restrict_resultlookupnegative. ff_h_pvs_restrict_resultlookupnegative + S (dst_negative_restrict_resultlookup) = S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultlookup)) /\ exists ff_q_pvs_restrict_resultlookupnegative. dst_negative_code_restrict_resultlookup = ff_q_pvs_restrict_resultlookupnegative * S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultlookup) + (dst_negative_restrict_resultlookup))) /\ (exists ge_balance_positive_restrict_resultlookupvalue ge_balance_negative_restrict_resultlookupvalue. (((((dm_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultlookupvalue) /\ (ge_balance_negative_restrict_resultlookupvalue) = 0) \/ exists ge_signed_half_restrict_resultlookupvaluedecode. (((dm_value_restrict_result) = 2 * ge_signed_half_restrict_resultlookupvaluedecode + 1 /\ (ge_balance_positive_restrict_resultlookupvalue) = 0) /\ (ge_balance_negative_restrict_resultlookupvalue) = S ge_signed_half_restrict_resultlookupvaluedecode))) /\ ((dst_positive_restrict_resultlookup) + ge_balance_negative_restrict_resultlookupvalue = (dst_negative_restrict_resultlookup) + ge_balance_positive_restrict_resultlookupvalue))))))))) -> ((((~((dm_index_restrict_result)=0)) /\ (exists dm_quotient_restrict_resultentry. (((n)=(dm_index_restrict_result)*dm_quotient_restrict_resultentry) /\ (exists dst_positive_code_restrict_resultentryinput dst_positive_scale_restrict_resultentryinput dst_negative_code_restrict_resultentryinput dst_negative_scale_restrict_resultentryinput dst_positive_restrict_resultentryinput dst_negative_restrict_resultentryinput. (((F) = (((((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) * S ((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) + ((dst_positive_scale_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput))) + (((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)))) * S ((((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) * S ((dst_positive_code_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput)) + ((dst_positive_scale_restrict_resultentryinput) + (dst_positive_scale_restrict_resultentryinput))) + (((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)))) + ((((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput))) + (((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) * S ((dst_negative_code_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)) + ((dst_negative_scale_restrict_resultentryinput) + (dst_negative_scale_restrict_resultentryinput)))))) /\ (((((exists ff_h_pvs_restrict_resultentryinputpositive. ff_h_pvs_restrict_resultentryinputpositive + S (dst_positive_restrict_resultentryinput) = S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultentryinput)) /\ exists ff_q_pvs_restrict_resultentryinputpositive. dst_positive_code_restrict_resultentryinput = ff_q_pvs_restrict_resultentryinputpositive * S ((S (dm_index_restrict_result)) * dst_positive_scale_restrict_resultentryinput) + (dst_positive_restrict_resultentryinput))) /\ (((((exists ff_h_pvs_restrict_resultentryinputnegative. ff_h_pvs_restrict_resultentryinputnegative + S (dst_negative_restrict_resultentryinput) = S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultentryinput)) /\ exists ff_q_pvs_restrict_resultentryinputnegative. dst_negative_code_restrict_resultentryinput = ff_q_pvs_restrict_resultentryinputnegative * S ((S (dm_index_restrict_result)) * dst_negative_scale_restrict_resultentryinput) + (dst_negative_restrict_resultentryinput))) /\ (exists ge_balance_positive_restrict_resultentryinputvalue ge_balance_negative_restrict_resultentryinputvalue. (((((dm_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultentryinputvalue) /\ (ge_balance_negative_restrict_resultentryinputvalue) = 0) \/ exists ge_signed_half_restrict_resultentryinputvaluedecode. (((dm_value_restrict_result) = 2 * ge_signed_half_restrict_resultentryinputvaluedecode + 1 /\ (ge_balance_positive_restrict_resultentryinputvalue) = 0) /\ (ge_balance_negative_restrict_resultentryinputvalue) = S ge_signed_half_restrict_resultentryinputvaluedecode))) /\ ((dst_positive_restrict_resultentryinput) + ge_balance_negative_restrict_resultentryinputvalue = (dst_negative_restrict_resultentryinput) + ge_balance_positive_restrict_resultentryinputvalue))))))))))))) \/ ((((dm_index_restrict_result)=0 \/ ~(exists pvs_factor_restrict_resultentrynondivisor. (n) = (dm_index_restrict_result) * pvs_factor_restrict_resultentrynondivisor)) /\ ((dm_value_restrict_result)=0)))))))

divisor_mask_positive_quotient_entry

new owned theorem · read exact theorem evidence

Bundle node 304; exact statement SHA-256 d451bced4a810ab7da0b49aed476cd4fed2c71cf7954f79c0fd3b0c1bad518d3

Exact first-order statement

forall F n l M d q z. (((exists dst_positive_code_keep_masktable dst_positive_scale_keep_masktable dst_negative_code_keep_masktable dst_negative_scale_keep_masktable. (((M) = (((((dst_positive_code_keep_masktable) + (dst_positive_scale_keep_masktable)) * S ((dst_positive_code_keep_masktable) + (dst_positive_scale_keep_masktable)) + ((dst_positive_scale_keep_masktable) + (dst_positive_scale_keep_masktable))) + (((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) * S ((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) + ((dst_negative_scale_keep_masktable) + (dst_negative_scale_keep_masktable)))) * S ((((dst_positive_code_keep_masktable) + (dst_positive_scale_keep_masktable)) * S ((dst_positive_code_keep_masktable) + (dst_positive_scale_keep_masktable)) + ((dst_positive_scale_keep_masktable) + (dst_positive_scale_keep_masktable))) + (((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) * S ((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) + ((dst_negative_scale_keep_masktable) + (dst_negative_scale_keep_masktable)))) + ((((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) * S ((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) + ((dst_negative_scale_keep_masktable) + (dst_negative_scale_keep_masktable))) + (((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) * S ((dst_negative_code_keep_masktable) + (dst_negative_scale_keep_masktable)) + ((dst_negative_scale_keep_masktable) + (dst_negative_scale_keep_masktable)))))) /\ (forall dst_index_keep_masktable. (exists pvs_le_gap_keep_masktabledomain. pvs_le_gap_keep_masktabledomain + (dst_index_keep_masktable) = (l)) -> exists dst_positive_keep_masktable dst_negative_keep_masktable dst_value_keep_masktable. ((((exists ff_h_pvs_keep_masktableentrypositive. ff_h_pvs_keep_masktableentrypositive + S (dst_positive_keep_masktable) = S ((S (dst_index_keep_masktable)) * dst_positive_scale_keep_masktable)) /\ exists ff_q_pvs_keep_masktableentrypositive. dst_positive_code_keep_masktable = ff_q_pvs_keep_masktableentrypositive * S ((S (dst_index_keep_masktable)) * dst_positive_scale_keep_masktable) + (dst_positive_keep_masktable))) /\ (((((exists ff_h_pvs_keep_masktableentrynegative. ff_h_pvs_keep_masktableentrynegative + S (dst_negative_keep_masktable) = S ((S (dst_index_keep_masktable)) * dst_negative_scale_keep_masktable)) /\ exists ff_q_pvs_keep_masktableentrynegative. dst_negative_code_keep_masktable = ff_q_pvs_keep_masktableentrynegative * S ((S (dst_index_keep_masktable)) * dst_negative_scale_keep_masktable) + (dst_negative_keep_masktable))) /\ (exists ge_balance_positive_keep_masktableentryvalue ge_balance_negative_keep_masktableentryvalue. (((((dst_value_keep_masktable) = 2 * (ge_balance_positive_keep_masktableentryvalue) /\ (ge_balance_negative_keep_masktableentryvalue) = 0) \/ exists ge_signed_half_keep_masktableentryvaluedecode. (((dst_value_keep_masktable) = 2 * ge_signed_half_keep_masktableentryvaluedecode + 1 /\ (ge_balance_positive_keep_masktableentryvalue) = 0) /\ (ge_balance_negative_keep_masktableentryvalue) = S ge_signed_half_keep_masktableentryvaluedecode))) /\ ((dst_positive_keep_masktable) + ge_balance_negative_keep_masktableentryvalue = (dst_negative_keep_masktable) + ge_balance_positive_keep_masktableentryvalue))))))))) /\ (forall dm_index_keep_mask dm_value_keep_mask. (exists pvs_le_gap_keep_maskdomain. pvs_le_gap_keep_maskdomain + (dm_index_keep_mask) = (l)) -> (exists dst_positive_code_keep_masklookup dst_positive_scale_keep_masklookup dst_negative_code_keep_masklookup dst_negative_scale_keep_masklookup dst_positive_keep_masklookup dst_negative_keep_masklookup. (((M) = (((((dst_positive_code_keep_masklookup) + (dst_positive_scale_keep_masklookup)) * S ((dst_positive_code_keep_masklookup) + (dst_positive_scale_keep_masklookup)) + ((dst_positive_scale_keep_masklookup) + (dst_positive_scale_keep_masklookup))) + (((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) * S ((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) + ((dst_negative_scale_keep_masklookup) + (dst_negative_scale_keep_masklookup)))) * S ((((dst_positive_code_keep_masklookup) + (dst_positive_scale_keep_masklookup)) * S ((dst_positive_code_keep_masklookup) + (dst_positive_scale_keep_masklookup)) + ((dst_positive_scale_keep_masklookup) + (dst_positive_scale_keep_masklookup))) + (((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) * S ((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) + ((dst_negative_scale_keep_masklookup) + (dst_negative_scale_keep_masklookup)))) + ((((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) * S ((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) + ((dst_negative_scale_keep_masklookup) + (dst_negative_scale_keep_masklookup))) + (((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) * S ((dst_negative_code_keep_masklookup) + (dst_negative_scale_keep_masklookup)) + ((dst_negative_scale_keep_masklookup) + (dst_negative_scale_keep_masklookup)))))) /\ (((((exists ff_h_pvs_keep_masklookuppositive. ff_h_pvs_keep_masklookuppositive + S (dst_positive_keep_masklookup) = S ((S (dm_index_keep_mask)) * dst_positive_scale_keep_masklookup)) /\ exists ff_q_pvs_keep_masklookuppositive. dst_positive_code_keep_masklookup = ff_q_pvs_keep_masklookuppositive * S ((S (dm_index_keep_mask)) * dst_positive_scale_keep_masklookup) + (dst_positive_keep_masklookup))) /\ (((((exists ff_h_pvs_keep_masklookupnegative. ff_h_pvs_keep_masklookupnegative + S (dst_negative_keep_masklookup) = S ((S (dm_index_keep_mask)) * dst_negative_scale_keep_masklookup)) /\ exists ff_q_pvs_keep_masklookupnegative. dst_negative_code_keep_masklookup = ff_q_pvs_keep_masklookupnegative * S ((S (dm_index_keep_mask)) * dst_negative_scale_keep_masklookup) + (dst_negative_keep_masklookup))) /\ (exists ge_balance_positive_keep_masklookupvalue ge_balance_negative_keep_masklookupvalue. (((((dm_value_keep_mask) = 2 * (ge_balance_positive_keep_masklookupvalue) /\ (ge_balance_negative_keep_masklookupvalue) = 0) \/ exists ge_signed_half_keep_masklookupvaluedecode. (((dm_value_keep_mask) = 2 * ge_signed_half_keep_masklookupvaluedecode + 1 /\ (ge_balance_positive_keep_masklookupvalue) = 0) /\ (ge_balance_negative_keep_masklookupvalue) = S ge_signed_half_keep_masklookupvaluedecode))) /\ ((dst_positive_keep_masklookup) + ge_balance_negative_keep_masklookupvalue = (dst_negative_keep_masklookup) + ge_balance_positive_keep_masklookupvalue))))))))) -> ((((~((dm_index_keep_mask)=0)) /\ (exists dm_quotient_keep_maskentry. (((n)=(dm_index_keep_mask)*dm_quotient_keep_maskentry) /\ (exists dst_positive_code_keep_maskentryinput dst_positive_scale_keep_maskentryinput dst_negative_code_keep_maskentryinput dst_negative_scale_keep_maskentryinput dst_positive_keep_maskentryinput dst_negative_keep_maskentryinput. (((F) = (((((dst_positive_code_keep_maskentryinput) + (dst_positive_scale_keep_maskentryinput)) * S ((dst_positive_code_keep_maskentryinput) + (dst_positive_scale_keep_maskentryinput)) + ((dst_positive_scale_keep_maskentryinput) + (dst_positive_scale_keep_maskentryinput))) + (((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) * S ((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) + ((dst_negative_scale_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)))) * S ((((dst_positive_code_keep_maskentryinput) + (dst_positive_scale_keep_maskentryinput)) * S ((dst_positive_code_keep_maskentryinput) + (dst_positive_scale_keep_maskentryinput)) + ((dst_positive_scale_keep_maskentryinput) + (dst_positive_scale_keep_maskentryinput))) + (((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) * S ((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) + ((dst_negative_scale_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)))) + ((((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) * S ((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) + ((dst_negative_scale_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput))) + (((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) * S ((dst_negative_code_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)) + ((dst_negative_scale_keep_maskentryinput) + (dst_negative_scale_keep_maskentryinput)))))) /\ (((((exists ff_h_pvs_keep_maskentryinputpositive. ff_h_pvs_keep_maskentryinputpositive + S (dst_positive_keep_maskentryinput) = S ((S (dm_index_keep_mask)) * dst_positive_scale_keep_maskentryinput)) /\ exists ff_q_pvs_keep_maskentryinputpositive. dst_positive_code_keep_maskentryinput = ff_q_pvs_keep_maskentryinputpositive * S ((S (dm_index_keep_mask)) * dst_positive_scale_keep_maskentryinput) + (dst_positive_keep_maskentryinput))) /\ (((((exists ff_h_pvs_keep_maskentryinputnegative. ff_h_pvs_keep_maskentryinputnegative + S (dst_negative_keep_maskentryinput) = S ((S (dm_index_keep_mask)) * dst_negative_scale_keep_maskentryinput)) /\ exists ff_q_pvs_keep_maskentryinputnegative. dst_negative_code_keep_maskentryinput = ff_q_pvs_keep_maskentryinputnegative * S ((S (dm_index_keep_mask)) * dst_negative_scale_keep_maskentryinput) + (dst_negative_keep_maskentryinput))) /\ (exists ge_balance_positive_keep_maskentryinputvalue ge_balance_negative_keep_maskentryinputvalue. (((((dm_value_keep_mask) = 2 * (ge_balance_positive_keep_maskentryinputvalue) /\ (ge_balance_negative_keep_maskentryinputvalue) = 0) \/ exists ge_signed_half_keep_maskentryinputvaluedecode. (((dm_value_keep_mask) = 2 * ge_signed_half_keep_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_keep_maskentryinputvalue) = 0) /\ (ge_balance_negative_keep_maskentryinputvalue) = S ge_signed_half_keep_maskentryinputvaluedecode))) /\ ((dst_positive_keep_maskentryinput) + ge_balance_negative_keep_maskentryinputvalue = (dst_negative_keep_maskentryinput) + ge_balance_positive_keep_maskentryinputvalue))))))))))))) \/ ((((dm_index_keep_mask)=0 \/ ~(exists pvs_factor_keep_maskentrynondivisor. (n) = (dm_index_keep_mask) * pvs_factor_keep_maskentrynondivisor)) /\ ((dm_value_keep_mask)=0))))))) -> (exists pvs_le_gap_keep_bound. pvs_le_gap_keep_bound + (d) = (l)) -> ~(d=0) -> n=d*q -> (exists dst_positive_code_keep_source dst_positive_scale_keep_source dst_negative_code_keep_source dst_negative_scale_keep_source dst_positive_keep_source dst_negative_keep_source. (((F) = (((((dst_positive_code_keep_source) + (dst_positive_scale_keep_source)) * S ((dst_positive_code_keep_source) + (dst_positive_scale_keep_source)) + ((dst_positive_scale_keep_source) + (dst_positive_scale_keep_source))) + (((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) * S ((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) + ((dst_negative_scale_keep_source) + (dst_negative_scale_keep_source)))) * S ((((dst_positive_code_keep_source) + (dst_positive_scale_keep_source)) * S ((dst_positive_code_keep_source) + (dst_positive_scale_keep_source)) + ((dst_positive_scale_keep_source) + (dst_positive_scale_keep_source))) + (((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) * S ((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) + ((dst_negative_scale_keep_source) + (dst_negative_scale_keep_source)))) + ((((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) * S ((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) + ((dst_negative_scale_keep_source) + (dst_negative_scale_keep_source))) + (((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) * S ((dst_negative_code_keep_source) + (dst_negative_scale_keep_source)) + ((dst_negative_scale_keep_source) + (dst_negative_scale_keep_source)))))) /\ (((((exists ff_h_pvs_keep_sourcepositive. ff_h_pvs_keep_sourcepositive + S (dst_positive_keep_source) = S ((S (d)) * dst_positive_scale_keep_source)) /\ exists ff_q_pvs_keep_sourcepositive. dst_positive_code_keep_source = ff_q_pvs_keep_sourcepositive * S ((S (d)) * dst_positive_scale_keep_source) + (dst_positive_keep_source))) /\ (((((exists ff_h_pvs_keep_sourcenegative. ff_h_pvs_keep_sourcenegative + S (dst_negative_keep_source) = S ((S (d)) * dst_negative_scale_keep_source)) /\ exists ff_q_pvs_keep_sourcenegative. dst_negative_code_keep_source = ff_q_pvs_keep_sourcenegative * S ((S (d)) * dst_negative_scale_keep_source) + (dst_negative_keep_source))) /\ (exists ge_balance_positive_keep_sourcevalue ge_balance_negative_keep_sourcevalue. (((((z) = 2 * (ge_balance_positive_keep_sourcevalue) /\ (ge_balance_negative_keep_sourcevalue) = 0) \/ exists ge_signed_half_keep_sourcevaluedecode. (((z) = 2 * ge_signed_half_keep_sourcevaluedecode + 1 /\ (ge_balance_positive_keep_sourcevalue) = 0) /\ (ge_balance_negative_keep_sourcevalue) = S ge_signed_half_keep_sourcevaluedecode))) /\ ((dst_positive_keep_source) + ge_balance_negative_keep_sourcevalue = (dst_negative_keep_source) + ge_balance_positive_keep_sourcevalue))))))))) -> (exists dst_positive_code_keep_mask_entry dst_positive_scale_keep_mask_entry dst_negative_code_keep_mask_entry dst_negative_scale_keep_mask_entry dst_positive_keep_mask_entry dst_negative_keep_mask_entry. (((M) = (((((dst_positive_code_keep_mask_entry) + (dst_positive_scale_keep_mask_entry)) * S ((dst_positive_code_keep_mask_entry) + (dst_positive_scale_keep_mask_entry)) + ((dst_positive_scale_keep_mask_entry) + (dst_positive_scale_keep_mask_entry))) + (((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) * S ((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) + ((dst_negative_scale_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)))) * S ((((dst_positive_code_keep_mask_entry) + (dst_positive_scale_keep_mask_entry)) * S ((dst_positive_code_keep_mask_entry) + (dst_positive_scale_keep_mask_entry)) + ((dst_positive_scale_keep_mask_entry) + (dst_positive_scale_keep_mask_entry))) + (((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) * S ((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) + ((dst_negative_scale_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)))) + ((((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) * S ((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) + ((dst_negative_scale_keep_mask_entry) + (dst_negative_scale_keep_mask_entry))) + (((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) * S ((dst_negative_code_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)) + ((dst_negative_scale_keep_mask_entry) + (dst_negative_scale_keep_mask_entry)))))) /\ (((((exists ff_h_pvs_keep_mask_entrypositive. ff_h_pvs_keep_mask_entrypositive + S (dst_positive_keep_mask_entry) = S ((S (d)) * dst_positive_scale_keep_mask_entry)) /\ exists ff_q_pvs_keep_mask_entrypositive. dst_positive_code_keep_mask_entry = ff_q_pvs_keep_mask_entrypositive * S ((S (d)) * dst_positive_scale_keep_mask_entry) + (dst_positive_keep_mask_entry))) /\ (((((exists ff_h_pvs_keep_mask_entrynegative. ff_h_pvs_keep_mask_entrynegative + S (dst_negative_keep_mask_entry) = S ((S (d)) * dst_negative_scale_keep_mask_entry)) /\ exists ff_q_pvs_keep_mask_entrynegative. dst_negative_code_keep_mask_entry = ff_q_pvs_keep_mask_entrynegative * S ((S (d)) * dst_negative_scale_keep_mask_entry) + (dst_negative_keep_mask_entry))) /\ (exists ge_balance_positive_keep_mask_entryvalue ge_balance_negative_keep_mask_entryvalue. (((((z) = 2 * (ge_balance_positive_keep_mask_entryvalue) /\ (ge_balance_negative_keep_mask_entryvalue) = 0) \/ exists ge_signed_half_keep_mask_entryvaluedecode. (((z) = 2 * ge_signed_half_keep_mask_entryvaluedecode + 1 /\ (ge_balance_positive_keep_mask_entryvalue) = 0) /\ (ge_balance_negative_keep_mask_entryvalue) = S ge_signed_half_keep_mask_entryvaluedecode))) /\ ((dst_positive_keep_mask_entry) + ge_balance_negative_keep_mask_entryvalue = (dst_negative_keep_mask_entry) + ge_balance_positive_keep_mask_entryvalue)))))))))

divisor_mask_omitted_entry

new owned theorem · read exact theorem evidence

Bundle node 305; exact statement SHA-256 a766ef8ee57cbde2b3bf5eccd6500de01537091de9d4fb893392aeaf4d8580c6

Exact first-order statement

forall F n l M d. (((exists dst_positive_code_omit_masktable dst_positive_scale_omit_masktable dst_negative_code_omit_masktable dst_negative_scale_omit_masktable. (((M) = (((((dst_positive_code_omit_masktable) + (dst_positive_scale_omit_masktable)) * S ((dst_positive_code_omit_masktable) + (dst_positive_scale_omit_masktable)) + ((dst_positive_scale_omit_masktable) + (dst_positive_scale_omit_masktable))) + (((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) * S ((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) + ((dst_negative_scale_omit_masktable) + (dst_negative_scale_omit_masktable)))) * S ((((dst_positive_code_omit_masktable) + (dst_positive_scale_omit_masktable)) * S ((dst_positive_code_omit_masktable) + (dst_positive_scale_omit_masktable)) + ((dst_positive_scale_omit_masktable) + (dst_positive_scale_omit_masktable))) + (((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) * S ((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) + ((dst_negative_scale_omit_masktable) + (dst_negative_scale_omit_masktable)))) + ((((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) * S ((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) + ((dst_negative_scale_omit_masktable) + (dst_negative_scale_omit_masktable))) + (((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) * S ((dst_negative_code_omit_masktable) + (dst_negative_scale_omit_masktable)) + ((dst_negative_scale_omit_masktable) + (dst_negative_scale_omit_masktable)))))) /\ (forall dst_index_omit_masktable. (exists pvs_le_gap_omit_masktabledomain. pvs_le_gap_omit_masktabledomain + (dst_index_omit_masktable) = (l)) -> exists dst_positive_omit_masktable dst_negative_omit_masktable dst_value_omit_masktable. ((((exists ff_h_pvs_omit_masktableentrypositive. ff_h_pvs_omit_masktableentrypositive + S (dst_positive_omit_masktable) = S ((S (dst_index_omit_masktable)) * dst_positive_scale_omit_masktable)) /\ exists ff_q_pvs_omit_masktableentrypositive. dst_positive_code_omit_masktable = ff_q_pvs_omit_masktableentrypositive * S ((S (dst_index_omit_masktable)) * dst_positive_scale_omit_masktable) + (dst_positive_omit_masktable))) /\ (((((exists ff_h_pvs_omit_masktableentrynegative. ff_h_pvs_omit_masktableentrynegative + S (dst_negative_omit_masktable) = S ((S (dst_index_omit_masktable)) * dst_negative_scale_omit_masktable)) /\ exists ff_q_pvs_omit_masktableentrynegative. dst_negative_code_omit_masktable = ff_q_pvs_omit_masktableentrynegative * S ((S (dst_index_omit_masktable)) * dst_negative_scale_omit_masktable) + (dst_negative_omit_masktable))) /\ (exists ge_balance_positive_omit_masktableentryvalue ge_balance_negative_omit_masktableentryvalue. (((((dst_value_omit_masktable) = 2 * (ge_balance_positive_omit_masktableentryvalue) /\ (ge_balance_negative_omit_masktableentryvalue) = 0) \/ exists ge_signed_half_omit_masktableentryvaluedecode. (((dst_value_omit_masktable) = 2 * ge_signed_half_omit_masktableentryvaluedecode + 1 /\ (ge_balance_positive_omit_masktableentryvalue) = 0) /\ (ge_balance_negative_omit_masktableentryvalue) = S ge_signed_half_omit_masktableentryvaluedecode))) /\ ((dst_positive_omit_masktable) + ge_balance_negative_omit_masktableentryvalue = (dst_negative_omit_masktable) + ge_balance_positive_omit_masktableentryvalue))))))))) /\ (forall dm_index_omit_mask dm_value_omit_mask. (exists pvs_le_gap_omit_maskdomain. pvs_le_gap_omit_maskdomain + (dm_index_omit_mask) = (l)) -> (exists dst_positive_code_omit_masklookup dst_positive_scale_omit_masklookup dst_negative_code_omit_masklookup dst_negative_scale_omit_masklookup dst_positive_omit_masklookup dst_negative_omit_masklookup. (((M) = (((((dst_positive_code_omit_masklookup) + (dst_positive_scale_omit_masklookup)) * S ((dst_positive_code_omit_masklookup) + (dst_positive_scale_omit_masklookup)) + ((dst_positive_scale_omit_masklookup) + (dst_positive_scale_omit_masklookup))) + (((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) * S ((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) + ((dst_negative_scale_omit_masklookup) + (dst_negative_scale_omit_masklookup)))) * S ((((dst_positive_code_omit_masklookup) + (dst_positive_scale_omit_masklookup)) * S ((dst_positive_code_omit_masklookup) + (dst_positive_scale_omit_masklookup)) + ((dst_positive_scale_omit_masklookup) + (dst_positive_scale_omit_masklookup))) + (((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) * S ((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) + ((dst_negative_scale_omit_masklookup) + (dst_negative_scale_omit_masklookup)))) + ((((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) * S ((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) + ((dst_negative_scale_omit_masklookup) + (dst_negative_scale_omit_masklookup))) + (((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) * S ((dst_negative_code_omit_masklookup) + (dst_negative_scale_omit_masklookup)) + ((dst_negative_scale_omit_masklookup) + (dst_negative_scale_omit_masklookup)))))) /\ (((((exists ff_h_pvs_omit_masklookuppositive. ff_h_pvs_omit_masklookuppositive + S (dst_positive_omit_masklookup) = S ((S (dm_index_omit_mask)) * dst_positive_scale_omit_masklookup)) /\ exists ff_q_pvs_omit_masklookuppositive. dst_positive_code_omit_masklookup = ff_q_pvs_omit_masklookuppositive * S ((S (dm_index_omit_mask)) * dst_positive_scale_omit_masklookup) + (dst_positive_omit_masklookup))) /\ (((((exists ff_h_pvs_omit_masklookupnegative. ff_h_pvs_omit_masklookupnegative + S (dst_negative_omit_masklookup) = S ((S (dm_index_omit_mask)) * dst_negative_scale_omit_masklookup)) /\ exists ff_q_pvs_omit_masklookupnegative. dst_negative_code_omit_masklookup = ff_q_pvs_omit_masklookupnegative * S ((S (dm_index_omit_mask)) * dst_negative_scale_omit_masklookup) + (dst_negative_omit_masklookup))) /\ (exists ge_balance_positive_omit_masklookupvalue ge_balance_negative_omit_masklookupvalue. (((((dm_value_omit_mask) = 2 * (ge_balance_positive_omit_masklookupvalue) /\ (ge_balance_negative_omit_masklookupvalue) = 0) \/ exists ge_signed_half_omit_masklookupvaluedecode. (((dm_value_omit_mask) = 2 * ge_signed_half_omit_masklookupvaluedecode + 1 /\ (ge_balance_positive_omit_masklookupvalue) = 0) /\ (ge_balance_negative_omit_masklookupvalue) = S ge_signed_half_omit_masklookupvaluedecode))) /\ ((dst_positive_omit_masklookup) + ge_balance_negative_omit_masklookupvalue = (dst_negative_omit_masklookup) + ge_balance_positive_omit_masklookupvalue))))))))) -> ((((~((dm_index_omit_mask)=0)) /\ (exists dm_quotient_omit_maskentry. (((n)=(dm_index_omit_mask)*dm_quotient_omit_maskentry) /\ (exists dst_positive_code_omit_maskentryinput dst_positive_scale_omit_maskentryinput dst_negative_code_omit_maskentryinput dst_negative_scale_omit_maskentryinput dst_positive_omit_maskentryinput dst_negative_omit_maskentryinput. (((F) = (((((dst_positive_code_omit_maskentryinput) + (dst_positive_scale_omit_maskentryinput)) * S ((dst_positive_code_omit_maskentryinput) + (dst_positive_scale_omit_maskentryinput)) + ((dst_positive_scale_omit_maskentryinput) + (dst_positive_scale_omit_maskentryinput))) + (((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) * S ((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) + ((dst_negative_scale_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)))) * S ((((dst_positive_code_omit_maskentryinput) + (dst_positive_scale_omit_maskentryinput)) * S ((dst_positive_code_omit_maskentryinput) + (dst_positive_scale_omit_maskentryinput)) + ((dst_positive_scale_omit_maskentryinput) + (dst_positive_scale_omit_maskentryinput))) + (((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) * S ((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) + ((dst_negative_scale_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)))) + ((((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) * S ((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) + ((dst_negative_scale_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput))) + (((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) * S ((dst_negative_code_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)) + ((dst_negative_scale_omit_maskentryinput) + (dst_negative_scale_omit_maskentryinput)))))) /\ (((((exists ff_h_pvs_omit_maskentryinputpositive. ff_h_pvs_omit_maskentryinputpositive + S (dst_positive_omit_maskentryinput) = S ((S (dm_index_omit_mask)) * dst_positive_scale_omit_maskentryinput)) /\ exists ff_q_pvs_omit_maskentryinputpositive. dst_positive_code_omit_maskentryinput = ff_q_pvs_omit_maskentryinputpositive * S ((S (dm_index_omit_mask)) * dst_positive_scale_omit_maskentryinput) + (dst_positive_omit_maskentryinput))) /\ (((((exists ff_h_pvs_omit_maskentryinputnegative. ff_h_pvs_omit_maskentryinputnegative + S (dst_negative_omit_maskentryinput) = S ((S (dm_index_omit_mask)) * dst_negative_scale_omit_maskentryinput)) /\ exists ff_q_pvs_omit_maskentryinputnegative. dst_negative_code_omit_maskentryinput = ff_q_pvs_omit_maskentryinputnegative * S ((S (dm_index_omit_mask)) * dst_negative_scale_omit_maskentryinput) + (dst_negative_omit_maskentryinput))) /\ (exists ge_balance_positive_omit_maskentryinputvalue ge_balance_negative_omit_maskentryinputvalue. (((((dm_value_omit_mask) = 2 * (ge_balance_positive_omit_maskentryinputvalue) /\ (ge_balance_negative_omit_maskentryinputvalue) = 0) \/ exists ge_signed_half_omit_maskentryinputvaluedecode. (((dm_value_omit_mask) = 2 * ge_signed_half_omit_maskentryinputvaluedecode + 1 /\ (ge_balance_positive_omit_maskentryinputvalue) = 0) /\ (ge_balance_negative_omit_maskentryinputvalue) = S ge_signed_half_omit_maskentryinputvaluedecode))) /\ ((dst_positive_omit_maskentryinput) + ge_balance_negative_omit_maskentryinputvalue = (dst_negative_omit_maskentryinput) + ge_balance_positive_omit_maskentryinputvalue))))))))))))) \/ ((((dm_index_omit_mask)=0 \/ ~(exists pvs_factor_omit_maskentrynondivisor. (n) = (dm_index_omit_mask) * pvs_factor_omit_maskentrynondivisor)) /\ ((dm_value_omit_mask)=0))))))) -> (exists pvs_le_gap_omit_bound. pvs_le_gap_omit_bound + (d) = (l)) -> (d=0 \/ ~(exists pvs_factor_omit_reason. (n) = (d) * pvs_factor_omit_reason)) -> (exists dst_positive_code_omit_mask_entry dst_positive_scale_omit_mask_entry dst_negative_code_omit_mask_entry dst_negative_scale_omit_mask_entry dst_positive_omit_mask_entry dst_negative_omit_mask_entry. (((M) = (((((dst_positive_code_omit_mask_entry) + (dst_positive_scale_omit_mask_entry)) * S ((dst_positive_code_omit_mask_entry) + (dst_positive_scale_omit_mask_entry)) + ((dst_positive_scale_omit_mask_entry) + (dst_positive_scale_omit_mask_entry))) + (((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) * S ((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) + ((dst_negative_scale_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)))) * S ((((dst_positive_code_omit_mask_entry) + (dst_positive_scale_omit_mask_entry)) * S ((dst_positive_code_omit_mask_entry) + (dst_positive_scale_omit_mask_entry)) + ((dst_positive_scale_omit_mask_entry) + (dst_positive_scale_omit_mask_entry))) + (((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) * S ((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) + ((dst_negative_scale_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)))) + ((((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) * S ((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) + ((dst_negative_scale_omit_mask_entry) + (dst_negative_scale_omit_mask_entry))) + (((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) * S ((dst_negative_code_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)) + ((dst_negative_scale_omit_mask_entry) + (dst_negative_scale_omit_mask_entry)))))) /\ (((((exists ff_h_pvs_omit_mask_entrypositive. ff_h_pvs_omit_mask_entrypositive + S (dst_positive_omit_mask_entry) = S ((S (d)) * dst_positive_scale_omit_mask_entry)) /\ exists ff_q_pvs_omit_mask_entrypositive. dst_positive_code_omit_mask_entry = ff_q_pvs_omit_mask_entrypositive * S ((S (d)) * dst_positive_scale_omit_mask_entry) + (dst_positive_omit_mask_entry))) /\ (((((exists ff_h_pvs_omit_mask_entrynegative. ff_h_pvs_omit_mask_entrynegative + S (dst_negative_omit_mask_entry) = S ((S (d)) * dst_negative_scale_omit_mask_entry)) /\ exists ff_q_pvs_omit_mask_entrynegative. dst_negative_code_omit_mask_entry = ff_q_pvs_omit_mask_entrynegative * S ((S (d)) * dst_negative_scale_omit_mask_entry) + (dst_negative_omit_mask_entry))) /\ (exists ge_balance_positive_omit_mask_entryvalue ge_balance_negative_omit_mask_entryvalue. (((((0) = 2 * (ge_balance_positive_omit_mask_entryvalue) /\ (ge_balance_negative_omit_mask_entryvalue) = 0) \/ exists ge_signed_half_omit_mask_entryvaluedecode. (((0) = 2 * ge_signed_half_omit_mask_entryvaluedecode + 1 /\ (ge_balance_positive_omit_mask_entryvalue) = 0) /\ (ge_balance_negative_omit_mask_entryvalue) = S ge_signed_half_omit_mask_entryvaluedecode))) /\ ((dst_positive_omit_mask_entry) + ge_balance_negative_omit_mask_entryvalue = (dst_negative_omit_mask_entry) + ge_balance_positive_omit_mask_entryvalue)))))))))

divisor_mask_entry_positive_source_extensional

new owned theorem · read exact theorem evidence

Bundle node 306; exact statement SHA-256 ac8c49b365031327b9d3ab1beebb04bd8a501417613b5608afbdef027714070b

Exact first-order statement

forall F G n d a b. (forall dm_index_source_equal dm_first_value_source_equal dm_second_value_source_equal. ~(dm_index_source_equal=0) -> (exists pvs_le_gap_source_equaldomain. pvs_le_gap_source_equaldomain + (dm_index_source_equal) = (n)) -> (exists dst_positive_code_source_equalfirst dst_positive_scale_source_equalfirst dst_negative_code_source_equalfirst dst_negative_scale_source_equalfirst dst_positive_source_equalfirst dst_negative_source_equalfirst. (((F) = (((((dst_positive_code_source_equalfirst) + (dst_positive_scale_source_equalfirst)) * S ((dst_positive_code_source_equalfirst) + (dst_positive_scale_source_equalfirst)) + ((dst_positive_scale_source_equalfirst) + (dst_positive_scale_source_equalfirst))) + (((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) * S ((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) + ((dst_negative_scale_source_equalfirst) + (dst_negative_scale_source_equalfirst)))) * S ((((dst_positive_code_source_equalfirst) + (dst_positive_scale_source_equalfirst)) * S ((dst_positive_code_source_equalfirst) + (dst_positive_scale_source_equalfirst)) + ((dst_positive_scale_source_equalfirst) + (dst_positive_scale_source_equalfirst))) + (((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) * S ((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) + ((dst_negative_scale_source_equalfirst) + (dst_negative_scale_source_equalfirst)))) + ((((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) * S ((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) + ((dst_negative_scale_source_equalfirst) + (dst_negative_scale_source_equalfirst))) + (((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) * S ((dst_negative_code_source_equalfirst) + (dst_negative_scale_source_equalfirst)) + ((dst_negative_scale_source_equalfirst) + (dst_negative_scale_source_equalfirst)))))) /\ (((((exists ff_h_pvs_source_equalfirstpositive. ff_h_pvs_source_equalfirstpositive + S (dst_positive_source_equalfirst) = S ((S (dm_index_source_equal)) * dst_positive_scale_source_equalfirst)) /\ exists ff_q_pvs_source_equalfirstpositive. dst_positive_code_source_equalfirst = ff_q_pvs_source_equalfirstpositive * S ((S (dm_index_source_equal)) * dst_positive_scale_source_equalfirst) + (dst_positive_source_equalfirst))) /\ (((((exists ff_h_pvs_source_equalfirstnegative. ff_h_pvs_source_equalfirstnegative + S (dst_negative_source_equalfirst) = S ((S (dm_index_source_equal)) * dst_negative_scale_source_equalfirst)) /\ exists ff_q_pvs_source_equalfirstnegative. dst_negative_code_source_equalfirst = ff_q_pvs_source_equalfirstnegative * S ((S (dm_index_source_equal)) * dst_negative_scale_source_equalfirst) + (dst_negative_source_equalfirst))) /\ (exists ge_balance_positive_source_equalfirstvalue ge_balance_negative_source_equalfirstvalue. (((((dm_first_value_source_equal) = 2 * (ge_balance_positive_source_equalfirstvalue) /\ (ge_balance_negative_source_equalfirstvalue) = 0) \/ exists ge_signed_half_source_equalfirstvaluedecode. (((dm_first_value_source_equal) = 2 * ge_signed_half_source_equalfirstvaluedecode + 1 /\ (ge_balance_positive_source_equalfirstvalue) = 0) /\ (ge_balance_negative_source_equalfirstvalue) = S ge_signed_half_source_equalfirstvaluedecode))) /\ ((dst_positive_source_equalfirst) + ge_balance_negative_source_equalfirstvalue = (dst_negative_source_equalfirst) + ge_balance_positive_source_equalfirstvalue))))))))) -> (exists dst_positive_code_source_equalsecond dst_positive_scale_source_equalsecond dst_negative_code_source_equalsecond dst_negative_scale_source_equalsecond dst_positive_source_equalsecond dst_negative_source_equalsecond. (((G) = (((((dst_positive_code_source_equalsecond) + (dst_positive_scale_source_equalsecond)) * S ((dst_positive_code_source_equalsecond) + (dst_positive_scale_source_equalsecond)) + ((dst_positive_scale_source_equalsecond) + (dst_positive_scale_source_equalsecond))) + (((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) * S ((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) + ((dst_negative_scale_source_equalsecond) + (dst_negative_scale_source_equalsecond)))) * S ((((dst_positive_code_source_equalsecond) + (dst_positive_scale_source_equalsecond)) * S ((dst_positive_code_source_equalsecond) + (dst_positive_scale_source_equalsecond)) + ((dst_positive_scale_source_equalsecond) + (dst_positive_scale_source_equalsecond))) + (((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) * S ((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) + ((dst_negative_scale_source_equalsecond) + (dst_negative_scale_source_equalsecond)))) + ((((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) * S ((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) + ((dst_negative_scale_source_equalsecond) + (dst_negative_scale_source_equalsecond))) + (((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) * S ((dst_negative_code_source_equalsecond) + (dst_negative_scale_source_equalsecond)) + ((dst_negative_scale_source_equalsecond) + (dst_negative_scale_source_equalsecond)))))) /\ (((((exists ff_h_pvs_source_equalsecondpositive. ff_h_pvs_source_equalsecondpositive + S (dst_positive_source_equalsecond) = S ((S (dm_index_source_equal)) * dst_positive_scale_source_equalsecond)) /\ exists ff_q_pvs_source_equalsecondpositive. dst_positive_code_source_equalsecond = ff_q_pvs_source_equalsecondpositive * S ((S (dm_index_source_equal)) * dst_positive_scale_source_equalsecond) + (dst_positive_source_equalsecond))) /\ (((((exists ff_h_pvs_source_equalsecondnegative. ff_h_pvs_source_equalsecondnegative + S (dst_negative_source_equalsecond) = S ((S (dm_index_source_equal)) * dst_negative_scale_source_equalsecond)) /\ exists ff_q_pvs_source_equalsecondnegative. dst_negative_code_source_equalsecond = ff_q_pvs_source_equalsecondnegative * S ((S (dm_index_source_equal)) * dst_negative_scale_source_equalsecond) + (dst_negative_source_equalsecond))) /\ (exists ge_balance_positive_source_equalsecondvalue ge_balance_negative_source_equalsecondvalue. (((((dm_second_value_source_equal) = 2 * (ge_balance_positive_source_equalsecondvalue) /\ (ge_balance_negative_source_equalsecondvalue) = 0) \/ exists ge_signed_half_source_equalsecondvaluedecode. (((dm_second_value_source_equal) = 2 * ge_signed_half_source_equalsecondvaluedecode + 1 /\ (ge_balance_positive_source_equalsecondvalue) = 0) /\ (ge_balance_negative_source_equalsecondvalue) = S ge_signed_half_source_equalsecondvaluedecode))) /\ ((dst_positive_source_equalsecond) + ge_balance_negative_source_equalsecondvalue = (dst_negative_source_equalsecond) + ge_balance_positive_source_equalsecondvalue))))))))) -> dm_first_value_source_equal=dm_second_value_source_equal) -> (exists pvs_le_gap_source_bound. pvs_le_gap_source_bound + (d) = (n)) -> ((((~((d)=0)) /\ (exists dm_quotient_source_first. (((n)=(d)*dm_quotient_source_first) /\ (exists dst_positive_code_source_firstinput dst_positive_scale_source_firstinput dst_negative_code_source_firstinput dst_negative_scale_source_firstinput dst_positive_source_firstinput dst_negative_source_firstinput. (((F) = (((((dst_positive_code_source_firstinput) + (dst_positive_scale_source_firstinput)) * S ((dst_positive_code_source_firstinput) + (dst_positive_scale_source_firstinput)) + ((dst_positive_scale_source_firstinput) + (dst_positive_scale_source_firstinput))) + (((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) * S ((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) + ((dst_negative_scale_source_firstinput) + (dst_negative_scale_source_firstinput)))) * S ((((dst_positive_code_source_firstinput) + (dst_positive_scale_source_firstinput)) * S ((dst_positive_code_source_firstinput) + (dst_positive_scale_source_firstinput)) + ((dst_positive_scale_source_firstinput) + (dst_positive_scale_source_firstinput))) + (((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) * S ((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) + ((dst_negative_scale_source_firstinput) + (dst_negative_scale_source_firstinput)))) + ((((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) * S ((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) + ((dst_negative_scale_source_firstinput) + (dst_negative_scale_source_firstinput))) + (((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) * S ((dst_negative_code_source_firstinput) + (dst_negative_scale_source_firstinput)) + ((dst_negative_scale_source_firstinput) + (dst_negative_scale_source_firstinput)))))) /\ (((((exists ff_h_pvs_source_firstinputpositive. ff_h_pvs_source_firstinputpositive + S (dst_positive_source_firstinput) = S ((S (d)) * dst_positive_scale_source_firstinput)) /\ exists ff_q_pvs_source_firstinputpositive. dst_positive_code_source_firstinput = ff_q_pvs_source_firstinputpositive * S ((S (d)) * dst_positive_scale_source_firstinput) + (dst_positive_source_firstinput))) /\ (((((exists ff_h_pvs_source_firstinputnegative. ff_h_pvs_source_firstinputnegative + S (dst_negative_source_firstinput) = S ((S (d)) * dst_negative_scale_source_firstinput)) /\ exists ff_q_pvs_source_firstinputnegative. dst_negative_code_source_firstinput = ff_q_pvs_source_firstinputnegative * S ((S (d)) * dst_negative_scale_source_firstinput) + (dst_negative_source_firstinput))) /\ (exists ge_balance_positive_source_firstinputvalue ge_balance_negative_source_firstinputvalue. (((((a) = 2 * (ge_balance_positive_source_firstinputvalue) /\ (ge_balance_negative_source_firstinputvalue) = 0) \/ exists ge_signed_half_source_firstinputvaluedecode. (((a) = 2 * ge_signed_half_source_firstinputvaluedecode + 1 /\ (ge_balance_positive_source_firstinputvalue) = 0) /\ (ge_balance_negative_source_firstinputvalue) = S ge_signed_half_source_firstinputvaluedecode))) /\ ((dst_positive_source_firstinput) + ge_balance_negative_source_firstinputvalue = (dst_negative_source_firstinput) + ge_balance_positive_source_firstinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_source_firstnondivisor. (n) = (d) * pvs_factor_source_firstnondivisor)) /\ ((a)=0)))) -> ((((~((d)=0)) /\ (exists dm_quotient_source_second. (((n)=(d)*dm_quotient_source_second) /\ (exists dst_positive_code_source_secondinput dst_positive_scale_source_secondinput dst_negative_code_source_secondinput dst_negative_scale_source_secondinput dst_positive_source_secondinput dst_negative_source_secondinput. (((G) = (((((dst_positive_code_source_secondinput) + (dst_positive_scale_source_secondinput)) * S ((dst_positive_code_source_secondinput) + (dst_positive_scale_source_secondinput)) + ((dst_positive_scale_source_secondinput) + (dst_positive_scale_source_secondinput))) + (((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) * S ((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) + ((dst_negative_scale_source_secondinput) + (dst_negative_scale_source_secondinput)))) * S ((((dst_positive_code_source_secondinput) + (dst_positive_scale_source_secondinput)) * S ((dst_positive_code_source_secondinput) + (dst_positive_scale_source_secondinput)) + ((dst_positive_scale_source_secondinput) + (dst_positive_scale_source_secondinput))) + (((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) * S ((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) + ((dst_negative_scale_source_secondinput) + (dst_negative_scale_source_secondinput)))) + ((((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) * S ((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) + ((dst_negative_scale_source_secondinput) + (dst_negative_scale_source_secondinput))) + (((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) * S ((dst_negative_code_source_secondinput) + (dst_negative_scale_source_secondinput)) + ((dst_negative_scale_source_secondinput) + (dst_negative_scale_source_secondinput)))))) /\ (((((exists ff_h_pvs_source_secondinputpositive. ff_h_pvs_source_secondinputpositive + S (dst_positive_source_secondinput) = S ((S (d)) * dst_positive_scale_source_secondinput)) /\ exists ff_q_pvs_source_secondinputpositive. dst_positive_code_source_secondinput = ff_q_pvs_source_secondinputpositive * S ((S (d)) * dst_positive_scale_source_secondinput) + (dst_positive_source_secondinput))) /\ (((((exists ff_h_pvs_source_secondinputnegative. ff_h_pvs_source_secondinputnegative + S (dst_negative_source_secondinput) = S ((S (d)) * dst_negative_scale_source_secondinput)) /\ exists ff_q_pvs_source_secondinputnegative. dst_negative_code_source_secondinput = ff_q_pvs_source_secondinputnegative * S ((S (d)) * dst_negative_scale_source_secondinput) + (dst_negative_source_secondinput))) /\ (exists ge_balance_positive_source_secondinputvalue ge_balance_negative_source_secondinputvalue. (((((b) = 2 * (ge_balance_positive_source_secondinputvalue) /\ (ge_balance_negative_source_secondinputvalue) = 0) \/ exists ge_signed_half_source_secondinputvaluedecode. (((b) = 2 * ge_signed_half_source_secondinputvaluedecode + 1 /\ (ge_balance_positive_source_secondinputvalue) = 0) /\ (ge_balance_negative_source_secondinputvalue) = S ge_signed_half_source_secondinputvaluedecode))) /\ ((dst_positive_source_secondinput) + ge_balance_negative_source_secondinputvalue = (dst_negative_source_secondinput) + ge_balance_positive_source_secondinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_source_secondnondivisor. (n) = (d) * pvs_factor_source_secondnondivisor)) /\ ((b)=0)))) -> a=b

divisor_mask_positive_source_extensional

new owned theorem · read exact theorem evidence

Bundle node 307; exact statement SHA-256 411bd547edefe8cdf0561ffc94ba99b749b29ac2a7e85d1b63c316c9bed61097

Exact first-order statement

forall F G n M K. (forall dm_index_mask_source_equal dm_first_value_mask_source_equal dm_second_value_mask_source_equal. ~(dm_index_mask_source_equal=0) -> (exists pvs_le_gap_mask_source_equaldomain. pvs_le_gap_mask_source_equaldomain + (dm_index_mask_source_equal) = (n)) -> (exists dst_positive_code_mask_source_equalfirst dst_positive_scale_mask_source_equalfirst dst_negative_code_mask_source_equalfirst dst_negative_scale_mask_source_equalfirst dst_positive_mask_source_equalfirst dst_negative_mask_source_equalfirst. (((F) = (((((dst_positive_code_mask_source_equalfirst) + (dst_positive_scale_mask_source_equalfirst)) * S ((dst_positive_code_mask_source_equalfirst) + (dst_positive_scale_mask_source_equalfirst)) + ((dst_positive_scale_mask_source_equalfirst) + (dst_positive_scale_mask_source_equalfirst))) + (((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) * S ((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) + ((dst_negative_scale_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)))) * S ((((dst_positive_code_mask_source_equalfirst) + (dst_positive_scale_mask_source_equalfirst)) * S ((dst_positive_code_mask_source_equalfirst) + (dst_positive_scale_mask_source_equalfirst)) + ((dst_positive_scale_mask_source_equalfirst) + (dst_positive_scale_mask_source_equalfirst))) + (((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) * S ((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) + ((dst_negative_scale_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)))) + ((((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) * S ((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) + ((dst_negative_scale_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst))) + (((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) * S ((dst_negative_code_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)) + ((dst_negative_scale_mask_source_equalfirst) + (dst_negative_scale_mask_source_equalfirst)))))) /\ (((((exists ff_h_pvs_mask_source_equalfirstpositive. ff_h_pvs_mask_source_equalfirstpositive + S (dst_positive_mask_source_equalfirst) = S ((S (dm_index_mask_source_equal)) * dst_positive_scale_mask_source_equalfirst)) /\ exists ff_q_pvs_mask_source_equalfirstpositive. dst_positive_code_mask_source_equalfirst = ff_q_pvs_mask_source_equalfirstpositive * S ((S (dm_index_mask_source_equal)) * dst_positive_scale_mask_source_equalfirst) + (dst_positive_mask_source_equalfirst))) /\ (((((exists ff_h_pvs_mask_source_equalfirstnegative. ff_h_pvs_mask_source_equalfirstnegative + S (dst_negative_mask_source_equalfirst) = S ((S (dm_index_mask_source_equal)) * dst_negative_scale_mask_source_equalfirst)) /\ exists ff_q_pvs_mask_source_equalfirstnegative. dst_negative_code_mask_source_equalfirst = ff_q_pvs_mask_source_equalfirstnegative * S ((S (dm_index_mask_source_equal)) * dst_negative_scale_mask_source_equalfirst) + (dst_negative_mask_source_equalfirst))) /\ (exists ge_balance_positive_mask_source_equalfirstvalue ge_balance_negative_mask_source_equalfirstvalue. (((((dm_first_value_mask_source_equal) = 2 * (ge_balance_positive_mask_source_equalfirstvalue) /\ (ge_balance_negative_mask_source_equalfirstvalue) = 0) \/ exists ge_signed_half_mask_source_equalfirstvaluedecode. (((dm_first_value_mask_source_equal) = 2 * ge_signed_half_mask_source_equalfirstvaluedecode + 1 /\ (ge_balance_positive_mask_source_equalfirstvalue) = 0) /\ (ge_balance_negative_mask_source_equalfirstvalue) = S ge_signed_half_mask_source_equalfirstvaluedecode))) /\ ((dst_positive_mask_source_equalfirst) + ge_balance_negative_mask_source_equalfirstvalue = (dst_negative_mask_source_equalfirst) + ge_balance_positive_mask_source_equalfirstvalue))))))))) -> (exists dst_positive_code_mask_source_equalsecond dst_positive_scale_mask_source_equalsecond dst_negative_code_mask_source_equalsecond dst_negative_scale_mask_source_equalsecond dst_positive_mask_source_equalsecond dst_negative_mask_source_equalsecond. (((G) = (((((dst_positive_code_mask_source_equalsecond) + (dst_positive_scale_mask_source_equalsecond)) * S ((dst_positive_code_mask_source_equalsecond) + (dst_positive_scale_mask_source_equalsecond)) + ((dst_positive_scale_mask_source_equalsecond) + (dst_positive_scale_mask_source_equalsecond))) + (((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) * S ((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) + ((dst_negative_scale_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)))) * S ((((dst_positive_code_mask_source_equalsecond) + (dst_positive_scale_mask_source_equalsecond)) * S ((dst_positive_code_mask_source_equalsecond) + (dst_positive_scale_mask_source_equalsecond)) + ((dst_positive_scale_mask_source_equalsecond) + (dst_positive_scale_mask_source_equalsecond))) + (((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) * S ((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) + ((dst_negative_scale_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)))) + ((((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) * S ((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) + ((dst_negative_scale_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond))) + (((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) * S ((dst_negative_code_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)) + ((dst_negative_scale_mask_source_equalsecond) + (dst_negative_scale_mask_source_equalsecond)))))) /\ (((((exists ff_h_pvs_mask_source_equalsecondpositive. ff_h_pvs_mask_source_equalsecondpositive + S (dst_positive_mask_source_equalsecond) = S ((S (dm_index_mask_source_equal)) * dst_positive_scale_mask_source_equalsecond)) /\ exists ff_q_pvs_mask_source_equalsecondpositive. dst_positive_code_mask_source_equalsecond = ff_q_pvs_mask_source_equalsecondpositive * S ((S (dm_index_mask_source_equal)) * dst_positive_scale_mask_source_equalsecond) + (dst_positive_mask_source_equalsecond))) /\ (((((exists ff_h_pvs_mask_source_equalsecondnegative. ff_h_pvs_mask_source_equalsecondnegative + S (dst_negative_mask_source_equalsecond) = S ((S (dm_index_mask_source_equal)) * dst_negative_scale_mask_source_equalsecond)) /\ exists ff_q_pvs_mask_source_equalsecondnegative. dst_negative_code_mask_source_equalsecond = ff_q_pvs_mask_source_equalsecondnegative * S ((S (dm_index_mask_source_equal)) * dst_negative_scale_mask_source_equalsecond) + (dst_negative_mask_source_equalsecond))) /\ (exists ge_balance_positive_mask_source_equalsecondvalue ge_balance_negative_mask_source_equalsecondvalue. (((((dm_second_value_mask_source_equal) = 2 * (ge_balance_positive_mask_source_equalsecondvalue) /\ (ge_balance_negative_mask_source_equalsecondvalue) = 0) \/ exists ge_signed_half_mask_source_equalsecondvaluedecode. (((dm_second_value_mask_source_equal) = 2 * ge_signed_half_mask_source_equalsecondvaluedecode + 1 /\ (ge_balance_positive_mask_source_equalsecondvalue) = 0) /\ (ge_balance_negative_mask_source_equalsecondvalue) = S ge_signed_half_mask_source_equalsecondvaluedecode))) /\ ((dst_positive_mask_source_equalsecond) + ge_balance_negative_mask_source_equalsecondvalue = (dst_negative_mask_source_equalsecond) + ge_balance_positive_mask_source_equalsecondvalue))))))))) -> dm_first_value_mask_source_equal=dm_second_value_mask_source_equal) -> (((exists dst_positive_code_mask_source_firsttable dst_positive_scale_mask_source_firsttable dst_negative_code_mask_source_firsttable dst_negative_scale_mask_source_firsttable. (((M) = (((((dst_positive_code_mask_source_firsttable) + (dst_positive_scale_mask_source_firsttable)) * S ((dst_positive_code_mask_source_firsttable) + (dst_positive_scale_mask_source_firsttable)) + ((dst_positive_scale_mask_source_firsttable) + (dst_positive_scale_mask_source_firsttable))) + (((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) * S ((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) + ((dst_negative_scale_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)))) * S ((((dst_positive_code_mask_source_firsttable) + (dst_positive_scale_mask_source_firsttable)) * S ((dst_positive_code_mask_source_firsttable) + (dst_positive_scale_mask_source_firsttable)) + ((dst_positive_scale_mask_source_firsttable) + (dst_positive_scale_mask_source_firsttable))) + (((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) * S ((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) + ((dst_negative_scale_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)))) + ((((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) * S ((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) + ((dst_negative_scale_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable))) + (((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) * S ((dst_negative_code_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)) + ((dst_negative_scale_mask_source_firsttable) + (dst_negative_scale_mask_source_firsttable)))))) /\ (forall dst_index_mask_source_firsttable. (exists pvs_le_gap_mask_source_firsttabledomain. pvs_le_gap_mask_source_firsttabledomain + (dst_index_mask_source_firsttable) = (n)) -> exists dst_positive_mask_source_firsttable dst_negative_mask_source_firsttable dst_value_mask_source_firsttable. ((((exists ff_h_pvs_mask_source_firsttableentrypositive. ff_h_pvs_mask_source_firsttableentrypositive + S (dst_positive_mask_source_firsttable) = S ((S (dst_index_mask_source_firsttable)) * dst_positive_scale_mask_source_firsttable)) /\ exists ff_q_pvs_mask_source_firsttableentrypositive. dst_positive_code_mask_source_firsttable = ff_q_pvs_mask_source_firsttableentrypositive * S ((S (dst_index_mask_source_firsttable)) * dst_positive_scale_mask_source_firsttable) + (dst_positive_mask_source_firsttable))) /\ (((((exists ff_h_pvs_mask_source_firsttableentrynegative. ff_h_pvs_mask_source_firsttableentrynegative + S (dst_negative_mask_source_firsttable) = S ((S (dst_index_mask_source_firsttable)) * dst_negative_scale_mask_source_firsttable)) /\ exists ff_q_pvs_mask_source_firsttableentrynegative. dst_negative_code_mask_source_firsttable = ff_q_pvs_mask_source_firsttableentrynegative * S ((S (dst_index_mask_source_firsttable)) * dst_negative_scale_mask_source_firsttable) + (dst_negative_mask_source_firsttable))) /\ (exists ge_balance_positive_mask_source_firsttableentryvalue ge_balance_negative_mask_source_firsttableentryvalue. (((((dst_value_mask_source_firsttable) = 2 * (ge_balance_positive_mask_source_firsttableentryvalue) /\ (ge_balance_negative_mask_source_firsttableentryvalue) = 0) \/ exists ge_signed_half_mask_source_firsttableentryvaluedecode. (((dst_value_mask_source_firsttable) = 2 * ge_signed_half_mask_source_firsttableentryvaluedecode + 1 /\ (ge_balance_positive_mask_source_firsttableentryvalue) = 0) /\ (ge_balance_negative_mask_source_firsttableentryvalue) = S ge_signed_half_mask_source_firsttableentryvaluedecode))) /\ ((dst_positive_mask_source_firsttable) + ge_balance_negative_mask_source_firsttableentryvalue = (dst_negative_mask_source_firsttable) + ge_balance_positive_mask_source_firsttableentryvalue))))))))) /\ (forall dm_index_mask_source_first dm_value_mask_source_first. (exists pvs_le_gap_mask_source_firstdomain. pvs_le_gap_mask_source_firstdomain + (dm_index_mask_source_first) = (n)) -> (exists dst_positive_code_mask_source_firstlookup dst_positive_scale_mask_source_firstlookup dst_negative_code_mask_source_firstlookup dst_negative_scale_mask_source_firstlookup dst_positive_mask_source_firstlookup dst_negative_mask_source_firstlookup. (((M) = (((((dst_positive_code_mask_source_firstlookup) + (dst_positive_scale_mask_source_firstlookup)) * S ((dst_positive_code_mask_source_firstlookup) + (dst_positive_scale_mask_source_firstlookup)) + ((dst_positive_scale_mask_source_firstlookup) + (dst_positive_scale_mask_source_firstlookup))) + (((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) * S ((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) + ((dst_negative_scale_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)))) * S ((((dst_positive_code_mask_source_firstlookup) + (dst_positive_scale_mask_source_firstlookup)) * S ((dst_positive_code_mask_source_firstlookup) + (dst_positive_scale_mask_source_firstlookup)) + ((dst_positive_scale_mask_source_firstlookup) + (dst_positive_scale_mask_source_firstlookup))) + (((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) * S ((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) + ((dst_negative_scale_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)))) + ((((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) * S ((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) + ((dst_negative_scale_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup))) + (((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) * S ((dst_negative_code_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)) + ((dst_negative_scale_mask_source_firstlookup) + (dst_negative_scale_mask_source_firstlookup)))))) /\ (((((exists ff_h_pvs_mask_source_firstlookuppositive. ff_h_pvs_mask_source_firstlookuppositive + S (dst_positive_mask_source_firstlookup) = S ((S (dm_index_mask_source_first)) * dst_positive_scale_mask_source_firstlookup)) /\ exists ff_q_pvs_mask_source_firstlookuppositive. dst_positive_code_mask_source_firstlookup = ff_q_pvs_mask_source_firstlookuppositive * S ((S (dm_index_mask_source_first)) * dst_positive_scale_mask_source_firstlookup) + (dst_positive_mask_source_firstlookup))) /\ (((((exists ff_h_pvs_mask_source_firstlookupnegative. ff_h_pvs_mask_source_firstlookupnegative + S (dst_negative_mask_source_firstlookup) = S ((S (dm_index_mask_source_first)) * dst_negative_scale_mask_source_firstlookup)) /\ exists ff_q_pvs_mask_source_firstlookupnegative. dst_negative_code_mask_source_firstlookup = ff_q_pvs_mask_source_firstlookupnegative * S ((S (dm_index_mask_source_first)) * dst_negative_scale_mask_source_firstlookup) + (dst_negative_mask_source_firstlookup))) /\ (exists ge_balance_positive_mask_source_firstlookupvalue ge_balance_negative_mask_source_firstlookupvalue. (((((dm_value_mask_source_first) = 2 * (ge_balance_positive_mask_source_firstlookupvalue) /\ (ge_balance_negative_mask_source_firstlookupvalue) = 0) \/ exists ge_signed_half_mask_source_firstlookupvaluedecode. (((dm_value_mask_source_first) = 2 * ge_signed_half_mask_source_firstlookupvaluedecode + 1 /\ (ge_balance_positive_mask_source_firstlookupvalue) = 0) /\ (ge_balance_negative_mask_source_firstlookupvalue) = S ge_signed_half_mask_source_firstlookupvaluedecode))) /\ ((dst_positive_mask_source_firstlookup) + ge_balance_negative_mask_source_firstlookupvalue = (dst_negative_mask_source_firstlookup) + ge_balance_positive_mask_source_firstlookupvalue))))))))) -> ((((~((dm_index_mask_source_first)=0)) /\ (exists dm_quotient_mask_source_firstentry. (((n)=(dm_index_mask_source_first)*dm_quotient_mask_source_firstentry) /\ (exists dst_positive_code_mask_source_firstentryinput dst_positive_scale_mask_source_firstentryinput dst_negative_code_mask_source_firstentryinput dst_negative_scale_mask_source_firstentryinput dst_positive_mask_source_firstentryinput dst_negative_mask_source_firstentryinput. (((F) = (((((dst_positive_code_mask_source_firstentryinput) + (dst_positive_scale_mask_source_firstentryinput)) * S ((dst_positive_code_mask_source_firstentryinput) + (dst_positive_scale_mask_source_firstentryinput)) + ((dst_positive_scale_mask_source_firstentryinput) + (dst_positive_scale_mask_source_firstentryinput))) + (((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) * S ((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) + ((dst_negative_scale_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)))) * S ((((dst_positive_code_mask_source_firstentryinput) + (dst_positive_scale_mask_source_firstentryinput)) * S ((dst_positive_code_mask_source_firstentryinput) + (dst_positive_scale_mask_source_firstentryinput)) + ((dst_positive_scale_mask_source_firstentryinput) + (dst_positive_scale_mask_source_firstentryinput))) + (((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) * S ((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) + ((dst_negative_scale_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)))) + ((((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) * S ((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) + ((dst_negative_scale_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput))) + (((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) * S ((dst_negative_code_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)) + ((dst_negative_scale_mask_source_firstentryinput) + (dst_negative_scale_mask_source_firstentryinput)))))) /\ (((((exists ff_h_pvs_mask_source_firstentryinputpositive. ff_h_pvs_mask_source_firstentryinputpositive + S (dst_positive_mask_source_firstentryinput) = S ((S (dm_index_mask_source_first)) * dst_positive_scale_mask_source_firstentryinput)) /\ exists ff_q_pvs_mask_source_firstentryinputpositive. dst_positive_code_mask_source_firstentryinput = ff_q_pvs_mask_source_firstentryinputpositive * S ((S (dm_index_mask_source_first)) * dst_positive_scale_mask_source_firstentryinput) + (dst_positive_mask_source_firstentryinput))) /\ (((((exists ff_h_pvs_mask_source_firstentryinputnegative. ff_h_pvs_mask_source_firstentryinputnegative + S (dst_negative_mask_source_firstentryinput) = S ((S (dm_index_mask_source_first)) * dst_negative_scale_mask_source_firstentryinput)) /\ exists ff_q_pvs_mask_source_firstentryinputnegative. dst_negative_code_mask_source_firstentryinput = ff_q_pvs_mask_source_firstentryinputnegative * S ((S (dm_index_mask_source_first)) * dst_negative_scale_mask_source_firstentryinput) + (dst_negative_mask_source_firstentryinput))) /\ (exists ge_balance_positive_mask_source_firstentryinputvalue ge_balance_negative_mask_source_firstentryinputvalue. (((((dm_value_mask_source_first) = 2 * (ge_balance_positive_mask_source_firstentryinputvalue) /\ (ge_balance_negative_mask_source_firstentryinputvalue) = 0) \/ exists ge_signed_half_mask_source_firstentryinputvaluedecode. (((dm_value_mask_source_first) = 2 * ge_signed_half_mask_source_firstentryinputvaluedecode + 1 /\ (ge_balance_positive_mask_source_firstentryinputvalue) = 0) /\ (ge_balance_negative_mask_source_firstentryinputvalue) = S ge_signed_half_mask_source_firstentryinputvaluedecode))) /\ ((dst_positive_mask_source_firstentryinput) + ge_balance_negative_mask_source_firstentryinputvalue = (dst_negative_mask_source_firstentryinput) + ge_balance_positive_mask_source_firstentryinputvalue))))))))))))) \/ ((((dm_index_mask_source_first)=0 \/ ~(exists pvs_factor_mask_source_firstentrynondivisor. (n) = (dm_index_mask_source_first) * pvs_factor_mask_source_firstentrynondivisor)) /\ ((dm_value_mask_source_first)=0))))))) -> (((exists dst_positive_code_mask_source_secondtable dst_positive_scale_mask_source_secondtable dst_negative_code_mask_source_secondtable dst_negative_scale_mask_source_secondtable. (((K) = (((((dst_positive_code_mask_source_secondtable) + (dst_positive_scale_mask_source_secondtable)) * S ((dst_positive_code_mask_source_secondtable) + (dst_positive_scale_mask_source_secondtable)) + ((dst_positive_scale_mask_source_secondtable) + (dst_positive_scale_mask_source_secondtable))) + (((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) * S ((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) + ((dst_negative_scale_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)))) * S ((((dst_positive_code_mask_source_secondtable) + (dst_positive_scale_mask_source_secondtable)) * S ((dst_positive_code_mask_source_secondtable) + (dst_positive_scale_mask_source_secondtable)) + ((dst_positive_scale_mask_source_secondtable) + (dst_positive_scale_mask_source_secondtable))) + (((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) * S ((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) + ((dst_negative_scale_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)))) + ((((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) * S ((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) + ((dst_negative_scale_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable))) + (((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) * S ((dst_negative_code_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)) + ((dst_negative_scale_mask_source_secondtable) + (dst_negative_scale_mask_source_secondtable)))))) /\ (forall dst_index_mask_source_secondtable. (exists pvs_le_gap_mask_source_secondtabledomain. pvs_le_gap_mask_source_secondtabledomain + (dst_index_mask_source_secondtable) = (n)) -> exists dst_positive_mask_source_secondtable dst_negative_mask_source_secondtable dst_value_mask_source_secondtable. ((((exists ff_h_pvs_mask_source_secondtableentrypositive. ff_h_pvs_mask_source_secondtableentrypositive + S (dst_positive_mask_source_secondtable) = S ((S (dst_index_mask_source_secondtable)) * dst_positive_scale_mask_source_secondtable)) /\ exists ff_q_pvs_mask_source_secondtableentrypositive. dst_positive_code_mask_source_secondtable = ff_q_pvs_mask_source_secondtableentrypositive * S ((S (dst_index_mask_source_secondtable)) * dst_positive_scale_mask_source_secondtable) + (dst_positive_mask_source_secondtable))) /\ (((((exists ff_h_pvs_mask_source_secondtableentrynegative. ff_h_pvs_mask_source_secondtableentrynegative + S (dst_negative_mask_source_secondtable) = S ((S (dst_index_mask_source_secondtable)) * dst_negative_scale_mask_source_secondtable)) /\ exists ff_q_pvs_mask_source_secondtableentrynegative. dst_negative_code_mask_source_secondtable = ff_q_pvs_mask_source_secondtableentrynegative * S ((S (dst_index_mask_source_secondtable)) * dst_negative_scale_mask_source_secondtable) + (dst_negative_mask_source_secondtable))) /\ (exists ge_balance_positive_mask_source_secondtableentryvalue ge_balance_negative_mask_source_secondtableentryvalue. (((((dst_value_mask_source_secondtable) = 2 * (ge_balance_positive_mask_source_secondtableentryvalue) /\ (ge_balance_negative_mask_source_secondtableentryvalue) = 0) \/ exists ge_signed_half_mask_source_secondtableentryvaluedecode. (((dst_value_mask_source_secondtable) = 2 * ge_signed_half_mask_source_secondtableentryvaluedecode + 1 /\ (ge_balance_positive_mask_source_secondtableentryvalue) = 0) /\ (ge_balance_negative_mask_source_secondtableentryvalue) = S ge_signed_half_mask_source_secondtableentryvaluedecode))) /\ ((dst_positive_mask_source_secondtable) + ge_balance_negative_mask_source_secondtableentryvalue = (dst_negative_mask_source_secondtable) + ge_balance_positive_mask_source_secondtableentryvalue))))))))) /\ (forall dm_index_mask_source_second dm_value_mask_source_second. (exists pvs_le_gap_mask_source_seconddomain. pvs_le_gap_mask_source_seconddomain + (dm_index_mask_source_second) = (n)) -> (exists dst_positive_code_mask_source_secondlookup dst_positive_scale_mask_source_secondlookup dst_negative_code_mask_source_secondlookup dst_negative_scale_mask_source_secondlookup dst_positive_mask_source_secondlookup dst_negative_mask_source_secondlookup. (((K) = (((((dst_positive_code_mask_source_secondlookup) + (dst_positive_scale_mask_source_secondlookup)) * S ((dst_positive_code_mask_source_secondlookup) + (dst_positive_scale_mask_source_secondlookup)) + ((dst_positive_scale_mask_source_secondlookup) + (dst_positive_scale_mask_source_secondlookup))) + (((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) * S ((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) + ((dst_negative_scale_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)))) * S ((((dst_positive_code_mask_source_secondlookup) + (dst_positive_scale_mask_source_secondlookup)) * S ((dst_positive_code_mask_source_secondlookup) + (dst_positive_scale_mask_source_secondlookup)) + ((dst_positive_scale_mask_source_secondlookup) + (dst_positive_scale_mask_source_secondlookup))) + (((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) * S ((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) + ((dst_negative_scale_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)))) + ((((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) * S ((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) + ((dst_negative_scale_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup))) + (((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) * S ((dst_negative_code_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)) + ((dst_negative_scale_mask_source_secondlookup) + (dst_negative_scale_mask_source_secondlookup)))))) /\ (((((exists ff_h_pvs_mask_source_secondlookuppositive. ff_h_pvs_mask_source_secondlookuppositive + S (dst_positive_mask_source_secondlookup) = S ((S (dm_index_mask_source_second)) * dst_positive_scale_mask_source_secondlookup)) /\ exists ff_q_pvs_mask_source_secondlookuppositive. dst_positive_code_mask_source_secondlookup = ff_q_pvs_mask_source_secondlookuppositive * S ((S (dm_index_mask_source_second)) * dst_positive_scale_mask_source_secondlookup) + (dst_positive_mask_source_secondlookup))) /\ (((((exists ff_h_pvs_mask_source_secondlookupnegative. ff_h_pvs_mask_source_secondlookupnegative + S (dst_negative_mask_source_secondlookup) = S ((S (dm_index_mask_source_second)) * dst_negative_scale_mask_source_secondlookup)) /\ exists ff_q_pvs_mask_source_secondlookupnegative. dst_negative_code_mask_source_secondlookup = ff_q_pvs_mask_source_secondlookupnegative * S ((S (dm_index_mask_source_second)) * dst_negative_scale_mask_source_secondlookup) + (dst_negative_mask_source_secondlookup))) /\ (exists ge_balance_positive_mask_source_secondlookupvalue ge_balance_negative_mask_source_secondlookupvalue. (((((dm_value_mask_source_second) = 2 * (ge_balance_positive_mask_source_secondlookupvalue) /\ (ge_balance_negative_mask_source_secondlookupvalue) = 0) \/ exists ge_signed_half_mask_source_secondlookupvaluedecode. (((dm_value_mask_source_second) = 2 * ge_signed_half_mask_source_secondlookupvaluedecode + 1 /\ (ge_balance_positive_mask_source_secondlookupvalue) = 0) /\ (ge_balance_negative_mask_source_secondlookupvalue) = S ge_signed_half_mask_source_secondlookupvaluedecode))) /\ ((dst_positive_mask_source_secondlookup) + ge_balance_negative_mask_source_secondlookupvalue = (dst_negative_mask_source_secondlookup) + ge_balance_positive_mask_source_secondlookupvalue))))))))) -> ((((~((dm_index_mask_source_second)=0)) /\ (exists dm_quotient_mask_source_secondentry. (((n)=(dm_index_mask_source_second)*dm_quotient_mask_source_secondentry) /\ (exists dst_positive_code_mask_source_secondentryinput dst_positive_scale_mask_source_secondentryinput dst_negative_code_mask_source_secondentryinput dst_negative_scale_mask_source_secondentryinput dst_positive_mask_source_secondentryinput dst_negative_mask_source_secondentryinput. (((G) = (((((dst_positive_code_mask_source_secondentryinput) + (dst_positive_scale_mask_source_secondentryinput)) * S ((dst_positive_code_mask_source_secondentryinput) + (dst_positive_scale_mask_source_secondentryinput)) + ((dst_positive_scale_mask_source_secondentryinput) + (dst_positive_scale_mask_source_secondentryinput))) + (((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) * S ((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) + ((dst_negative_scale_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)))) * S ((((dst_positive_code_mask_source_secondentryinput) + (dst_positive_scale_mask_source_secondentryinput)) * S ((dst_positive_code_mask_source_secondentryinput) + (dst_positive_scale_mask_source_secondentryinput)) + ((dst_positive_scale_mask_source_secondentryinput) + (dst_positive_scale_mask_source_secondentryinput))) + (((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) * S ((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) + ((dst_negative_scale_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)))) + ((((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) * S ((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) + ((dst_negative_scale_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput))) + (((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) * S ((dst_negative_code_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)) + ((dst_negative_scale_mask_source_secondentryinput) + (dst_negative_scale_mask_source_secondentryinput)))))) /\ (((((exists ff_h_pvs_mask_source_secondentryinputpositive. ff_h_pvs_mask_source_secondentryinputpositive + S (dst_positive_mask_source_secondentryinput) = S ((S (dm_index_mask_source_second)) * dst_positive_scale_mask_source_secondentryinput)) /\ exists ff_q_pvs_mask_source_secondentryinputpositive. dst_positive_code_mask_source_secondentryinput = ff_q_pvs_mask_source_secondentryinputpositive * S ((S (dm_index_mask_source_second)) * dst_positive_scale_mask_source_secondentryinput) + (dst_positive_mask_source_secondentryinput))) /\ (((((exists ff_h_pvs_mask_source_secondentryinputnegative. ff_h_pvs_mask_source_secondentryinputnegative + S (dst_negative_mask_source_secondentryinput) = S ((S (dm_index_mask_source_second)) * dst_negative_scale_mask_source_secondentryinput)) /\ exists ff_q_pvs_mask_source_secondentryinputnegative. dst_negative_code_mask_source_secondentryinput = ff_q_pvs_mask_source_secondentryinputnegative * S ((S (dm_index_mask_source_second)) * dst_negative_scale_mask_source_secondentryinput) + (dst_negative_mask_source_secondentryinput))) /\ (exists ge_balance_positive_mask_source_secondentryinputvalue ge_balance_negative_mask_source_secondentryinputvalue. (((((dm_value_mask_source_second) = 2 * (ge_balance_positive_mask_source_secondentryinputvalue) /\ (ge_balance_negative_mask_source_secondentryinputvalue) = 0) \/ exists ge_signed_half_mask_source_secondentryinputvaluedecode. (((dm_value_mask_source_second) = 2 * ge_signed_half_mask_source_secondentryinputvaluedecode + 1 /\ (ge_balance_positive_mask_source_secondentryinputvalue) = 0) /\ (ge_balance_negative_mask_source_secondentryinputvalue) = S ge_signed_half_mask_source_secondentryinputvaluedecode))) /\ ((dst_positive_mask_source_secondentryinput) + ge_balance_negative_mask_source_secondentryinputvalue = (dst_negative_mask_source_secondentryinput) + ge_balance_positive_mask_source_secondentryinputvalue))))))))))))) \/ ((((dm_index_mask_source_second)=0 \/ ~(exists pvs_factor_mask_source_secondentrynondivisor. (n) = (dm_index_mask_source_second) * pvs_factor_mask_source_secondentrynondivisor)) /\ ((dm_value_mask_source_second)=0))))))) -> (forall dst_index_mask_source_result dst_first_mask_source_result dst_second_mask_source_result. (exists pvs_gap_mask_source_resultbound. pvs_gap_mask_source_resultbound + S (dst_index_mask_source_result) = (S n)) -> (exists dst_positive_code_mask_source_resultfirst dst_positive_scale_mask_source_resultfirst dst_negative_code_mask_source_resultfirst dst_negative_scale_mask_source_resultfirst dst_positive_mask_source_resultfirst dst_negative_mask_source_resultfirst. (((M) = (((((dst_positive_code_mask_source_resultfirst) + (dst_positive_scale_mask_source_resultfirst)) * S ((dst_positive_code_mask_source_resultfirst) + (dst_positive_scale_mask_source_resultfirst)) + ((dst_positive_scale_mask_source_resultfirst) + (dst_positive_scale_mask_source_resultfirst))) + (((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) * S ((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) + ((dst_negative_scale_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)))) * S ((((dst_positive_code_mask_source_resultfirst) + (dst_positive_scale_mask_source_resultfirst)) * S ((dst_positive_code_mask_source_resultfirst) + (dst_positive_scale_mask_source_resultfirst)) + ((dst_positive_scale_mask_source_resultfirst) + (dst_positive_scale_mask_source_resultfirst))) + (((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) * S ((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) + ((dst_negative_scale_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)))) + ((((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) * S ((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) + ((dst_negative_scale_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst))) + (((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) * S ((dst_negative_code_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)) + ((dst_negative_scale_mask_source_resultfirst) + (dst_negative_scale_mask_source_resultfirst)))))) /\ (((((exists ff_h_pvs_mask_source_resultfirstpositive. ff_h_pvs_mask_source_resultfirstpositive + S (dst_positive_mask_source_resultfirst) = S ((S (dst_index_mask_source_result)) * dst_positive_scale_mask_source_resultfirst)) /\ exists ff_q_pvs_mask_source_resultfirstpositive. dst_positive_code_mask_source_resultfirst = ff_q_pvs_mask_source_resultfirstpositive * S ((S (dst_index_mask_source_result)) * dst_positive_scale_mask_source_resultfirst) + (dst_positive_mask_source_resultfirst))) /\ (((((exists ff_h_pvs_mask_source_resultfirstnegative. ff_h_pvs_mask_source_resultfirstnegative + S (dst_negative_mask_source_resultfirst) = S ((S (dst_index_mask_source_result)) * dst_negative_scale_mask_source_resultfirst)) /\ exists ff_q_pvs_mask_source_resultfirstnegative. dst_negative_code_mask_source_resultfirst = ff_q_pvs_mask_source_resultfirstnegative * S ((S (dst_index_mask_source_result)) * dst_negative_scale_mask_source_resultfirst) + (dst_negative_mask_source_resultfirst))) /\ (exists ge_balance_positive_mask_source_resultfirstvalue ge_balance_negative_mask_source_resultfirstvalue. (((((dst_first_mask_source_result) = 2 * (ge_balance_positive_mask_source_resultfirstvalue) /\ (ge_balance_negative_mask_source_resultfirstvalue) = 0) \/ exists ge_signed_half_mask_source_resultfirstvaluedecode. (((dst_first_mask_source_result) = 2 * ge_signed_half_mask_source_resultfirstvaluedecode + 1 /\ (ge_balance_positive_mask_source_resultfirstvalue) = 0) /\ (ge_balance_negative_mask_source_resultfirstvalue) = S ge_signed_half_mask_source_resultfirstvaluedecode))) /\ ((dst_positive_mask_source_resultfirst) + ge_balance_negative_mask_source_resultfirstvalue = (dst_negative_mask_source_resultfirst) + ge_balance_positive_mask_source_resultfirstvalue))))))))) -> (exists dst_positive_code_mask_source_resultsecond dst_positive_scale_mask_source_resultsecond dst_negative_code_mask_source_resultsecond dst_negative_scale_mask_source_resultsecond dst_positive_mask_source_resultsecond dst_negative_mask_source_resultsecond. (((K) = (((((dst_positive_code_mask_source_resultsecond) + (dst_positive_scale_mask_source_resultsecond)) * S ((dst_positive_code_mask_source_resultsecond) + (dst_positive_scale_mask_source_resultsecond)) + ((dst_positive_scale_mask_source_resultsecond) + (dst_positive_scale_mask_source_resultsecond))) + (((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) * S ((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) + ((dst_negative_scale_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)))) * S ((((dst_positive_code_mask_source_resultsecond) + (dst_positive_scale_mask_source_resultsecond)) * S ((dst_positive_code_mask_source_resultsecond) + (dst_positive_scale_mask_source_resultsecond)) + ((dst_positive_scale_mask_source_resultsecond) + (dst_positive_scale_mask_source_resultsecond))) + (((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) * S ((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) + ((dst_negative_scale_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)))) + ((((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) * S ((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) + ((dst_negative_scale_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond))) + (((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) * S ((dst_negative_code_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)) + ((dst_negative_scale_mask_source_resultsecond) + (dst_negative_scale_mask_source_resultsecond)))))) /\ (((((exists ff_h_pvs_mask_source_resultsecondpositive. ff_h_pvs_mask_source_resultsecondpositive + S (dst_positive_mask_source_resultsecond) = S ((S (dst_index_mask_source_result)) * dst_positive_scale_mask_source_resultsecond)) /\ exists ff_q_pvs_mask_source_resultsecondpositive. dst_positive_code_mask_source_resultsecond = ff_q_pvs_mask_source_resultsecondpositive * S ((S (dst_index_mask_source_result)) * dst_positive_scale_mask_source_resultsecond) + (dst_positive_mask_source_resultsecond))) /\ (((((exists ff_h_pvs_mask_source_resultsecondnegative. ff_h_pvs_mask_source_resultsecondnegative + S (dst_negative_mask_source_resultsecond) = S ((S (dst_index_mask_source_result)) * dst_negative_scale_mask_source_resultsecond)) /\ exists ff_q_pvs_mask_source_resultsecondnegative. dst_negative_code_mask_source_resultsecond = ff_q_pvs_mask_source_resultsecondnegative * S ((S (dst_index_mask_source_result)) * dst_negative_scale_mask_source_resultsecond) + (dst_negative_mask_source_resultsecond))) /\ (exists ge_balance_positive_mask_source_resultsecondvalue ge_balance_negative_mask_source_resultsecondvalue. (((((dst_second_mask_source_result) = 2 * (ge_balance_positive_mask_source_resultsecondvalue) /\ (ge_balance_negative_mask_source_resultsecondvalue) = 0) \/ exists ge_signed_half_mask_source_resultsecondvaluedecode. (((dst_second_mask_source_result) = 2 * ge_signed_half_mask_source_resultsecondvaluedecode + 1 /\ (ge_balance_positive_mask_source_resultsecondvalue) = 0) /\ (ge_balance_negative_mask_source_resultsecondvalue) = S ge_signed_half_mask_source_resultsecondvaluedecode))) /\ ((dst_positive_mask_source_resultsecond) + ge_balance_negative_mask_source_resultsecondvalue = (dst_negative_mask_source_resultsecond) + ge_balance_positive_mask_source_resultsecondvalue))))))))) -> dst_first_mask_source_result = dst_second_mask_source_result)

signed_divisor_sum_exists

new owned theorem · read exact theorem evidence

Bundle node 308; exact statement SHA-256 a153320907e32d01c960581b45a1b83bc754ede7c2e22f3fd5baf8a416fce7cd

Exact first-order statement

forall N F n. (exists dst_positive_code_sum_total_input dst_positive_scale_sum_total_input dst_negative_code_sum_total_input dst_negative_scale_sum_total_input. (((F) = (((((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) * S ((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) + ((dst_positive_scale_sum_total_input) + (dst_positive_scale_sum_total_input))) + (((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input)))) * S ((((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) * S ((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) + ((dst_positive_scale_sum_total_input) + (dst_positive_scale_sum_total_input))) + (((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input)))) + ((((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input))) + (((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input)))))) /\ (forall dst_index_sum_total_input. (exists pvs_le_gap_sum_total_inputdomain. pvs_le_gap_sum_total_inputdomain + (dst_index_sum_total_input) = (N)) -> exists dst_positive_sum_total_input dst_negative_sum_total_input dst_value_sum_total_input. ((((exists ff_h_pvs_sum_total_inputentrypositive. ff_h_pvs_sum_total_inputentrypositive + S (dst_positive_sum_total_input) = S ((S (dst_index_sum_total_input)) * dst_positive_scale_sum_total_input)) /\ exists ff_q_pvs_sum_total_inputentrypositive. dst_positive_code_sum_total_input = ff_q_pvs_sum_total_inputentrypositive * S ((S (dst_index_sum_total_input)) * dst_positive_scale_sum_total_input) + (dst_positive_sum_total_input))) /\ (((((exists ff_h_pvs_sum_total_inputentrynegative. ff_h_pvs_sum_total_inputentrynegative + S (dst_negative_sum_total_input) = S ((S (dst_index_sum_total_input)) * dst_negative_scale_sum_total_input)) /\ exists ff_q_pvs_sum_total_inputentrynegative. dst_negative_code_sum_total_input = ff_q_pvs_sum_total_inputentrynegative * S ((S (dst_index_sum_total_input)) * dst_negative_scale_sum_total_input) + (dst_negative_sum_total_input))) /\ (exists ge_balance_positive_sum_total_inputentryvalue ge_balance_negative_sum_total_inputentryvalue. (((((dst_value_sum_total_input) = 2 * (ge_balance_positive_sum_total_inputentryvalue) /\ (ge_balance_negative_sum_total_inputentryvalue) = 0) \/ exists ge_signed_half_sum_total_inputentryvaluedecode. (((dst_value_sum_total_input) = 2 * ge_signed_half_sum_total_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_total_inputentryvalue) = 0) /\ (ge_balance_negative_sum_total_inputentryvalue) = S ge_signed_half_sum_total_inputentryvaluedecode))) /\ ((dst_positive_sum_total_input) + ge_balance_negative_sum_total_inputentryvalue = (dst_negative_sum_total_input) + ge_balance_positive_sum_total_inputentryvalue))))))))) -> ~(n=0) -> (exists pvs_le_gap_sum_total_bound. pvs_le_gap_sum_total_bound + (n) = (N)) -> exists z. (((~((n)=0)) /\ (exists dm_mask_table_sum_total_result. ((((exists dst_positive_code_sum_total_resultmasktable dst_positive_scale_sum_total_resultmasktable dst_negative_code_sum_total_resultmasktable dst_negative_scale_sum_total_resultmasktable. (((dm_mask_table_sum_total_result) = (((((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) * S ((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) + ((dst_positive_scale_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable))) + (((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)))) * S ((((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) * S ((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) + ((dst_positive_scale_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable))) + (((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)))) + ((((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable))) + (((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)))))) /\ (forall dst_index_sum_total_resultmasktable. (exists pvs_le_gap_sum_total_resultmasktabledomain. pvs_le_gap_sum_total_resultmasktabledomain + (dst_index_sum_total_resultmasktable) = (n)) -> exists dst_positive_sum_total_resultmasktable dst_negative_sum_total_resultmasktable dst_value_sum_total_resultmasktable. ((((exists ff_h_pvs_sum_total_resultmasktableentrypositive. ff_h_pvs_sum_total_resultmasktableentrypositive + S (dst_positive_sum_total_resultmasktable) = S ((S (dst_index_sum_total_resultmasktable)) * dst_positive_scale_sum_total_resultmasktable)) /\ exists ff_q_pvs_sum_total_resultmasktableentrypositive. dst_positive_code_sum_total_resultmasktable = ff_q_pvs_sum_total_resultmasktableentrypositive * S ((S (dst_index_sum_total_resultmasktable)) * dst_positive_scale_sum_total_resultmasktable) + (dst_positive_sum_total_resultmasktable))) /\ (((((exists ff_h_pvs_sum_total_resultmasktableentrynegative. ff_h_pvs_sum_total_resultmasktableentrynegative + S (dst_negative_sum_total_resultmasktable) = S ((S (dst_index_sum_total_resultmasktable)) * dst_negative_scale_sum_total_resultmasktable)) /\ exists ff_q_pvs_sum_total_resultmasktableentrynegative. dst_negative_code_sum_total_resultmasktable = ff_q_pvs_sum_total_resultmasktableentrynegative * S ((S (dst_index_sum_total_resultmasktable)) * dst_negative_scale_sum_total_resultmasktable) + (dst_negative_sum_total_resultmasktable))) /\ (exists ge_balance_positive_sum_total_resultmasktableentryvalue ge_balance_negative_sum_total_resultmasktableentryvalue. (((((dst_value_sum_total_resultmasktable) = 2 * (ge_balance_positive_sum_total_resultmasktableentryvalue) /\ (ge_balance_negative_sum_total_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_total_resultmasktableentryvaluedecode. (((dst_value_sum_total_resultmasktable) = 2 * ge_signed_half_sum_total_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_total_resultmasktableentryvalue) = S ge_signed_half_sum_total_resultmasktableentryvaluedecode))) /\ ((dst_positive_sum_total_resultmasktable) + ge_balance_negative_sum_total_resultmasktableentryvalue = (dst_negative_sum_total_resultmasktable) + ge_balance_positive_sum_total_resultmasktableentryvalue))))))))) /\ (forall dm_index_sum_total_resultmask dm_value_sum_total_resultmask. (exists pvs_le_gap_sum_total_resultmaskdomain. pvs_le_gap_sum_total_resultmaskdomain + (dm_index_sum_total_resultmask) = (n)) -> (exists dst_positive_code_sum_total_resultmasklookup dst_positive_scale_sum_total_resultmasklookup dst_negative_code_sum_total_resultmasklookup dst_negative_scale_sum_total_resultmasklookup dst_positive_sum_total_resultmasklookup dst_negative_sum_total_resultmasklookup. (((dm_mask_table_sum_total_result) = (((((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) * S ((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) + ((dst_positive_scale_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup))) + (((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)))) * S ((((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) * S ((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) + ((dst_positive_scale_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup))) + (((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)))) + ((((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup))) + (((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)))))) /\ (((((exists ff_h_pvs_sum_total_resultmasklookuppositive. ff_h_pvs_sum_total_resultmasklookuppositive + S (dst_positive_sum_total_resultmasklookup) = S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmasklookup)) /\ exists ff_q_pvs_sum_total_resultmasklookuppositive. dst_positive_code_sum_total_resultmasklookup = ff_q_pvs_sum_total_resultmasklookuppositive * S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmasklookup) + (dst_positive_sum_total_resultmasklookup))) /\ (((((exists ff_h_pvs_sum_total_resultmasklookupnegative. ff_h_pvs_sum_total_resultmasklookupnegative + S (dst_negative_sum_total_resultmasklookup) = S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmasklookup)) /\ exists ff_q_pvs_sum_total_resultmasklookupnegative. dst_negative_code_sum_total_resultmasklookup = ff_q_pvs_sum_total_resultmasklookupnegative * S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_sum_total_resultmasklookup))) /\ (exists ge_balance_positive_sum_total_resultmasklookupvalue ge_balance_negative_sum_total_resultmasklookupvalue. (((((dm_value_sum_total_resultmask) = 2 * (ge_balance_positive_sum_total_resultmasklookupvalue) /\ (ge_balance_negative_sum_total_resultmasklookupvalue) = 0) \/ exists ge_signed_half_sum_total_resultmasklookupvaluedecode. (((dm_value_sum_total_resultmask) = 2 * ge_signed_half_sum_total_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmasklookupvalue) = 0) /\ (ge_balance_negative_sum_total_resultmasklookupvalue) = S ge_signed_half_sum_total_resultmasklookupvaluedecode))) /\ ((dst_positive_sum_total_resultmasklookup) + ge_balance_negative_sum_total_resultmasklookupvalue = (dst_negative_sum_total_resultmasklookup) + ge_balance_positive_sum_total_resultmasklookupvalue))))))))) -> ((((~((dm_index_sum_total_resultmask)=0)) /\ (exists dm_quotient_sum_total_resultmaskentry. (((n)=(dm_index_sum_total_resultmask)*dm_quotient_sum_total_resultmaskentry) /\ (exists dst_positive_code_sum_total_resultmaskentryinput dst_positive_scale_sum_total_resultmaskentryinput dst_negative_code_sum_total_resultmaskentryinput dst_negative_scale_sum_total_resultmaskentryinput dst_positive_sum_total_resultmaskentryinput dst_negative_sum_total_resultmaskentryinput. (((F) = (((((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) * S ((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) + ((dst_positive_scale_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput))) + (((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)))) * S ((((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) * S ((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) + ((dst_positive_scale_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput))) + (((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)))) + ((((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput))) + (((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryinputpositive. ff_h_pvs_sum_total_resultmaskentryinputpositive + S (dst_positive_sum_total_resultmaskentryinput) = S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmaskentryinput)) /\ exists ff_q_pvs_sum_total_resultmaskentryinputpositive. dst_positive_code_sum_total_resultmaskentryinput = ff_q_pvs_sum_total_resultmaskentryinputpositive * S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmaskentryinput) + (dst_positive_sum_total_resultmaskentryinput))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryinputnegative. ff_h_pvs_sum_total_resultmaskentryinputnegative + S (dst_negative_sum_total_resultmaskentryinput) = S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmaskentryinput)) /\ exists ff_q_pvs_sum_total_resultmaskentryinputnegative. dst_negative_code_sum_total_resultmaskentryinput = ff_q_pvs_sum_total_resultmaskentryinputnegative * S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_sum_total_resultmaskentryinput))) /\ (exists ge_balance_positive_sum_total_resultmaskentryinputvalue ge_balance_negative_sum_total_resultmaskentryinputvalue. (((((dm_value_sum_total_resultmask) = 2 * (ge_balance_positive_sum_total_resultmaskentryinputvalue) /\ (ge_balance_negative_sum_total_resultmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryinputvaluedecode. (((dm_value_sum_total_resultmask) = 2 * ge_signed_half_sum_total_resultmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_total_resultmaskentryinputvalue) = S ge_signed_half_sum_total_resultmaskentryinputvaluedecode))) /\ ((dst_positive_sum_total_resultmaskentryinput) + ge_balance_negative_sum_total_resultmaskentryinputvalue = (dst_negative_sum_total_resultmaskentryinput) + ge_balance_positive_sum_total_resultmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_total_resultmask)=0 \/ ~(exists pvs_factor_sum_total_resultmaskentrynondivisor. (n) = (dm_index_sum_total_resultmask) * pvs_factor_sum_total_resultmaskentrynondivisor)) /\ ((dm_value_sum_total_resultmask)=0))))))) /\ (exists dst_positive_code_sum_total_resultfold dst_positive_scale_sum_total_resultfold dst_negative_code_sum_total_resultfold dst_negative_scale_sum_total_resultfold dst_positive_sum_sum_total_resultfold dst_negative_sum_sum_total_resultfold. (((dm_mask_table_sum_total_result) = (((((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) * S ((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) + ((dst_positive_scale_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold))) + (((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)))) * S ((((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) * S ((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) + ((dst_positive_scale_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold))) + (((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)))) + ((((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold))) + (((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)))))) /\ (((exists fs_u_dst_sum_total_resultfoldpositive fs_v_dst_sum_total_resultfoldpositive. ((((exists fs_h_dst_sum_total_resultfoldpositive_body_start. fs_h_dst_sum_total_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_start. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_total_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_total_resultfoldpositive_body_terminal. fs_h_dst_sum_total_resultfoldpositive_body_terminal + S (dst_positive_sum_sum_total_resultfold) = S ((S (S (n))) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_terminal. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_total_resultfoldpositive) + (dst_positive_sum_sum_total_resultfold))) /\ forall fs_i_dst_sum_total_resultfoldpositive_body_steps. (exists fs_lt_dst_sum_total_resultfoldpositive_body_steps_bound. fs_lt_dst_sum_total_resultfoldpositive_body_steps_bound + S fs_i_dst_sum_total_resultfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_total_resultfoldpositive_body_steps fs_r_dst_sum_total_resultfoldpositive_body_steps fs_s_dst_sum_total_resultfoldpositive_body_steps. ((((exists fs_h_dst_sum_total_resultfoldpositive_body_steps_summand. fs_h_dst_sum_total_resultfoldpositive_body_steps_summand + S (fs_a_dst_sum_total_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * dst_positive_scale_sum_total_resultfold)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_steps_summand. dst_positive_code_sum_total_resultfold = fs_q_dst_sum_total_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * dst_positive_scale_sum_total_resultfold) + (fs_a_dst_sum_total_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldpositive_body_steps_partial. fs_h_dst_sum_total_resultfoldpositive_body_steps_partial + S (fs_r_dst_sum_total_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_steps_partial. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive) + (fs_r_dst_sum_total_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldpositive_body_steps_successor. fs_h_dst_sum_total_resultfoldpositive_body_steps_successor + S (fs_s_dst_sum_total_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_steps_successor. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive) + (fs_s_dst_sum_total_resultfoldpositive_body_steps))) /\ fs_s_dst_sum_total_resultfoldpositive_body_steps = fs_r_dst_sum_total_resultfoldpositive_body_steps + fs_a_dst_sum_total_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_total_resultfoldnegative fs_v_dst_sum_total_resultfoldnegative. ((((exists fs_h_dst_sum_total_resultfoldnegative_body_start. fs_h_dst_sum_total_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_start. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_total_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_total_resultfoldnegative_body_terminal. fs_h_dst_sum_total_resultfoldnegative_body_terminal + S (dst_negative_sum_sum_total_resultfold) = S ((S (S (n))) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_terminal. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_total_resultfoldnegative) + (dst_negative_sum_sum_total_resultfold))) /\ forall fs_i_dst_sum_total_resultfoldnegative_body_steps. (exists fs_lt_dst_sum_total_resultfoldnegative_body_steps_bound. fs_lt_dst_sum_total_resultfoldnegative_body_steps_bound + S fs_i_dst_sum_total_resultfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_total_resultfoldnegative_body_steps fs_r_dst_sum_total_resultfoldnegative_body_steps fs_s_dst_sum_total_resultfoldnegative_body_steps. ((((exists fs_h_dst_sum_total_resultfoldnegative_body_steps_summand. fs_h_dst_sum_total_resultfoldnegative_body_steps_summand + S (fs_a_dst_sum_total_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * dst_negative_scale_sum_total_resultfold)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_steps_summand. dst_negative_code_sum_total_resultfold = fs_q_dst_sum_total_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * dst_negative_scale_sum_total_resultfold) + (fs_a_dst_sum_total_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldnegative_body_steps_partial. fs_h_dst_sum_total_resultfoldnegative_body_steps_partial + S (fs_r_dst_sum_total_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_steps_partial. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative) + (fs_r_dst_sum_total_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldnegative_body_steps_successor. fs_h_dst_sum_total_resultfoldnegative_body_steps_successor + S (fs_s_dst_sum_total_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_steps_successor. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative) + (fs_s_dst_sum_total_resultfoldnegative_body_steps))) /\ fs_s_dst_sum_total_resultfoldnegative_body_steps = fs_r_dst_sum_total_resultfoldnegative_body_steps + fs_a_dst_sum_total_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_total_resultfoldresult ge_balance_negative_sum_total_resultfoldresult. (((((z) = 2 * (ge_balance_positive_sum_total_resultfoldresult) /\ (ge_balance_negative_sum_total_resultfoldresult) = 0) \/ exists ge_signed_half_sum_total_resultfoldresultdecode. (((z) = 2 * ge_signed_half_sum_total_resultfoldresultdecode + 1 /\ (ge_balance_positive_sum_total_resultfoldresult) = 0) /\ (ge_balance_negative_sum_total_resultfoldresult) = S ge_signed_half_sum_total_resultfoldresultdecode))) /\ ((dst_positive_sum_sum_total_resultfold) + ge_balance_negative_sum_total_resultfoldresult = (dst_negative_sum_sum_total_resultfold) + ge_balance_positive_sum_total_resultfoldresult)))))))))))))

signed_divisor_sum_functional

new owned theorem · read exact theorem evidence

Bundle node 309; exact statement SHA-256 0df947fc9c15fba73773e15a24388a08795eb8dd45cef4adddf4f7abc7b825a5

Exact first-order statement

forall F n a b. (((~((n)=0)) /\ (exists dm_mask_table_sum_unique_first. ((((exists dst_positive_code_sum_unique_firstmasktable dst_positive_scale_sum_unique_firstmasktable dst_negative_code_sum_unique_firstmasktable dst_negative_scale_sum_unique_firstmasktable. (((dm_mask_table_sum_unique_first) = (((((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) * S ((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) + ((dst_positive_scale_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable))) + (((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)))) * S ((((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) * S ((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) + ((dst_positive_scale_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable))) + (((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)))) + ((((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable))) + (((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)))))) /\ (forall dst_index_sum_unique_firstmasktable. (exists pvs_le_gap_sum_unique_firstmasktabledomain. pvs_le_gap_sum_unique_firstmasktabledomain + (dst_index_sum_unique_firstmasktable) = (n)) -> exists dst_positive_sum_unique_firstmasktable dst_negative_sum_unique_firstmasktable dst_value_sum_unique_firstmasktable. ((((exists ff_h_pvs_sum_unique_firstmasktableentrypositive. ff_h_pvs_sum_unique_firstmasktableentrypositive + S (dst_positive_sum_unique_firstmasktable) = S ((S (dst_index_sum_unique_firstmasktable)) * dst_positive_scale_sum_unique_firstmasktable)) /\ exists ff_q_pvs_sum_unique_firstmasktableentrypositive. dst_positive_code_sum_unique_firstmasktable = ff_q_pvs_sum_unique_firstmasktableentrypositive * S ((S (dst_index_sum_unique_firstmasktable)) * dst_positive_scale_sum_unique_firstmasktable) + (dst_positive_sum_unique_firstmasktable))) /\ (((((exists ff_h_pvs_sum_unique_firstmasktableentrynegative. ff_h_pvs_sum_unique_firstmasktableentrynegative + S (dst_negative_sum_unique_firstmasktable) = S ((S (dst_index_sum_unique_firstmasktable)) * dst_negative_scale_sum_unique_firstmasktable)) /\ exists ff_q_pvs_sum_unique_firstmasktableentrynegative. dst_negative_code_sum_unique_firstmasktable = ff_q_pvs_sum_unique_firstmasktableentrynegative * S ((S (dst_index_sum_unique_firstmasktable)) * dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_sum_unique_firstmasktable))) /\ (exists ge_balance_positive_sum_unique_firstmasktableentryvalue ge_balance_negative_sum_unique_firstmasktableentryvalue. (((((dst_value_sum_unique_firstmasktable) = 2 * (ge_balance_positive_sum_unique_firstmasktableentryvalue) /\ (ge_balance_negative_sum_unique_firstmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmasktableentryvaluedecode. (((dst_value_sum_unique_firstmasktable) = 2 * ge_signed_half_sum_unique_firstmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmasktableentryvalue) = S ge_signed_half_sum_unique_firstmasktableentryvaluedecode))) /\ ((dst_positive_sum_unique_firstmasktable) + ge_balance_negative_sum_unique_firstmasktableentryvalue = (dst_negative_sum_unique_firstmasktable) + ge_balance_positive_sum_unique_firstmasktableentryvalue))))))))) /\ (forall dm_index_sum_unique_firstmask dm_value_sum_unique_firstmask. (exists pvs_le_gap_sum_unique_firstmaskdomain. pvs_le_gap_sum_unique_firstmaskdomain + (dm_index_sum_unique_firstmask) = (n)) -> (exists dst_positive_code_sum_unique_firstmasklookup dst_positive_scale_sum_unique_firstmasklookup dst_negative_code_sum_unique_firstmasklookup dst_negative_scale_sum_unique_firstmasklookup dst_positive_sum_unique_firstmasklookup dst_negative_sum_unique_firstmasklookup. (((dm_mask_table_sum_unique_first) = (((((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) * S ((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) + ((dst_positive_scale_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup))) + (((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)))) * S ((((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) * S ((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) + ((dst_positive_scale_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup))) + (((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)))) + ((((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup))) + (((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)))))) /\ (((((exists ff_h_pvs_sum_unique_firstmasklookuppositive. ff_h_pvs_sum_unique_firstmasklookuppositive + S (dst_positive_sum_unique_firstmasklookup) = S ((S (dm_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmasklookup)) /\ exists ff_q_pvs_sum_unique_firstmasklookuppositive. dst_positive_code_sum_unique_firstmasklookup = ff_q_pvs_sum_unique_firstmasklookuppositive * S ((S (dm_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmasklookup) + (dst_positive_sum_unique_firstmasklookup))) /\ (((((exists ff_h_pvs_sum_unique_firstmasklookupnegative. ff_h_pvs_sum_unique_firstmasklookupnegative + S (dst_negative_sum_unique_firstmasklookup) = S ((S (dm_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmasklookup)) /\ exists ff_q_pvs_sum_unique_firstmasklookupnegative. dst_negative_code_sum_unique_firstmasklookup = ff_q_pvs_sum_unique_firstmasklookupnegative * S ((S (dm_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_sum_unique_firstmasklookup))) /\ (exists ge_balance_positive_sum_unique_firstmasklookupvalue ge_balance_negative_sum_unique_firstmasklookupvalue. (((((dm_value_sum_unique_firstmask) = 2 * (ge_balance_positive_sum_unique_firstmasklookupvalue) /\ (ge_balance_negative_sum_unique_firstmasklookupvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmasklookupvaluedecode. (((dm_value_sum_unique_firstmask) = 2 * ge_signed_half_sum_unique_firstmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmasklookupvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmasklookupvalue) = S ge_signed_half_sum_unique_firstmasklookupvaluedecode))) /\ ((dst_positive_sum_unique_firstmasklookup) + ge_balance_negative_sum_unique_firstmasklookupvalue = (dst_negative_sum_unique_firstmasklookup) + ge_balance_positive_sum_unique_firstmasklookupvalue))))))))) -> ((((~((dm_index_sum_unique_firstmask)=0)) /\ (exists dm_quotient_sum_unique_firstmaskentry. (((n)=(dm_index_sum_unique_firstmask)*dm_quotient_sum_unique_firstmaskentry) /\ (exists dst_positive_code_sum_unique_firstmaskentryinput dst_positive_scale_sum_unique_firstmaskentryinput dst_negative_code_sum_unique_firstmaskentryinput dst_negative_scale_sum_unique_firstmaskentryinput dst_positive_sum_unique_firstmaskentryinput dst_negative_sum_unique_firstmaskentryinput. (((F) = (((((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) * S ((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) + ((dst_positive_scale_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput))) + (((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)))) * S ((((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) * S ((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) + ((dst_positive_scale_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput))) + (((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)))) + ((((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput))) + (((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryinputpositive. ff_h_pvs_sum_unique_firstmaskentryinputpositive + S (dst_positive_sum_unique_firstmaskentryinput) = S ((S (dm_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmaskentryinput)) /\ exists ff_q_pvs_sum_unique_firstmaskentryinputpositive. dst_positive_code_sum_unique_firstmaskentryinput = ff_q_pvs_sum_unique_firstmaskentryinputpositive * S ((S (dm_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmaskentryinput) + (dst_positive_sum_unique_firstmaskentryinput))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryinputnegative. ff_h_pvs_sum_unique_firstmaskentryinputnegative + S (dst_negative_sum_unique_firstmaskentryinput) = S ((S (dm_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmaskentryinput)) /\ exists ff_q_pvs_sum_unique_firstmaskentryinputnegative. dst_negative_code_sum_unique_firstmaskentryinput = ff_q_pvs_sum_unique_firstmaskentryinputnegative * S ((S (dm_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_sum_unique_firstmaskentryinput))) /\ (exists ge_balance_positive_sum_unique_firstmaskentryinputvalue ge_balance_negative_sum_unique_firstmaskentryinputvalue. (((((dm_value_sum_unique_firstmask) = 2 * (ge_balance_positive_sum_unique_firstmaskentryinputvalue) /\ (ge_balance_negative_sum_unique_firstmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryinputvaluedecode. (((dm_value_sum_unique_firstmask) = 2 * ge_signed_half_sum_unique_firstmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmaskentryinputvalue) = S ge_signed_half_sum_unique_firstmaskentryinputvaluedecode))) /\ ((dst_positive_sum_unique_firstmaskentryinput) + ge_balance_negative_sum_unique_firstmaskentryinputvalue = (dst_negative_sum_unique_firstmaskentryinput) + ge_balance_positive_sum_unique_firstmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_unique_firstmask)=0 \/ ~(exists pvs_factor_sum_unique_firstmaskentrynondivisor. (n) = (dm_index_sum_unique_firstmask) * pvs_factor_sum_unique_firstmaskentrynondivisor)) /\ ((dm_value_sum_unique_firstmask)=0))))))) /\ (exists dst_positive_code_sum_unique_firstfold dst_positive_scale_sum_unique_firstfold dst_negative_code_sum_unique_firstfold dst_negative_scale_sum_unique_firstfold dst_positive_sum_sum_unique_firstfold dst_negative_sum_sum_unique_firstfold. (((dm_mask_table_sum_unique_first) = (((((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) * S ((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) + ((dst_positive_scale_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold))) + (((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)))) * S ((((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) * S ((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) + ((dst_positive_scale_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold))) + (((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)))) + ((((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold))) + (((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)))))) /\ (((exists fs_u_dst_sum_unique_firstfoldpositive fs_v_dst_sum_unique_firstfoldpositive. ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_start. fs_h_dst_sum_unique_firstfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_start. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_terminal. fs_h_dst_sum_unique_firstfoldpositive_body_terminal + S (dst_positive_sum_sum_unique_firstfold) = S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_terminal. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldpositive) + (dst_positive_sum_sum_unique_firstfold))) /\ forall fs_i_dst_sum_unique_firstfoldpositive_body_steps. (exists fs_lt_dst_sum_unique_firstfoldpositive_body_steps_bound. fs_lt_dst_sum_unique_firstfoldpositive_body_steps_bound + S fs_i_dst_sum_unique_firstfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_unique_firstfoldpositive_body_steps fs_r_dst_sum_unique_firstfoldpositive_body_steps fs_s_dst_sum_unique_firstfoldpositive_body_steps. ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_steps_summand. fs_h_dst_sum_unique_firstfoldpositive_body_steps_summand + S (fs_a_dst_sum_unique_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * dst_positive_scale_sum_unique_firstfold)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_steps_summand. dst_positive_code_sum_unique_firstfold = fs_q_dst_sum_unique_firstfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * dst_positive_scale_sum_unique_firstfold) + (fs_a_dst_sum_unique_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_steps_partial. fs_h_dst_sum_unique_firstfoldpositive_body_steps_partial + S (fs_r_dst_sum_unique_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_steps_partial. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive) + (fs_r_dst_sum_unique_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_steps_successor. fs_h_dst_sum_unique_firstfoldpositive_body_steps_successor + S (fs_s_dst_sum_unique_firstfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_steps_successor. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive) + (fs_s_dst_sum_unique_firstfoldpositive_body_steps))) /\ fs_s_dst_sum_unique_firstfoldpositive_body_steps = fs_r_dst_sum_unique_firstfoldpositive_body_steps + fs_a_dst_sum_unique_firstfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_firstfoldnegative fs_v_dst_sum_unique_firstfoldnegative. ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_start. fs_h_dst_sum_unique_firstfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_start. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_terminal. fs_h_dst_sum_unique_firstfoldnegative_body_terminal + S (dst_negative_sum_sum_unique_firstfold) = S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_terminal. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldnegative) + (dst_negative_sum_sum_unique_firstfold))) /\ forall fs_i_dst_sum_unique_firstfoldnegative_body_steps. (exists fs_lt_dst_sum_unique_firstfoldnegative_body_steps_bound. fs_lt_dst_sum_unique_firstfoldnegative_body_steps_bound + S fs_i_dst_sum_unique_firstfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_unique_firstfoldnegative_body_steps fs_r_dst_sum_unique_firstfoldnegative_body_steps fs_s_dst_sum_unique_firstfoldnegative_body_steps. ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_steps_summand. fs_h_dst_sum_unique_firstfoldnegative_body_steps_summand + S (fs_a_dst_sum_unique_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * dst_negative_scale_sum_unique_firstfold)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_steps_summand. dst_negative_code_sum_unique_firstfold = fs_q_dst_sum_unique_firstfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * dst_negative_scale_sum_unique_firstfold) + (fs_a_dst_sum_unique_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_steps_partial. fs_h_dst_sum_unique_firstfoldnegative_body_steps_partial + S (fs_r_dst_sum_unique_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_steps_partial. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative) + (fs_r_dst_sum_unique_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_steps_successor. fs_h_dst_sum_unique_firstfoldnegative_body_steps_successor + S (fs_s_dst_sum_unique_firstfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_steps_successor. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative) + (fs_s_dst_sum_unique_firstfoldnegative_body_steps))) /\ fs_s_dst_sum_unique_firstfoldnegative_body_steps = fs_r_dst_sum_unique_firstfoldnegative_body_steps + fs_a_dst_sum_unique_firstfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_firstfoldresult ge_balance_negative_sum_unique_firstfoldresult. (((((a) = 2 * (ge_balance_positive_sum_unique_firstfoldresult) /\ (ge_balance_negative_sum_unique_firstfoldresult) = 0) \/ exists ge_signed_half_sum_unique_firstfoldresultdecode. (((a) = 2 * ge_signed_half_sum_unique_firstfoldresultdecode + 1 /\ (ge_balance_positive_sum_unique_firstfoldresult) = 0) /\ (ge_balance_negative_sum_unique_firstfoldresult) = S ge_signed_half_sum_unique_firstfoldresultdecode))) /\ ((dst_positive_sum_sum_unique_firstfold) + ge_balance_negative_sum_unique_firstfoldresult = (dst_negative_sum_sum_unique_firstfold) + ge_balance_positive_sum_unique_firstfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dm_mask_table_sum_unique_second. ((((exists dst_positive_code_sum_unique_secondmasktable dst_positive_scale_sum_unique_secondmasktable dst_negative_code_sum_unique_secondmasktable dst_negative_scale_sum_unique_secondmasktable. (((dm_mask_table_sum_unique_second) = (((((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) * S ((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) + ((dst_positive_scale_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable))) + (((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)))) * S ((((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) * S ((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) + ((dst_positive_scale_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable))) + (((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)))) + ((((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable))) + (((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)))))) /\ (forall dst_index_sum_unique_secondmasktable. (exists pvs_le_gap_sum_unique_secondmasktabledomain. pvs_le_gap_sum_unique_secondmasktabledomain + (dst_index_sum_unique_secondmasktable) = (n)) -> exists dst_positive_sum_unique_secondmasktable dst_negative_sum_unique_secondmasktable dst_value_sum_unique_secondmasktable. ((((exists ff_h_pvs_sum_unique_secondmasktableentrypositive. ff_h_pvs_sum_unique_secondmasktableentrypositive + S (dst_positive_sum_unique_secondmasktable) = S ((S (dst_index_sum_unique_secondmasktable)) * dst_positive_scale_sum_unique_secondmasktable)) /\ exists ff_q_pvs_sum_unique_secondmasktableentrypositive. dst_positive_code_sum_unique_secondmasktable = ff_q_pvs_sum_unique_secondmasktableentrypositive * S ((S (dst_index_sum_unique_secondmasktable)) * dst_positive_scale_sum_unique_secondmasktable) + (dst_positive_sum_unique_secondmasktable))) /\ (((((exists ff_h_pvs_sum_unique_secondmasktableentrynegative. ff_h_pvs_sum_unique_secondmasktableentrynegative + S (dst_negative_sum_unique_secondmasktable) = S ((S (dst_index_sum_unique_secondmasktable)) * dst_negative_scale_sum_unique_secondmasktable)) /\ exists ff_q_pvs_sum_unique_secondmasktableentrynegative. dst_negative_code_sum_unique_secondmasktable = ff_q_pvs_sum_unique_secondmasktableentrynegative * S ((S (dst_index_sum_unique_secondmasktable)) * dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_sum_unique_secondmasktable))) /\ (exists ge_balance_positive_sum_unique_secondmasktableentryvalue ge_balance_negative_sum_unique_secondmasktableentryvalue. (((((dst_value_sum_unique_secondmasktable) = 2 * (ge_balance_positive_sum_unique_secondmasktableentryvalue) /\ (ge_balance_negative_sum_unique_secondmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmasktableentryvaluedecode. (((dst_value_sum_unique_secondmasktable) = 2 * ge_signed_half_sum_unique_secondmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmasktableentryvalue) = S ge_signed_half_sum_unique_secondmasktableentryvaluedecode))) /\ ((dst_positive_sum_unique_secondmasktable) + ge_balance_negative_sum_unique_secondmasktableentryvalue = (dst_negative_sum_unique_secondmasktable) + ge_balance_positive_sum_unique_secondmasktableentryvalue))))))))) /\ (forall dm_index_sum_unique_secondmask dm_value_sum_unique_secondmask. (exists pvs_le_gap_sum_unique_secondmaskdomain. pvs_le_gap_sum_unique_secondmaskdomain + (dm_index_sum_unique_secondmask) = (n)) -> (exists dst_positive_code_sum_unique_secondmasklookup dst_positive_scale_sum_unique_secondmasklookup dst_negative_code_sum_unique_secondmasklookup dst_negative_scale_sum_unique_secondmasklookup dst_positive_sum_unique_secondmasklookup dst_negative_sum_unique_secondmasklookup. (((dm_mask_table_sum_unique_second) = (((((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) * S ((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) + ((dst_positive_scale_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup))) + (((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)))) * S ((((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) * S ((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) + ((dst_positive_scale_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup))) + (((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)))) + ((((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup))) + (((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)))))) /\ (((((exists ff_h_pvs_sum_unique_secondmasklookuppositive. ff_h_pvs_sum_unique_secondmasklookuppositive + S (dst_positive_sum_unique_secondmasklookup) = S ((S (dm_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmasklookup)) /\ exists ff_q_pvs_sum_unique_secondmasklookuppositive. dst_positive_code_sum_unique_secondmasklookup = ff_q_pvs_sum_unique_secondmasklookuppositive * S ((S (dm_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmasklookup) + (dst_positive_sum_unique_secondmasklookup))) /\ (((((exists ff_h_pvs_sum_unique_secondmasklookupnegative. ff_h_pvs_sum_unique_secondmasklookupnegative + S (dst_negative_sum_unique_secondmasklookup) = S ((S (dm_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmasklookup)) /\ exists ff_q_pvs_sum_unique_secondmasklookupnegative. dst_negative_code_sum_unique_secondmasklookup = ff_q_pvs_sum_unique_secondmasklookupnegative * S ((S (dm_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_sum_unique_secondmasklookup))) /\ (exists ge_balance_positive_sum_unique_secondmasklookupvalue ge_balance_negative_sum_unique_secondmasklookupvalue. (((((dm_value_sum_unique_secondmask) = 2 * (ge_balance_positive_sum_unique_secondmasklookupvalue) /\ (ge_balance_negative_sum_unique_secondmasklookupvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmasklookupvaluedecode. (((dm_value_sum_unique_secondmask) = 2 * ge_signed_half_sum_unique_secondmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmasklookupvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmasklookupvalue) = S ge_signed_half_sum_unique_secondmasklookupvaluedecode))) /\ ((dst_positive_sum_unique_secondmasklookup) + ge_balance_negative_sum_unique_secondmasklookupvalue = (dst_negative_sum_unique_secondmasklookup) + ge_balance_positive_sum_unique_secondmasklookupvalue))))))))) -> ((((~((dm_index_sum_unique_secondmask)=0)) /\ (exists dm_quotient_sum_unique_secondmaskentry. (((n)=(dm_index_sum_unique_secondmask)*dm_quotient_sum_unique_secondmaskentry) /\ (exists dst_positive_code_sum_unique_secondmaskentryinput dst_positive_scale_sum_unique_secondmaskentryinput dst_negative_code_sum_unique_secondmaskentryinput dst_negative_scale_sum_unique_secondmaskentryinput dst_positive_sum_unique_secondmaskentryinput dst_negative_sum_unique_secondmaskentryinput. (((F) = (((((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) * S ((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) + ((dst_positive_scale_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput))) + (((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)))) * S ((((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) * S ((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) + ((dst_positive_scale_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput))) + (((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)))) + ((((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput))) + (((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryinputpositive. ff_h_pvs_sum_unique_secondmaskentryinputpositive + S (dst_positive_sum_unique_secondmaskentryinput) = S ((S (dm_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmaskentryinput)) /\ exists ff_q_pvs_sum_unique_secondmaskentryinputpositive. dst_positive_code_sum_unique_secondmaskentryinput = ff_q_pvs_sum_unique_secondmaskentryinputpositive * S ((S (dm_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmaskentryinput) + (dst_positive_sum_unique_secondmaskentryinput))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryinputnegative. ff_h_pvs_sum_unique_secondmaskentryinputnegative + S (dst_negative_sum_unique_secondmaskentryinput) = S ((S (dm_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmaskentryinput)) /\ exists ff_q_pvs_sum_unique_secondmaskentryinputnegative. dst_negative_code_sum_unique_secondmaskentryinput = ff_q_pvs_sum_unique_secondmaskentryinputnegative * S ((S (dm_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_sum_unique_secondmaskentryinput))) /\ (exists ge_balance_positive_sum_unique_secondmaskentryinputvalue ge_balance_negative_sum_unique_secondmaskentryinputvalue. (((((dm_value_sum_unique_secondmask) = 2 * (ge_balance_positive_sum_unique_secondmaskentryinputvalue) /\ (ge_balance_negative_sum_unique_secondmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryinputvaluedecode. (((dm_value_sum_unique_secondmask) = 2 * ge_signed_half_sum_unique_secondmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmaskentryinputvalue) = S ge_signed_half_sum_unique_secondmaskentryinputvaluedecode))) /\ ((dst_positive_sum_unique_secondmaskentryinput) + ge_balance_negative_sum_unique_secondmaskentryinputvalue = (dst_negative_sum_unique_secondmaskentryinput) + ge_balance_positive_sum_unique_secondmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_unique_secondmask)=0 \/ ~(exists pvs_factor_sum_unique_secondmaskentrynondivisor. (n) = (dm_index_sum_unique_secondmask) * pvs_factor_sum_unique_secondmaskentrynondivisor)) /\ ((dm_value_sum_unique_secondmask)=0))))))) /\ (exists dst_positive_code_sum_unique_secondfold dst_positive_scale_sum_unique_secondfold dst_negative_code_sum_unique_secondfold dst_negative_scale_sum_unique_secondfold dst_positive_sum_sum_unique_secondfold dst_negative_sum_sum_unique_secondfold. (((dm_mask_table_sum_unique_second) = (((((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) * S ((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) + ((dst_positive_scale_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold))) + (((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)))) * S ((((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) * S ((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) + ((dst_positive_scale_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold))) + (((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)))) + ((((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold))) + (((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)))))) /\ (((exists fs_u_dst_sum_unique_secondfoldpositive fs_v_dst_sum_unique_secondfoldpositive. ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_start. fs_h_dst_sum_unique_secondfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_start. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_terminal. fs_h_dst_sum_unique_secondfoldpositive_body_terminal + S (dst_positive_sum_sum_unique_secondfold) = S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_terminal. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldpositive) + (dst_positive_sum_sum_unique_secondfold))) /\ forall fs_i_dst_sum_unique_secondfoldpositive_body_steps. (exists fs_lt_dst_sum_unique_secondfoldpositive_body_steps_bound. fs_lt_dst_sum_unique_secondfoldpositive_body_steps_bound + S fs_i_dst_sum_unique_secondfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_unique_secondfoldpositive_body_steps fs_r_dst_sum_unique_secondfoldpositive_body_steps fs_s_dst_sum_unique_secondfoldpositive_body_steps. ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_steps_summand. fs_h_dst_sum_unique_secondfoldpositive_body_steps_summand + S (fs_a_dst_sum_unique_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * dst_positive_scale_sum_unique_secondfold)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_steps_summand. dst_positive_code_sum_unique_secondfold = fs_q_dst_sum_unique_secondfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * dst_positive_scale_sum_unique_secondfold) + (fs_a_dst_sum_unique_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_steps_partial. fs_h_dst_sum_unique_secondfoldpositive_body_steps_partial + S (fs_r_dst_sum_unique_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_steps_partial. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive) + (fs_r_dst_sum_unique_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_steps_successor. fs_h_dst_sum_unique_secondfoldpositive_body_steps_successor + S (fs_s_dst_sum_unique_secondfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_steps_successor. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive) + (fs_s_dst_sum_unique_secondfoldpositive_body_steps))) /\ fs_s_dst_sum_unique_secondfoldpositive_body_steps = fs_r_dst_sum_unique_secondfoldpositive_body_steps + fs_a_dst_sum_unique_secondfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_secondfoldnegative fs_v_dst_sum_unique_secondfoldnegative. ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_start. fs_h_dst_sum_unique_secondfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_start. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_terminal. fs_h_dst_sum_unique_secondfoldnegative_body_terminal + S (dst_negative_sum_sum_unique_secondfold) = S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_terminal. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldnegative) + (dst_negative_sum_sum_unique_secondfold))) /\ forall fs_i_dst_sum_unique_secondfoldnegative_body_steps. (exists fs_lt_dst_sum_unique_secondfoldnegative_body_steps_bound. fs_lt_dst_sum_unique_secondfoldnegative_body_steps_bound + S fs_i_dst_sum_unique_secondfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_unique_secondfoldnegative_body_steps fs_r_dst_sum_unique_secondfoldnegative_body_steps fs_s_dst_sum_unique_secondfoldnegative_body_steps. ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_steps_summand. fs_h_dst_sum_unique_secondfoldnegative_body_steps_summand + S (fs_a_dst_sum_unique_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * dst_negative_scale_sum_unique_secondfold)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_steps_summand. dst_negative_code_sum_unique_secondfold = fs_q_dst_sum_unique_secondfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * dst_negative_scale_sum_unique_secondfold) + (fs_a_dst_sum_unique_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_steps_partial. fs_h_dst_sum_unique_secondfoldnegative_body_steps_partial + S (fs_r_dst_sum_unique_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_steps_partial. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative) + (fs_r_dst_sum_unique_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_steps_successor. fs_h_dst_sum_unique_secondfoldnegative_body_steps_successor + S (fs_s_dst_sum_unique_secondfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_steps_successor. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative) + (fs_s_dst_sum_unique_secondfoldnegative_body_steps))) /\ fs_s_dst_sum_unique_secondfoldnegative_body_steps = fs_r_dst_sum_unique_secondfoldnegative_body_steps + fs_a_dst_sum_unique_secondfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_secondfoldresult ge_balance_negative_sum_unique_secondfoldresult. (((((b) = 2 * (ge_balance_positive_sum_unique_secondfoldresult) /\ (ge_balance_negative_sum_unique_secondfoldresult) = 0) \/ exists ge_signed_half_sum_unique_secondfoldresultdecode. (((b) = 2 * ge_signed_half_sum_unique_secondfoldresultdecode + 1 /\ (ge_balance_positive_sum_unique_secondfoldresult) = 0) /\ (ge_balance_negative_sum_unique_secondfoldresult) = S ge_signed_half_sum_unique_secondfoldresultdecode))) /\ ((dst_positive_sum_sum_unique_secondfold) + ge_balance_negative_sum_unique_secondfoldresult = (dst_negative_sum_sum_unique_secondfold) + ge_balance_positive_sum_unique_secondfoldresult))))))))))))) -> a=b

signed_divisor_sum_exists_unique

new owned theorem · read exact theorem evidence

Bundle node 310; exact statement SHA-256 c148a766390471cd871ca467503a9a7c380142964aff8830ca412a20f743ba6d

Exact first-order statement

forall N F n. (exists dst_positive_code_sum_unique_input dst_positive_scale_sum_unique_input dst_negative_code_sum_unique_input dst_negative_scale_sum_unique_input. (((F) = (((((dst_positive_code_sum_unique_input) + (dst_positive_scale_sum_unique_input)) * S ((dst_positive_code_sum_unique_input) + (dst_positive_scale_sum_unique_input)) + ((dst_positive_scale_sum_unique_input) + (dst_positive_scale_sum_unique_input))) + (((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) * S ((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) + ((dst_negative_scale_sum_unique_input) + (dst_negative_scale_sum_unique_input)))) * S ((((dst_positive_code_sum_unique_input) + (dst_positive_scale_sum_unique_input)) * S ((dst_positive_code_sum_unique_input) + (dst_positive_scale_sum_unique_input)) + ((dst_positive_scale_sum_unique_input) + (dst_positive_scale_sum_unique_input))) + (((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) * S ((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) + ((dst_negative_scale_sum_unique_input) + (dst_negative_scale_sum_unique_input)))) + ((((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) * S ((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) + ((dst_negative_scale_sum_unique_input) + (dst_negative_scale_sum_unique_input))) + (((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) * S ((dst_negative_code_sum_unique_input) + (dst_negative_scale_sum_unique_input)) + ((dst_negative_scale_sum_unique_input) + (dst_negative_scale_sum_unique_input)))))) /\ (forall dst_index_sum_unique_input. (exists pvs_le_gap_sum_unique_inputdomain. pvs_le_gap_sum_unique_inputdomain + (dst_index_sum_unique_input) = (N)) -> exists dst_positive_sum_unique_input dst_negative_sum_unique_input dst_value_sum_unique_input. ((((exists ff_h_pvs_sum_unique_inputentrypositive. ff_h_pvs_sum_unique_inputentrypositive + S (dst_positive_sum_unique_input) = S ((S (dst_index_sum_unique_input)) * dst_positive_scale_sum_unique_input)) /\ exists ff_q_pvs_sum_unique_inputentrypositive. dst_positive_code_sum_unique_input = ff_q_pvs_sum_unique_inputentrypositive * S ((S (dst_index_sum_unique_input)) * dst_positive_scale_sum_unique_input) + (dst_positive_sum_unique_input))) /\ (((((exists ff_h_pvs_sum_unique_inputentrynegative. ff_h_pvs_sum_unique_inputentrynegative + S (dst_negative_sum_unique_input) = S ((S (dst_index_sum_unique_input)) * dst_negative_scale_sum_unique_input)) /\ exists ff_q_pvs_sum_unique_inputentrynegative. dst_negative_code_sum_unique_input = ff_q_pvs_sum_unique_inputentrynegative * S ((S (dst_index_sum_unique_input)) * dst_negative_scale_sum_unique_input) + (dst_negative_sum_unique_input))) /\ (exists ge_balance_positive_sum_unique_inputentryvalue ge_balance_negative_sum_unique_inputentryvalue. (((((dst_value_sum_unique_input) = 2 * (ge_balance_positive_sum_unique_inputentryvalue) /\ (ge_balance_negative_sum_unique_inputentryvalue) = 0) \/ exists ge_signed_half_sum_unique_inputentryvaluedecode. (((dst_value_sum_unique_input) = 2 * ge_signed_half_sum_unique_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_inputentryvalue) = 0) /\ (ge_balance_negative_sum_unique_inputentryvalue) = S ge_signed_half_sum_unique_inputentryvaluedecode))) /\ ((dst_positive_sum_unique_input) + ge_balance_negative_sum_unique_inputentryvalue = (dst_negative_sum_unique_input) + ge_balance_positive_sum_unique_inputentryvalue))))))))) -> ~(n=0) -> (exists pvs_le_gap_sum_unique_bound. pvs_le_gap_sum_unique_bound + (n) = (N)) -> exists z. (((~((n)=0)) /\ (exists dm_mask_table_sum_unique_value. ((((exists dst_positive_code_sum_unique_valuemasktable dst_positive_scale_sum_unique_valuemasktable dst_negative_code_sum_unique_valuemasktable dst_negative_scale_sum_unique_valuemasktable. (((dm_mask_table_sum_unique_value) = (((((dst_positive_code_sum_unique_valuemasktable) + (dst_positive_scale_sum_unique_valuemasktable)) * S ((dst_positive_code_sum_unique_valuemasktable) + (dst_positive_scale_sum_unique_valuemasktable)) + ((dst_positive_scale_sum_unique_valuemasktable) + (dst_positive_scale_sum_unique_valuemasktable))) + (((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) * S ((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) + ((dst_negative_scale_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)))) * S ((((dst_positive_code_sum_unique_valuemasktable) + (dst_positive_scale_sum_unique_valuemasktable)) * S ((dst_positive_code_sum_unique_valuemasktable) + (dst_positive_scale_sum_unique_valuemasktable)) + ((dst_positive_scale_sum_unique_valuemasktable) + (dst_positive_scale_sum_unique_valuemasktable))) + (((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) * S ((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) + ((dst_negative_scale_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)))) + ((((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) * S ((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) + ((dst_negative_scale_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable))) + (((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) * S ((dst_negative_code_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)) + ((dst_negative_scale_sum_unique_valuemasktable) + (dst_negative_scale_sum_unique_valuemasktable)))))) /\ (forall dst_index_sum_unique_valuemasktable. (exists pvs_le_gap_sum_unique_valuemasktabledomain. pvs_le_gap_sum_unique_valuemasktabledomain + (dst_index_sum_unique_valuemasktable) = (n)) -> exists dst_positive_sum_unique_valuemasktable dst_negative_sum_unique_valuemasktable dst_value_sum_unique_valuemasktable. ((((exists ff_h_pvs_sum_unique_valuemasktableentrypositive. ff_h_pvs_sum_unique_valuemasktableentrypositive + S (dst_positive_sum_unique_valuemasktable) = S ((S (dst_index_sum_unique_valuemasktable)) * dst_positive_scale_sum_unique_valuemasktable)) /\ exists ff_q_pvs_sum_unique_valuemasktableentrypositive. dst_positive_code_sum_unique_valuemasktable = ff_q_pvs_sum_unique_valuemasktableentrypositive * S ((S (dst_index_sum_unique_valuemasktable)) * dst_positive_scale_sum_unique_valuemasktable) + (dst_positive_sum_unique_valuemasktable))) /\ (((((exists ff_h_pvs_sum_unique_valuemasktableentrynegative. ff_h_pvs_sum_unique_valuemasktableentrynegative + S (dst_negative_sum_unique_valuemasktable) = S ((S (dst_index_sum_unique_valuemasktable)) * dst_negative_scale_sum_unique_valuemasktable)) /\ exists ff_q_pvs_sum_unique_valuemasktableentrynegative. dst_negative_code_sum_unique_valuemasktable = ff_q_pvs_sum_unique_valuemasktableentrynegative * S ((S (dst_index_sum_unique_valuemasktable)) * dst_negative_scale_sum_unique_valuemasktable) + (dst_negative_sum_unique_valuemasktable))) /\ (exists ge_balance_positive_sum_unique_valuemasktableentryvalue ge_balance_negative_sum_unique_valuemasktableentryvalue. (((((dst_value_sum_unique_valuemasktable) = 2 * (ge_balance_positive_sum_unique_valuemasktableentryvalue) /\ (ge_balance_negative_sum_unique_valuemasktableentryvalue) = 0) \/ exists ge_signed_half_sum_unique_valuemasktableentryvaluedecode. (((dst_value_sum_unique_valuemasktable) = 2 * ge_signed_half_sum_unique_valuemasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_valuemasktableentryvalue) = 0) /\ (ge_balance_negative_sum_unique_valuemasktableentryvalue) = S ge_signed_half_sum_unique_valuemasktableentryvaluedecode))) /\ ((dst_positive_sum_unique_valuemasktable) + ge_balance_negative_sum_unique_valuemasktableentryvalue = (dst_negative_sum_unique_valuemasktable) + ge_balance_positive_sum_unique_valuemasktableentryvalue))))))))) /\ (forall dm_index_sum_unique_valuemask dm_value_sum_unique_valuemask. (exists pvs_le_gap_sum_unique_valuemaskdomain. pvs_le_gap_sum_unique_valuemaskdomain + (dm_index_sum_unique_valuemask) = (n)) -> (exists dst_positive_code_sum_unique_valuemasklookup dst_positive_scale_sum_unique_valuemasklookup dst_negative_code_sum_unique_valuemasklookup dst_negative_scale_sum_unique_valuemasklookup dst_positive_sum_unique_valuemasklookup dst_negative_sum_unique_valuemasklookup. (((dm_mask_table_sum_unique_value) = (((((dst_positive_code_sum_unique_valuemasklookup) + (dst_positive_scale_sum_unique_valuemasklookup)) * S ((dst_positive_code_sum_unique_valuemasklookup) + (dst_positive_scale_sum_unique_valuemasklookup)) + ((dst_positive_scale_sum_unique_valuemasklookup) + (dst_positive_scale_sum_unique_valuemasklookup))) + (((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) * S ((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) + ((dst_negative_scale_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)))) * S ((((dst_positive_code_sum_unique_valuemasklookup) + (dst_positive_scale_sum_unique_valuemasklookup)) * S ((dst_positive_code_sum_unique_valuemasklookup) + (dst_positive_scale_sum_unique_valuemasklookup)) + ((dst_positive_scale_sum_unique_valuemasklookup) + (dst_positive_scale_sum_unique_valuemasklookup))) + (((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) * S ((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) + ((dst_negative_scale_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)))) + ((((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) * S ((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) + ((dst_negative_scale_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup))) + (((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) * S ((dst_negative_code_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)) + ((dst_negative_scale_sum_unique_valuemasklookup) + (dst_negative_scale_sum_unique_valuemasklookup)))))) /\ (((((exists ff_h_pvs_sum_unique_valuemasklookuppositive. ff_h_pvs_sum_unique_valuemasklookuppositive + S (dst_positive_sum_unique_valuemasklookup) = S ((S (dm_index_sum_unique_valuemask)) * dst_positive_scale_sum_unique_valuemasklookup)) /\ exists ff_q_pvs_sum_unique_valuemasklookuppositive. dst_positive_code_sum_unique_valuemasklookup = ff_q_pvs_sum_unique_valuemasklookuppositive * S ((S (dm_index_sum_unique_valuemask)) * dst_positive_scale_sum_unique_valuemasklookup) + (dst_positive_sum_unique_valuemasklookup))) /\ (((((exists ff_h_pvs_sum_unique_valuemasklookupnegative. ff_h_pvs_sum_unique_valuemasklookupnegative + S (dst_negative_sum_unique_valuemasklookup) = S ((S (dm_index_sum_unique_valuemask)) * dst_negative_scale_sum_unique_valuemasklookup)) /\ exists ff_q_pvs_sum_unique_valuemasklookupnegative. dst_negative_code_sum_unique_valuemasklookup = ff_q_pvs_sum_unique_valuemasklookupnegative * S ((S (dm_index_sum_unique_valuemask)) * dst_negative_scale_sum_unique_valuemasklookup) + (dst_negative_sum_unique_valuemasklookup))) /\ (exists ge_balance_positive_sum_unique_valuemasklookupvalue ge_balance_negative_sum_unique_valuemasklookupvalue. (((((dm_value_sum_unique_valuemask) = 2 * (ge_balance_positive_sum_unique_valuemasklookupvalue) /\ (ge_balance_negative_sum_unique_valuemasklookupvalue) = 0) \/ exists ge_signed_half_sum_unique_valuemasklookupvaluedecode. (((dm_value_sum_unique_valuemask) = 2 * ge_signed_half_sum_unique_valuemasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_unique_valuemasklookupvalue) = 0) /\ (ge_balance_negative_sum_unique_valuemasklookupvalue) = S ge_signed_half_sum_unique_valuemasklookupvaluedecode))) /\ ((dst_positive_sum_unique_valuemasklookup) + ge_balance_negative_sum_unique_valuemasklookupvalue = (dst_negative_sum_unique_valuemasklookup) + ge_balance_positive_sum_unique_valuemasklookupvalue))))))))) -> ((((~((dm_index_sum_unique_valuemask)=0)) /\ (exists dm_quotient_sum_unique_valuemaskentry. (((n)=(dm_index_sum_unique_valuemask)*dm_quotient_sum_unique_valuemaskentry) /\ (exists dst_positive_code_sum_unique_valuemaskentryinput dst_positive_scale_sum_unique_valuemaskentryinput dst_negative_code_sum_unique_valuemaskentryinput dst_negative_scale_sum_unique_valuemaskentryinput dst_positive_sum_unique_valuemaskentryinput dst_negative_sum_unique_valuemaskentryinput. (((F) = (((((dst_positive_code_sum_unique_valuemaskentryinput) + (dst_positive_scale_sum_unique_valuemaskentryinput)) * S ((dst_positive_code_sum_unique_valuemaskentryinput) + (dst_positive_scale_sum_unique_valuemaskentryinput)) + ((dst_positive_scale_sum_unique_valuemaskentryinput) + (dst_positive_scale_sum_unique_valuemaskentryinput))) + (((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) * S ((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) + ((dst_negative_scale_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)))) * S ((((dst_positive_code_sum_unique_valuemaskentryinput) + (dst_positive_scale_sum_unique_valuemaskentryinput)) * S ((dst_positive_code_sum_unique_valuemaskentryinput) + (dst_positive_scale_sum_unique_valuemaskentryinput)) + ((dst_positive_scale_sum_unique_valuemaskentryinput) + (dst_positive_scale_sum_unique_valuemaskentryinput))) + (((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) * S ((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) + ((dst_negative_scale_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)))) + ((((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) * S ((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) + ((dst_negative_scale_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput))) + (((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) * S ((dst_negative_code_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)) + ((dst_negative_scale_sum_unique_valuemaskentryinput) + (dst_negative_scale_sum_unique_valuemaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_unique_valuemaskentryinputpositive. ff_h_pvs_sum_unique_valuemaskentryinputpositive + S (dst_positive_sum_unique_valuemaskentryinput) = S ((S (dm_index_sum_unique_valuemask)) * dst_positive_scale_sum_unique_valuemaskentryinput)) /\ exists ff_q_pvs_sum_unique_valuemaskentryinputpositive. dst_positive_code_sum_unique_valuemaskentryinput = ff_q_pvs_sum_unique_valuemaskentryinputpositive * S ((S (dm_index_sum_unique_valuemask)) * dst_positive_scale_sum_unique_valuemaskentryinput) + (dst_positive_sum_unique_valuemaskentryinput))) /\ (((((exists ff_h_pvs_sum_unique_valuemaskentryinputnegative. ff_h_pvs_sum_unique_valuemaskentryinputnegative + S (dst_negative_sum_unique_valuemaskentryinput) = S ((S (dm_index_sum_unique_valuemask)) * dst_negative_scale_sum_unique_valuemaskentryinput)) /\ exists ff_q_pvs_sum_unique_valuemaskentryinputnegative. dst_negative_code_sum_unique_valuemaskentryinput = ff_q_pvs_sum_unique_valuemaskentryinputnegative * S ((S (dm_index_sum_unique_valuemask)) * dst_negative_scale_sum_unique_valuemaskentryinput) + (dst_negative_sum_unique_valuemaskentryinput))) /\ (exists ge_balance_positive_sum_unique_valuemaskentryinputvalue ge_balance_negative_sum_unique_valuemaskentryinputvalue. (((((dm_value_sum_unique_valuemask) = 2 * (ge_balance_positive_sum_unique_valuemaskentryinputvalue) /\ (ge_balance_negative_sum_unique_valuemaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_unique_valuemaskentryinputvaluedecode. (((dm_value_sum_unique_valuemask) = 2 * ge_signed_half_sum_unique_valuemaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_unique_valuemaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_unique_valuemaskentryinputvalue) = S ge_signed_half_sum_unique_valuemaskentryinputvaluedecode))) /\ ((dst_positive_sum_unique_valuemaskentryinput) + ge_balance_negative_sum_unique_valuemaskentryinputvalue = (dst_negative_sum_unique_valuemaskentryinput) + ge_balance_positive_sum_unique_valuemaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_unique_valuemask)=0 \/ ~(exists pvs_factor_sum_unique_valuemaskentrynondivisor. (n) = (dm_index_sum_unique_valuemask) * pvs_factor_sum_unique_valuemaskentrynondivisor)) /\ ((dm_value_sum_unique_valuemask)=0))))))) /\ (exists dst_positive_code_sum_unique_valuefold dst_positive_scale_sum_unique_valuefold dst_negative_code_sum_unique_valuefold dst_negative_scale_sum_unique_valuefold dst_positive_sum_sum_unique_valuefold dst_negative_sum_sum_unique_valuefold. (((dm_mask_table_sum_unique_value) = (((((dst_positive_code_sum_unique_valuefold) + (dst_positive_scale_sum_unique_valuefold)) * S ((dst_positive_code_sum_unique_valuefold) + (dst_positive_scale_sum_unique_valuefold)) + ((dst_positive_scale_sum_unique_valuefold) + (dst_positive_scale_sum_unique_valuefold))) + (((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) * S ((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) + ((dst_negative_scale_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)))) * S ((((dst_positive_code_sum_unique_valuefold) + (dst_positive_scale_sum_unique_valuefold)) * S ((dst_positive_code_sum_unique_valuefold) + (dst_positive_scale_sum_unique_valuefold)) + ((dst_positive_scale_sum_unique_valuefold) + (dst_positive_scale_sum_unique_valuefold))) + (((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) * S ((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) + ((dst_negative_scale_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)))) + ((((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) * S ((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) + ((dst_negative_scale_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold))) + (((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) * S ((dst_negative_code_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)) + ((dst_negative_scale_sum_unique_valuefold) + (dst_negative_scale_sum_unique_valuefold)))))) /\ (((exists fs_u_dst_sum_unique_valuefoldpositive fs_v_dst_sum_unique_valuefoldpositive. ((((exists fs_h_dst_sum_unique_valuefoldpositive_body_start. fs_h_dst_sum_unique_valuefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_valuefoldpositive)) /\ exists fs_q_dst_sum_unique_valuefoldpositive_body_start. fs_u_dst_sum_unique_valuefoldpositive = fs_q_dst_sum_unique_valuefoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_valuefoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_valuefoldpositive_body_terminal. fs_h_dst_sum_unique_valuefoldpositive_body_terminal + S (dst_positive_sum_sum_unique_valuefold) = S ((S (S (n))) * fs_v_dst_sum_unique_valuefoldpositive)) /\ exists fs_q_dst_sum_unique_valuefoldpositive_body_terminal. fs_u_dst_sum_unique_valuefoldpositive = fs_q_dst_sum_unique_valuefoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_valuefoldpositive) + (dst_positive_sum_sum_unique_valuefold))) /\ forall fs_i_dst_sum_unique_valuefoldpositive_body_steps. (exists fs_lt_dst_sum_unique_valuefoldpositive_body_steps_bound. fs_lt_dst_sum_unique_valuefoldpositive_body_steps_bound + S fs_i_dst_sum_unique_valuefoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_unique_valuefoldpositive_body_steps fs_r_dst_sum_unique_valuefoldpositive_body_steps fs_s_dst_sum_unique_valuefoldpositive_body_steps. ((((exists fs_h_dst_sum_unique_valuefoldpositive_body_steps_summand. fs_h_dst_sum_unique_valuefoldpositive_body_steps_summand + S (fs_a_dst_sum_unique_valuefoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_valuefoldpositive_body_steps)) * dst_positive_scale_sum_unique_valuefold)) /\ exists fs_q_dst_sum_unique_valuefoldpositive_body_steps_summand. dst_positive_code_sum_unique_valuefold = fs_q_dst_sum_unique_valuefoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_valuefoldpositive_body_steps)) * dst_positive_scale_sum_unique_valuefold) + (fs_a_dst_sum_unique_valuefoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_valuefoldpositive_body_steps_partial. fs_h_dst_sum_unique_valuefoldpositive_body_steps_partial + S (fs_r_dst_sum_unique_valuefoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_valuefoldpositive_body_steps)) * fs_v_dst_sum_unique_valuefoldpositive)) /\ exists fs_q_dst_sum_unique_valuefoldpositive_body_steps_partial. fs_u_dst_sum_unique_valuefoldpositive = fs_q_dst_sum_unique_valuefoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_valuefoldpositive_body_steps)) * fs_v_dst_sum_unique_valuefoldpositive) + (fs_r_dst_sum_unique_valuefoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_valuefoldpositive_body_steps_successor. fs_h_dst_sum_unique_valuefoldpositive_body_steps_successor + S (fs_s_dst_sum_unique_valuefoldpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_valuefoldpositive_body_steps)) * fs_v_dst_sum_unique_valuefoldpositive)) /\ exists fs_q_dst_sum_unique_valuefoldpositive_body_steps_successor. fs_u_dst_sum_unique_valuefoldpositive = fs_q_dst_sum_unique_valuefoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_valuefoldpositive_body_steps)) * fs_v_dst_sum_unique_valuefoldpositive) + (fs_s_dst_sum_unique_valuefoldpositive_body_steps))) /\ fs_s_dst_sum_unique_valuefoldpositive_body_steps = fs_r_dst_sum_unique_valuefoldpositive_body_steps + fs_a_dst_sum_unique_valuefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_valuefoldnegative fs_v_dst_sum_unique_valuefoldnegative. ((((exists fs_h_dst_sum_unique_valuefoldnegative_body_start. fs_h_dst_sum_unique_valuefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_valuefoldnegative)) /\ exists fs_q_dst_sum_unique_valuefoldnegative_body_start. fs_u_dst_sum_unique_valuefoldnegative = fs_q_dst_sum_unique_valuefoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_valuefoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_valuefoldnegative_body_terminal. fs_h_dst_sum_unique_valuefoldnegative_body_terminal + S (dst_negative_sum_sum_unique_valuefold) = S ((S (S (n))) * fs_v_dst_sum_unique_valuefoldnegative)) /\ exists fs_q_dst_sum_unique_valuefoldnegative_body_terminal. fs_u_dst_sum_unique_valuefoldnegative = fs_q_dst_sum_unique_valuefoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_valuefoldnegative) + (dst_negative_sum_sum_unique_valuefold))) /\ forall fs_i_dst_sum_unique_valuefoldnegative_body_steps. (exists fs_lt_dst_sum_unique_valuefoldnegative_body_steps_bound. fs_lt_dst_sum_unique_valuefoldnegative_body_steps_bound + S fs_i_dst_sum_unique_valuefoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_unique_valuefoldnegative_body_steps fs_r_dst_sum_unique_valuefoldnegative_body_steps fs_s_dst_sum_unique_valuefoldnegative_body_steps. ((((exists fs_h_dst_sum_unique_valuefoldnegative_body_steps_summand. fs_h_dst_sum_unique_valuefoldnegative_body_steps_summand + S (fs_a_dst_sum_unique_valuefoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_valuefoldnegative_body_steps)) * dst_negative_scale_sum_unique_valuefold)) /\ exists fs_q_dst_sum_unique_valuefoldnegative_body_steps_summand. dst_negative_code_sum_unique_valuefold = fs_q_dst_sum_unique_valuefoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_valuefoldnegative_body_steps)) * dst_negative_scale_sum_unique_valuefold) + (fs_a_dst_sum_unique_valuefoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_valuefoldnegative_body_steps_partial. fs_h_dst_sum_unique_valuefoldnegative_body_steps_partial + S (fs_r_dst_sum_unique_valuefoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_valuefoldnegative_body_steps)) * fs_v_dst_sum_unique_valuefoldnegative)) /\ exists fs_q_dst_sum_unique_valuefoldnegative_body_steps_partial. fs_u_dst_sum_unique_valuefoldnegative = fs_q_dst_sum_unique_valuefoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_valuefoldnegative_body_steps)) * fs_v_dst_sum_unique_valuefoldnegative) + (fs_r_dst_sum_unique_valuefoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_valuefoldnegative_body_steps_successor. fs_h_dst_sum_unique_valuefoldnegative_body_steps_successor + S (fs_s_dst_sum_unique_valuefoldnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_valuefoldnegative_body_steps)) * fs_v_dst_sum_unique_valuefoldnegative)) /\ exists fs_q_dst_sum_unique_valuefoldnegative_body_steps_successor. fs_u_dst_sum_unique_valuefoldnegative = fs_q_dst_sum_unique_valuefoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_valuefoldnegative_body_steps)) * fs_v_dst_sum_unique_valuefoldnegative) + (fs_s_dst_sum_unique_valuefoldnegative_body_steps))) /\ fs_s_dst_sum_unique_valuefoldnegative_body_steps = fs_r_dst_sum_unique_valuefoldnegative_body_steps + fs_a_dst_sum_unique_valuefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_valuefoldresult ge_balance_negative_sum_unique_valuefoldresult. (((((z) = 2 * (ge_balance_positive_sum_unique_valuefoldresult) /\ (ge_balance_negative_sum_unique_valuefoldresult) = 0) \/ exists ge_signed_half_sum_unique_valuefoldresultdecode. (((z) = 2 * ge_signed_half_sum_unique_valuefoldresultdecode + 1 /\ (ge_balance_positive_sum_unique_valuefoldresult) = 0) /\ (ge_balance_negative_sum_unique_valuefoldresult) = S ge_signed_half_sum_unique_valuefoldresultdecode))) /\ ((dst_positive_sum_sum_unique_valuefold) + ge_balance_negative_sum_unique_valuefoldresult = (dst_negative_sum_sum_unique_valuefold) + ge_balance_positive_sum_unique_valuefoldresult))))))))))))) /\ forall w. (((~((n)=0)) /\ (exists dm_mask_table_sum_unique_other. ((((exists dst_positive_code_sum_unique_othermasktable dst_positive_scale_sum_unique_othermasktable dst_negative_code_sum_unique_othermasktable dst_negative_scale_sum_unique_othermasktable. (((dm_mask_table_sum_unique_other) = (((((dst_positive_code_sum_unique_othermasktable) + (dst_positive_scale_sum_unique_othermasktable)) * S ((dst_positive_code_sum_unique_othermasktable) + (dst_positive_scale_sum_unique_othermasktable)) + ((dst_positive_scale_sum_unique_othermasktable) + (dst_positive_scale_sum_unique_othermasktable))) + (((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) * S ((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) + ((dst_negative_scale_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)))) * S ((((dst_positive_code_sum_unique_othermasktable) + (dst_positive_scale_sum_unique_othermasktable)) * S ((dst_positive_code_sum_unique_othermasktable) + (dst_positive_scale_sum_unique_othermasktable)) + ((dst_positive_scale_sum_unique_othermasktable) + (dst_positive_scale_sum_unique_othermasktable))) + (((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) * S ((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) + ((dst_negative_scale_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)))) + ((((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) * S ((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) + ((dst_negative_scale_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable))) + (((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) * S ((dst_negative_code_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)) + ((dst_negative_scale_sum_unique_othermasktable) + (dst_negative_scale_sum_unique_othermasktable)))))) /\ (forall dst_index_sum_unique_othermasktable. (exists pvs_le_gap_sum_unique_othermasktabledomain. pvs_le_gap_sum_unique_othermasktabledomain + (dst_index_sum_unique_othermasktable) = (n)) -> exists dst_positive_sum_unique_othermasktable dst_negative_sum_unique_othermasktable dst_value_sum_unique_othermasktable. ((((exists ff_h_pvs_sum_unique_othermasktableentrypositive. ff_h_pvs_sum_unique_othermasktableentrypositive + S (dst_positive_sum_unique_othermasktable) = S ((S (dst_index_sum_unique_othermasktable)) * dst_positive_scale_sum_unique_othermasktable)) /\ exists ff_q_pvs_sum_unique_othermasktableentrypositive. dst_positive_code_sum_unique_othermasktable = ff_q_pvs_sum_unique_othermasktableentrypositive * S ((S (dst_index_sum_unique_othermasktable)) * dst_positive_scale_sum_unique_othermasktable) + (dst_positive_sum_unique_othermasktable))) /\ (((((exists ff_h_pvs_sum_unique_othermasktableentrynegative. ff_h_pvs_sum_unique_othermasktableentrynegative + S (dst_negative_sum_unique_othermasktable) = S ((S (dst_index_sum_unique_othermasktable)) * dst_negative_scale_sum_unique_othermasktable)) /\ exists ff_q_pvs_sum_unique_othermasktableentrynegative. dst_negative_code_sum_unique_othermasktable = ff_q_pvs_sum_unique_othermasktableentrynegative * S ((S (dst_index_sum_unique_othermasktable)) * dst_negative_scale_sum_unique_othermasktable) + (dst_negative_sum_unique_othermasktable))) /\ (exists ge_balance_positive_sum_unique_othermasktableentryvalue ge_balance_negative_sum_unique_othermasktableentryvalue. (((((dst_value_sum_unique_othermasktable) = 2 * (ge_balance_positive_sum_unique_othermasktableentryvalue) /\ (ge_balance_negative_sum_unique_othermasktableentryvalue) = 0) \/ exists ge_signed_half_sum_unique_othermasktableentryvaluedecode. (((dst_value_sum_unique_othermasktable) = 2 * ge_signed_half_sum_unique_othermasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_othermasktableentryvalue) = 0) /\ (ge_balance_negative_sum_unique_othermasktableentryvalue) = S ge_signed_half_sum_unique_othermasktableentryvaluedecode))) /\ ((dst_positive_sum_unique_othermasktable) + ge_balance_negative_sum_unique_othermasktableentryvalue = (dst_negative_sum_unique_othermasktable) + ge_balance_positive_sum_unique_othermasktableentryvalue))))))))) /\ (forall dm_index_sum_unique_othermask dm_value_sum_unique_othermask. (exists pvs_le_gap_sum_unique_othermaskdomain. pvs_le_gap_sum_unique_othermaskdomain + (dm_index_sum_unique_othermask) = (n)) -> (exists dst_positive_code_sum_unique_othermasklookup dst_positive_scale_sum_unique_othermasklookup dst_negative_code_sum_unique_othermasklookup dst_negative_scale_sum_unique_othermasklookup dst_positive_sum_unique_othermasklookup dst_negative_sum_unique_othermasklookup. (((dm_mask_table_sum_unique_other) = (((((dst_positive_code_sum_unique_othermasklookup) + (dst_positive_scale_sum_unique_othermasklookup)) * S ((dst_positive_code_sum_unique_othermasklookup) + (dst_positive_scale_sum_unique_othermasklookup)) + ((dst_positive_scale_sum_unique_othermasklookup) + (dst_positive_scale_sum_unique_othermasklookup))) + (((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) * S ((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) + ((dst_negative_scale_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)))) * S ((((dst_positive_code_sum_unique_othermasklookup) + (dst_positive_scale_sum_unique_othermasklookup)) * S ((dst_positive_code_sum_unique_othermasklookup) + (dst_positive_scale_sum_unique_othermasklookup)) + ((dst_positive_scale_sum_unique_othermasklookup) + (dst_positive_scale_sum_unique_othermasklookup))) + (((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) * S ((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) + ((dst_negative_scale_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)))) + ((((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) * S ((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) + ((dst_negative_scale_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup))) + (((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) * S ((dst_negative_code_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)) + ((dst_negative_scale_sum_unique_othermasklookup) + (dst_negative_scale_sum_unique_othermasklookup)))))) /\ (((((exists ff_h_pvs_sum_unique_othermasklookuppositive. ff_h_pvs_sum_unique_othermasklookuppositive + S (dst_positive_sum_unique_othermasklookup) = S ((S (dm_index_sum_unique_othermask)) * dst_positive_scale_sum_unique_othermasklookup)) /\ exists ff_q_pvs_sum_unique_othermasklookuppositive. dst_positive_code_sum_unique_othermasklookup = ff_q_pvs_sum_unique_othermasklookuppositive * S ((S (dm_index_sum_unique_othermask)) * dst_positive_scale_sum_unique_othermasklookup) + (dst_positive_sum_unique_othermasklookup))) /\ (((((exists ff_h_pvs_sum_unique_othermasklookupnegative. ff_h_pvs_sum_unique_othermasklookupnegative + S (dst_negative_sum_unique_othermasklookup) = S ((S (dm_index_sum_unique_othermask)) * dst_negative_scale_sum_unique_othermasklookup)) /\ exists ff_q_pvs_sum_unique_othermasklookupnegative. dst_negative_code_sum_unique_othermasklookup = ff_q_pvs_sum_unique_othermasklookupnegative * S ((S (dm_index_sum_unique_othermask)) * dst_negative_scale_sum_unique_othermasklookup) + (dst_negative_sum_unique_othermasklookup))) /\ (exists ge_balance_positive_sum_unique_othermasklookupvalue ge_balance_negative_sum_unique_othermasklookupvalue. (((((dm_value_sum_unique_othermask) = 2 * (ge_balance_positive_sum_unique_othermasklookupvalue) /\ (ge_balance_negative_sum_unique_othermasklookupvalue) = 0) \/ exists ge_signed_half_sum_unique_othermasklookupvaluedecode. (((dm_value_sum_unique_othermask) = 2 * ge_signed_half_sum_unique_othermasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_unique_othermasklookupvalue) = 0) /\ (ge_balance_negative_sum_unique_othermasklookupvalue) = S ge_signed_half_sum_unique_othermasklookupvaluedecode))) /\ ((dst_positive_sum_unique_othermasklookup) + ge_balance_negative_sum_unique_othermasklookupvalue = (dst_negative_sum_unique_othermasklookup) + ge_balance_positive_sum_unique_othermasklookupvalue))))))))) -> ((((~((dm_index_sum_unique_othermask)=0)) /\ (exists dm_quotient_sum_unique_othermaskentry. (((n)=(dm_index_sum_unique_othermask)*dm_quotient_sum_unique_othermaskentry) /\ (exists dst_positive_code_sum_unique_othermaskentryinput dst_positive_scale_sum_unique_othermaskentryinput dst_negative_code_sum_unique_othermaskentryinput dst_negative_scale_sum_unique_othermaskentryinput dst_positive_sum_unique_othermaskentryinput dst_negative_sum_unique_othermaskentryinput. (((F) = (((((dst_positive_code_sum_unique_othermaskentryinput) + (dst_positive_scale_sum_unique_othermaskentryinput)) * S ((dst_positive_code_sum_unique_othermaskentryinput) + (dst_positive_scale_sum_unique_othermaskentryinput)) + ((dst_positive_scale_sum_unique_othermaskentryinput) + (dst_positive_scale_sum_unique_othermaskentryinput))) + (((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) * S ((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) + ((dst_negative_scale_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)))) * S ((((dst_positive_code_sum_unique_othermaskentryinput) + (dst_positive_scale_sum_unique_othermaskentryinput)) * S ((dst_positive_code_sum_unique_othermaskentryinput) + (dst_positive_scale_sum_unique_othermaskentryinput)) + ((dst_positive_scale_sum_unique_othermaskentryinput) + (dst_positive_scale_sum_unique_othermaskentryinput))) + (((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) * S ((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) + ((dst_negative_scale_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)))) + ((((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) * S ((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) + ((dst_negative_scale_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput))) + (((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) * S ((dst_negative_code_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)) + ((dst_negative_scale_sum_unique_othermaskentryinput) + (dst_negative_scale_sum_unique_othermaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_unique_othermaskentryinputpositive. ff_h_pvs_sum_unique_othermaskentryinputpositive + S (dst_positive_sum_unique_othermaskentryinput) = S ((S (dm_index_sum_unique_othermask)) * dst_positive_scale_sum_unique_othermaskentryinput)) /\ exists ff_q_pvs_sum_unique_othermaskentryinputpositive. dst_positive_code_sum_unique_othermaskentryinput = ff_q_pvs_sum_unique_othermaskentryinputpositive * S ((S (dm_index_sum_unique_othermask)) * dst_positive_scale_sum_unique_othermaskentryinput) + (dst_positive_sum_unique_othermaskentryinput))) /\ (((((exists ff_h_pvs_sum_unique_othermaskentryinputnegative. ff_h_pvs_sum_unique_othermaskentryinputnegative + S (dst_negative_sum_unique_othermaskentryinput) = S ((S (dm_index_sum_unique_othermask)) * dst_negative_scale_sum_unique_othermaskentryinput)) /\ exists ff_q_pvs_sum_unique_othermaskentryinputnegative. dst_negative_code_sum_unique_othermaskentryinput = ff_q_pvs_sum_unique_othermaskentryinputnegative * S ((S (dm_index_sum_unique_othermask)) * dst_negative_scale_sum_unique_othermaskentryinput) + (dst_negative_sum_unique_othermaskentryinput))) /\ (exists ge_balance_positive_sum_unique_othermaskentryinputvalue ge_balance_negative_sum_unique_othermaskentryinputvalue. (((((dm_value_sum_unique_othermask) = 2 * (ge_balance_positive_sum_unique_othermaskentryinputvalue) /\ (ge_balance_negative_sum_unique_othermaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_unique_othermaskentryinputvaluedecode. (((dm_value_sum_unique_othermask) = 2 * ge_signed_half_sum_unique_othermaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_unique_othermaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_unique_othermaskentryinputvalue) = S ge_signed_half_sum_unique_othermaskentryinputvaluedecode))) /\ ((dst_positive_sum_unique_othermaskentryinput) + ge_balance_negative_sum_unique_othermaskentryinputvalue = (dst_negative_sum_unique_othermaskentryinput) + ge_balance_positive_sum_unique_othermaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_unique_othermask)=0 \/ ~(exists pvs_factor_sum_unique_othermaskentrynondivisor. (n) = (dm_index_sum_unique_othermask) * pvs_factor_sum_unique_othermaskentrynondivisor)) /\ ((dm_value_sum_unique_othermask)=0))))))) /\ (exists dst_positive_code_sum_unique_otherfold dst_positive_scale_sum_unique_otherfold dst_negative_code_sum_unique_otherfold dst_negative_scale_sum_unique_otherfold dst_positive_sum_sum_unique_otherfold dst_negative_sum_sum_unique_otherfold. (((dm_mask_table_sum_unique_other) = (((((dst_positive_code_sum_unique_otherfold) + (dst_positive_scale_sum_unique_otherfold)) * S ((dst_positive_code_sum_unique_otherfold) + (dst_positive_scale_sum_unique_otherfold)) + ((dst_positive_scale_sum_unique_otherfold) + (dst_positive_scale_sum_unique_otherfold))) + (((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) * S ((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) + ((dst_negative_scale_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)))) * S ((((dst_positive_code_sum_unique_otherfold) + (dst_positive_scale_sum_unique_otherfold)) * S ((dst_positive_code_sum_unique_otherfold) + (dst_positive_scale_sum_unique_otherfold)) + ((dst_positive_scale_sum_unique_otherfold) + (dst_positive_scale_sum_unique_otherfold))) + (((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) * S ((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) + ((dst_negative_scale_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)))) + ((((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) * S ((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) + ((dst_negative_scale_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold))) + (((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) * S ((dst_negative_code_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)) + ((dst_negative_scale_sum_unique_otherfold) + (dst_negative_scale_sum_unique_otherfold)))))) /\ (((exists fs_u_dst_sum_unique_otherfoldpositive fs_v_dst_sum_unique_otherfoldpositive. ((((exists fs_h_dst_sum_unique_otherfoldpositive_body_start. fs_h_dst_sum_unique_otherfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_otherfoldpositive)) /\ exists fs_q_dst_sum_unique_otherfoldpositive_body_start. fs_u_dst_sum_unique_otherfoldpositive = fs_q_dst_sum_unique_otherfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_otherfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_otherfoldpositive_body_terminal. fs_h_dst_sum_unique_otherfoldpositive_body_terminal + S (dst_positive_sum_sum_unique_otherfold) = S ((S (S (n))) * fs_v_dst_sum_unique_otherfoldpositive)) /\ exists fs_q_dst_sum_unique_otherfoldpositive_body_terminal. fs_u_dst_sum_unique_otherfoldpositive = fs_q_dst_sum_unique_otherfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_otherfoldpositive) + (dst_positive_sum_sum_unique_otherfold))) /\ forall fs_i_dst_sum_unique_otherfoldpositive_body_steps. (exists fs_lt_dst_sum_unique_otherfoldpositive_body_steps_bound. fs_lt_dst_sum_unique_otherfoldpositive_body_steps_bound + S fs_i_dst_sum_unique_otherfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_unique_otherfoldpositive_body_steps fs_r_dst_sum_unique_otherfoldpositive_body_steps fs_s_dst_sum_unique_otherfoldpositive_body_steps. ((((exists fs_h_dst_sum_unique_otherfoldpositive_body_steps_summand. fs_h_dst_sum_unique_otherfoldpositive_body_steps_summand + S (fs_a_dst_sum_unique_otherfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_otherfoldpositive_body_steps)) * dst_positive_scale_sum_unique_otherfold)) /\ exists fs_q_dst_sum_unique_otherfoldpositive_body_steps_summand. dst_positive_code_sum_unique_otherfold = fs_q_dst_sum_unique_otherfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_otherfoldpositive_body_steps)) * dst_positive_scale_sum_unique_otherfold) + (fs_a_dst_sum_unique_otherfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_otherfoldpositive_body_steps_partial. fs_h_dst_sum_unique_otherfoldpositive_body_steps_partial + S (fs_r_dst_sum_unique_otherfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_otherfoldpositive_body_steps)) * fs_v_dst_sum_unique_otherfoldpositive)) /\ exists fs_q_dst_sum_unique_otherfoldpositive_body_steps_partial. fs_u_dst_sum_unique_otherfoldpositive = fs_q_dst_sum_unique_otherfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_otherfoldpositive_body_steps)) * fs_v_dst_sum_unique_otherfoldpositive) + (fs_r_dst_sum_unique_otherfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_otherfoldpositive_body_steps_successor. fs_h_dst_sum_unique_otherfoldpositive_body_steps_successor + S (fs_s_dst_sum_unique_otherfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_otherfoldpositive_body_steps)) * fs_v_dst_sum_unique_otherfoldpositive)) /\ exists fs_q_dst_sum_unique_otherfoldpositive_body_steps_successor. fs_u_dst_sum_unique_otherfoldpositive = fs_q_dst_sum_unique_otherfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_otherfoldpositive_body_steps)) * fs_v_dst_sum_unique_otherfoldpositive) + (fs_s_dst_sum_unique_otherfoldpositive_body_steps))) /\ fs_s_dst_sum_unique_otherfoldpositive_body_steps = fs_r_dst_sum_unique_otherfoldpositive_body_steps + fs_a_dst_sum_unique_otherfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_otherfoldnegative fs_v_dst_sum_unique_otherfoldnegative. ((((exists fs_h_dst_sum_unique_otherfoldnegative_body_start. fs_h_dst_sum_unique_otherfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_otherfoldnegative)) /\ exists fs_q_dst_sum_unique_otherfoldnegative_body_start. fs_u_dst_sum_unique_otherfoldnegative = fs_q_dst_sum_unique_otherfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_otherfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_otherfoldnegative_body_terminal. fs_h_dst_sum_unique_otherfoldnegative_body_terminal + S (dst_negative_sum_sum_unique_otherfold) = S ((S (S (n))) * fs_v_dst_sum_unique_otherfoldnegative)) /\ exists fs_q_dst_sum_unique_otherfoldnegative_body_terminal. fs_u_dst_sum_unique_otherfoldnegative = fs_q_dst_sum_unique_otherfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_otherfoldnegative) + (dst_negative_sum_sum_unique_otherfold))) /\ forall fs_i_dst_sum_unique_otherfoldnegative_body_steps. (exists fs_lt_dst_sum_unique_otherfoldnegative_body_steps_bound. fs_lt_dst_sum_unique_otherfoldnegative_body_steps_bound + S fs_i_dst_sum_unique_otherfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_unique_otherfoldnegative_body_steps fs_r_dst_sum_unique_otherfoldnegative_body_steps fs_s_dst_sum_unique_otherfoldnegative_body_steps. ((((exists fs_h_dst_sum_unique_otherfoldnegative_body_steps_summand. fs_h_dst_sum_unique_otherfoldnegative_body_steps_summand + S (fs_a_dst_sum_unique_otherfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_otherfoldnegative_body_steps)) * dst_negative_scale_sum_unique_otherfold)) /\ exists fs_q_dst_sum_unique_otherfoldnegative_body_steps_summand. dst_negative_code_sum_unique_otherfold = fs_q_dst_sum_unique_otherfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_otherfoldnegative_body_steps)) * dst_negative_scale_sum_unique_otherfold) + (fs_a_dst_sum_unique_otherfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_otherfoldnegative_body_steps_partial. fs_h_dst_sum_unique_otherfoldnegative_body_steps_partial + S (fs_r_dst_sum_unique_otherfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_otherfoldnegative_body_steps)) * fs_v_dst_sum_unique_otherfoldnegative)) /\ exists fs_q_dst_sum_unique_otherfoldnegative_body_steps_partial. fs_u_dst_sum_unique_otherfoldnegative = fs_q_dst_sum_unique_otherfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_otherfoldnegative_body_steps)) * fs_v_dst_sum_unique_otherfoldnegative) + (fs_r_dst_sum_unique_otherfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_otherfoldnegative_body_steps_successor. fs_h_dst_sum_unique_otherfoldnegative_body_steps_successor + S (fs_s_dst_sum_unique_otherfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_otherfoldnegative_body_steps)) * fs_v_dst_sum_unique_otherfoldnegative)) /\ exists fs_q_dst_sum_unique_otherfoldnegative_body_steps_successor. fs_u_dst_sum_unique_otherfoldnegative = fs_q_dst_sum_unique_otherfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_otherfoldnegative_body_steps)) * fs_v_dst_sum_unique_otherfoldnegative) + (fs_s_dst_sum_unique_otherfoldnegative_body_steps))) /\ fs_s_dst_sum_unique_otherfoldnegative_body_steps = fs_r_dst_sum_unique_otherfoldnegative_body_steps + fs_a_dst_sum_unique_otherfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_otherfoldresult ge_balance_negative_sum_unique_otherfoldresult. (((((w) = 2 * (ge_balance_positive_sum_unique_otherfoldresult) /\ (ge_balance_negative_sum_unique_otherfoldresult) = 0) \/ exists ge_signed_half_sum_unique_otherfoldresultdecode. (((w) = 2 * ge_signed_half_sum_unique_otherfoldresultdecode + 1 /\ (ge_balance_positive_sum_unique_otherfoldresult) = 0) /\ (ge_balance_negative_sum_unique_otherfoldresult) = S ge_signed_half_sum_unique_otherfoldresultdecode))) /\ ((dst_positive_sum_sum_unique_otherfold) + ge_balance_negative_sum_unique_otherfoldresult = (dst_negative_sum_sum_unique_otherfold) + ge_balance_positive_sum_unique_otherfoldresult))))))))))))) -> w=z

signed_divisor_sum_zero_excluded

new owned theorem · read exact theorem evidence

Bundle node 311; exact statement SHA-256 46416ce9415f13047867367a6853f97ba118e7f922ce2518903c830091496c7a

Exact first-order statement

forall F z. (((~((0)=0)) /\ (exists dm_mask_table_sum_zero_excluded. ((((exists dst_positive_code_sum_zero_excludedmasktable dst_positive_scale_sum_zero_excludedmasktable dst_negative_code_sum_zero_excludedmasktable dst_negative_scale_sum_zero_excludedmasktable. (((dm_mask_table_sum_zero_excluded) = (((((dst_positive_code_sum_zero_excludedmasktable) + (dst_positive_scale_sum_zero_excludedmasktable)) * S ((dst_positive_code_sum_zero_excludedmasktable) + (dst_positive_scale_sum_zero_excludedmasktable)) + ((dst_positive_scale_sum_zero_excludedmasktable) + (dst_positive_scale_sum_zero_excludedmasktable))) + (((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) * S ((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) + ((dst_negative_scale_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)))) * S ((((dst_positive_code_sum_zero_excludedmasktable) + (dst_positive_scale_sum_zero_excludedmasktable)) * S ((dst_positive_code_sum_zero_excludedmasktable) + (dst_positive_scale_sum_zero_excludedmasktable)) + ((dst_positive_scale_sum_zero_excludedmasktable) + (dst_positive_scale_sum_zero_excludedmasktable))) + (((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) * S ((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) + ((dst_negative_scale_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)))) + ((((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) * S ((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) + ((dst_negative_scale_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable))) + (((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) * S ((dst_negative_code_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)) + ((dst_negative_scale_sum_zero_excludedmasktable) + (dst_negative_scale_sum_zero_excludedmasktable)))))) /\ (forall dst_index_sum_zero_excludedmasktable. (exists pvs_le_gap_sum_zero_excludedmasktabledomain. pvs_le_gap_sum_zero_excludedmasktabledomain + (dst_index_sum_zero_excludedmasktable) = (0)) -> exists dst_positive_sum_zero_excludedmasktable dst_negative_sum_zero_excludedmasktable dst_value_sum_zero_excludedmasktable. ((((exists ff_h_pvs_sum_zero_excludedmasktableentrypositive. ff_h_pvs_sum_zero_excludedmasktableentrypositive + S (dst_positive_sum_zero_excludedmasktable) = S ((S (dst_index_sum_zero_excludedmasktable)) * dst_positive_scale_sum_zero_excludedmasktable)) /\ exists ff_q_pvs_sum_zero_excludedmasktableentrypositive. dst_positive_code_sum_zero_excludedmasktable = ff_q_pvs_sum_zero_excludedmasktableentrypositive * S ((S (dst_index_sum_zero_excludedmasktable)) * dst_positive_scale_sum_zero_excludedmasktable) + (dst_positive_sum_zero_excludedmasktable))) /\ (((((exists ff_h_pvs_sum_zero_excludedmasktableentrynegative. ff_h_pvs_sum_zero_excludedmasktableentrynegative + S (dst_negative_sum_zero_excludedmasktable) = S ((S (dst_index_sum_zero_excludedmasktable)) * dst_negative_scale_sum_zero_excludedmasktable)) /\ exists ff_q_pvs_sum_zero_excludedmasktableentrynegative. dst_negative_code_sum_zero_excludedmasktable = ff_q_pvs_sum_zero_excludedmasktableentrynegative * S ((S (dst_index_sum_zero_excludedmasktable)) * dst_negative_scale_sum_zero_excludedmasktable) + (dst_negative_sum_zero_excludedmasktable))) /\ (exists ge_balance_positive_sum_zero_excludedmasktableentryvalue ge_balance_negative_sum_zero_excludedmasktableentryvalue. (((((dst_value_sum_zero_excludedmasktable) = 2 * (ge_balance_positive_sum_zero_excludedmasktableentryvalue) /\ (ge_balance_negative_sum_zero_excludedmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_zero_excludedmasktableentryvaluedecode. (((dst_value_sum_zero_excludedmasktable) = 2 * ge_signed_half_sum_zero_excludedmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_zero_excludedmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_zero_excludedmasktableentryvalue) = S ge_signed_half_sum_zero_excludedmasktableentryvaluedecode))) /\ ((dst_positive_sum_zero_excludedmasktable) + ge_balance_negative_sum_zero_excludedmasktableentryvalue = (dst_negative_sum_zero_excludedmasktable) + ge_balance_positive_sum_zero_excludedmasktableentryvalue))))))))) /\ (forall dm_index_sum_zero_excludedmask dm_value_sum_zero_excludedmask. (exists pvs_le_gap_sum_zero_excludedmaskdomain. pvs_le_gap_sum_zero_excludedmaskdomain + (dm_index_sum_zero_excludedmask) = (0)) -> (exists dst_positive_code_sum_zero_excludedmasklookup dst_positive_scale_sum_zero_excludedmasklookup dst_negative_code_sum_zero_excludedmasklookup dst_negative_scale_sum_zero_excludedmasklookup dst_positive_sum_zero_excludedmasklookup dst_negative_sum_zero_excludedmasklookup. (((dm_mask_table_sum_zero_excluded) = (((((dst_positive_code_sum_zero_excludedmasklookup) + (dst_positive_scale_sum_zero_excludedmasklookup)) * S ((dst_positive_code_sum_zero_excludedmasklookup) + (dst_positive_scale_sum_zero_excludedmasklookup)) + ((dst_positive_scale_sum_zero_excludedmasklookup) + (dst_positive_scale_sum_zero_excludedmasklookup))) + (((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) * S ((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) + ((dst_negative_scale_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)))) * S ((((dst_positive_code_sum_zero_excludedmasklookup) + (dst_positive_scale_sum_zero_excludedmasklookup)) * S ((dst_positive_code_sum_zero_excludedmasklookup) + (dst_positive_scale_sum_zero_excludedmasklookup)) + ((dst_positive_scale_sum_zero_excludedmasklookup) + (dst_positive_scale_sum_zero_excludedmasklookup))) + (((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) * S ((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) + ((dst_negative_scale_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)))) + ((((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) * S ((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) + ((dst_negative_scale_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup))) + (((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) * S ((dst_negative_code_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)) + ((dst_negative_scale_sum_zero_excludedmasklookup) + (dst_negative_scale_sum_zero_excludedmasklookup)))))) /\ (((((exists ff_h_pvs_sum_zero_excludedmasklookuppositive. ff_h_pvs_sum_zero_excludedmasklookuppositive + S (dst_positive_sum_zero_excludedmasklookup) = S ((S (dm_index_sum_zero_excludedmask)) * dst_positive_scale_sum_zero_excludedmasklookup)) /\ exists ff_q_pvs_sum_zero_excludedmasklookuppositive. dst_positive_code_sum_zero_excludedmasklookup = ff_q_pvs_sum_zero_excludedmasklookuppositive * S ((S (dm_index_sum_zero_excludedmask)) * dst_positive_scale_sum_zero_excludedmasklookup) + (dst_positive_sum_zero_excludedmasklookup))) /\ (((((exists ff_h_pvs_sum_zero_excludedmasklookupnegative. ff_h_pvs_sum_zero_excludedmasklookupnegative + S (dst_negative_sum_zero_excludedmasklookup) = S ((S (dm_index_sum_zero_excludedmask)) * dst_negative_scale_sum_zero_excludedmasklookup)) /\ exists ff_q_pvs_sum_zero_excludedmasklookupnegative. dst_negative_code_sum_zero_excludedmasklookup = ff_q_pvs_sum_zero_excludedmasklookupnegative * S ((S (dm_index_sum_zero_excludedmask)) * dst_negative_scale_sum_zero_excludedmasklookup) + (dst_negative_sum_zero_excludedmasklookup))) /\ (exists ge_balance_positive_sum_zero_excludedmasklookupvalue ge_balance_negative_sum_zero_excludedmasklookupvalue. (((((dm_value_sum_zero_excludedmask) = 2 * (ge_balance_positive_sum_zero_excludedmasklookupvalue) /\ (ge_balance_negative_sum_zero_excludedmasklookupvalue) = 0) \/ exists ge_signed_half_sum_zero_excludedmasklookupvaluedecode. (((dm_value_sum_zero_excludedmask) = 2 * ge_signed_half_sum_zero_excludedmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_zero_excludedmasklookupvalue) = 0) /\ (ge_balance_negative_sum_zero_excludedmasklookupvalue) = S ge_signed_half_sum_zero_excludedmasklookupvaluedecode))) /\ ((dst_positive_sum_zero_excludedmasklookup) + ge_balance_negative_sum_zero_excludedmasklookupvalue = (dst_negative_sum_zero_excludedmasklookup) + ge_balance_positive_sum_zero_excludedmasklookupvalue))))))))) -> ((((~((dm_index_sum_zero_excludedmask)=0)) /\ (exists dm_quotient_sum_zero_excludedmaskentry. (((0)=(dm_index_sum_zero_excludedmask)*dm_quotient_sum_zero_excludedmaskentry) /\ (exists dst_positive_code_sum_zero_excludedmaskentryinput dst_positive_scale_sum_zero_excludedmaskentryinput dst_negative_code_sum_zero_excludedmaskentryinput dst_negative_scale_sum_zero_excludedmaskentryinput dst_positive_sum_zero_excludedmaskentryinput dst_negative_sum_zero_excludedmaskentryinput. (((F) = (((((dst_positive_code_sum_zero_excludedmaskentryinput) + (dst_positive_scale_sum_zero_excludedmaskentryinput)) * S ((dst_positive_code_sum_zero_excludedmaskentryinput) + (dst_positive_scale_sum_zero_excludedmaskentryinput)) + ((dst_positive_scale_sum_zero_excludedmaskentryinput) + (dst_positive_scale_sum_zero_excludedmaskentryinput))) + (((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) * S ((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) + ((dst_negative_scale_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)))) * S ((((dst_positive_code_sum_zero_excludedmaskentryinput) + (dst_positive_scale_sum_zero_excludedmaskentryinput)) * S ((dst_positive_code_sum_zero_excludedmaskentryinput) + (dst_positive_scale_sum_zero_excludedmaskentryinput)) + ((dst_positive_scale_sum_zero_excludedmaskentryinput) + (dst_positive_scale_sum_zero_excludedmaskentryinput))) + (((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) * S ((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) + ((dst_negative_scale_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)))) + ((((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) * S ((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) + ((dst_negative_scale_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput))) + (((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) * S ((dst_negative_code_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)) + ((dst_negative_scale_sum_zero_excludedmaskentryinput) + (dst_negative_scale_sum_zero_excludedmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_zero_excludedmaskentryinputpositive. ff_h_pvs_sum_zero_excludedmaskentryinputpositive + S (dst_positive_sum_zero_excludedmaskentryinput) = S ((S (dm_index_sum_zero_excludedmask)) * dst_positive_scale_sum_zero_excludedmaskentryinput)) /\ exists ff_q_pvs_sum_zero_excludedmaskentryinputpositive. dst_positive_code_sum_zero_excludedmaskentryinput = ff_q_pvs_sum_zero_excludedmaskentryinputpositive * S ((S (dm_index_sum_zero_excludedmask)) * dst_positive_scale_sum_zero_excludedmaskentryinput) + (dst_positive_sum_zero_excludedmaskentryinput))) /\ (((((exists ff_h_pvs_sum_zero_excludedmaskentryinputnegative. ff_h_pvs_sum_zero_excludedmaskentryinputnegative + S (dst_negative_sum_zero_excludedmaskentryinput) = S ((S (dm_index_sum_zero_excludedmask)) * dst_negative_scale_sum_zero_excludedmaskentryinput)) /\ exists ff_q_pvs_sum_zero_excludedmaskentryinputnegative. dst_negative_code_sum_zero_excludedmaskentryinput = ff_q_pvs_sum_zero_excludedmaskentryinputnegative * S ((S (dm_index_sum_zero_excludedmask)) * dst_negative_scale_sum_zero_excludedmaskentryinput) + (dst_negative_sum_zero_excludedmaskentryinput))) /\ (exists ge_balance_positive_sum_zero_excludedmaskentryinputvalue ge_balance_negative_sum_zero_excludedmaskentryinputvalue. (((((dm_value_sum_zero_excludedmask) = 2 * (ge_balance_positive_sum_zero_excludedmaskentryinputvalue) /\ (ge_balance_negative_sum_zero_excludedmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_zero_excludedmaskentryinputvaluedecode. (((dm_value_sum_zero_excludedmask) = 2 * ge_signed_half_sum_zero_excludedmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_zero_excludedmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_zero_excludedmaskentryinputvalue) = S ge_signed_half_sum_zero_excludedmaskentryinputvaluedecode))) /\ ((dst_positive_sum_zero_excludedmaskentryinput) + ge_balance_negative_sum_zero_excludedmaskentryinputvalue = (dst_negative_sum_zero_excludedmaskentryinput) + ge_balance_positive_sum_zero_excludedmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_zero_excludedmask)=0 \/ ~(exists pvs_factor_sum_zero_excludedmaskentrynondivisor. (0) = (dm_index_sum_zero_excludedmask) * pvs_factor_sum_zero_excludedmaskentrynondivisor)) /\ ((dm_value_sum_zero_excludedmask)=0))))))) /\ (exists dst_positive_code_sum_zero_excludedfold dst_positive_scale_sum_zero_excludedfold dst_negative_code_sum_zero_excludedfold dst_negative_scale_sum_zero_excludedfold dst_positive_sum_sum_zero_excludedfold dst_negative_sum_sum_zero_excludedfold. (((dm_mask_table_sum_zero_excluded) = (((((dst_positive_code_sum_zero_excludedfold) + (dst_positive_scale_sum_zero_excludedfold)) * S ((dst_positive_code_sum_zero_excludedfold) + (dst_positive_scale_sum_zero_excludedfold)) + ((dst_positive_scale_sum_zero_excludedfold) + (dst_positive_scale_sum_zero_excludedfold))) + (((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) * S ((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) + ((dst_negative_scale_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)))) * S ((((dst_positive_code_sum_zero_excludedfold) + (dst_positive_scale_sum_zero_excludedfold)) * S ((dst_positive_code_sum_zero_excludedfold) + (dst_positive_scale_sum_zero_excludedfold)) + ((dst_positive_scale_sum_zero_excludedfold) + (dst_positive_scale_sum_zero_excludedfold))) + (((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) * S ((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) + ((dst_negative_scale_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)))) + ((((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) * S ((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) + ((dst_negative_scale_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold))) + (((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) * S ((dst_negative_code_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)) + ((dst_negative_scale_sum_zero_excludedfold) + (dst_negative_scale_sum_zero_excludedfold)))))) /\ (((exists fs_u_dst_sum_zero_excludedfoldpositive fs_v_dst_sum_zero_excludedfoldpositive. ((((exists fs_h_dst_sum_zero_excludedfoldpositive_body_start. fs_h_dst_sum_zero_excludedfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_zero_excludedfoldpositive)) /\ exists fs_q_dst_sum_zero_excludedfoldpositive_body_start. fs_u_dst_sum_zero_excludedfoldpositive = fs_q_dst_sum_zero_excludedfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_zero_excludedfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_zero_excludedfoldpositive_body_terminal. fs_h_dst_sum_zero_excludedfoldpositive_body_terminal + S (dst_positive_sum_sum_zero_excludedfold) = S ((S (S (0))) * fs_v_dst_sum_zero_excludedfoldpositive)) /\ exists fs_q_dst_sum_zero_excludedfoldpositive_body_terminal. fs_u_dst_sum_zero_excludedfoldpositive = fs_q_dst_sum_zero_excludedfoldpositive_body_terminal * S ((S (S (0))) * fs_v_dst_sum_zero_excludedfoldpositive) + (dst_positive_sum_sum_zero_excludedfold))) /\ forall fs_i_dst_sum_zero_excludedfoldpositive_body_steps. (exists fs_lt_dst_sum_zero_excludedfoldpositive_body_steps_bound. fs_lt_dst_sum_zero_excludedfoldpositive_body_steps_bound + S fs_i_dst_sum_zero_excludedfoldpositive_body_steps = S (0)) -> exists fs_a_dst_sum_zero_excludedfoldpositive_body_steps fs_r_dst_sum_zero_excludedfoldpositive_body_steps fs_s_dst_sum_zero_excludedfoldpositive_body_steps. ((((exists fs_h_dst_sum_zero_excludedfoldpositive_body_steps_summand. fs_h_dst_sum_zero_excludedfoldpositive_body_steps_summand + S (fs_a_dst_sum_zero_excludedfoldpositive_body_steps) = S ((S (fs_i_dst_sum_zero_excludedfoldpositive_body_steps)) * dst_positive_scale_sum_zero_excludedfold)) /\ exists fs_q_dst_sum_zero_excludedfoldpositive_body_steps_summand. dst_positive_code_sum_zero_excludedfold = fs_q_dst_sum_zero_excludedfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_zero_excludedfoldpositive_body_steps)) * dst_positive_scale_sum_zero_excludedfold) + (fs_a_dst_sum_zero_excludedfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_zero_excludedfoldpositive_body_steps_partial. fs_h_dst_sum_zero_excludedfoldpositive_body_steps_partial + S (fs_r_dst_sum_zero_excludedfoldpositive_body_steps) = S ((S (fs_i_dst_sum_zero_excludedfoldpositive_body_steps)) * fs_v_dst_sum_zero_excludedfoldpositive)) /\ exists fs_q_dst_sum_zero_excludedfoldpositive_body_steps_partial. fs_u_dst_sum_zero_excludedfoldpositive = fs_q_dst_sum_zero_excludedfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_zero_excludedfoldpositive_body_steps)) * fs_v_dst_sum_zero_excludedfoldpositive) + (fs_r_dst_sum_zero_excludedfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_zero_excludedfoldpositive_body_steps_successor. fs_h_dst_sum_zero_excludedfoldpositive_body_steps_successor + S (fs_s_dst_sum_zero_excludedfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_zero_excludedfoldpositive_body_steps)) * fs_v_dst_sum_zero_excludedfoldpositive)) /\ exists fs_q_dst_sum_zero_excludedfoldpositive_body_steps_successor. fs_u_dst_sum_zero_excludedfoldpositive = fs_q_dst_sum_zero_excludedfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_zero_excludedfoldpositive_body_steps)) * fs_v_dst_sum_zero_excludedfoldpositive) + (fs_s_dst_sum_zero_excludedfoldpositive_body_steps))) /\ fs_s_dst_sum_zero_excludedfoldpositive_body_steps = fs_r_dst_sum_zero_excludedfoldpositive_body_steps + fs_a_dst_sum_zero_excludedfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_zero_excludedfoldnegative fs_v_dst_sum_zero_excludedfoldnegative. ((((exists fs_h_dst_sum_zero_excludedfoldnegative_body_start. fs_h_dst_sum_zero_excludedfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_zero_excludedfoldnegative)) /\ exists fs_q_dst_sum_zero_excludedfoldnegative_body_start. fs_u_dst_sum_zero_excludedfoldnegative = fs_q_dst_sum_zero_excludedfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_zero_excludedfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_zero_excludedfoldnegative_body_terminal. fs_h_dst_sum_zero_excludedfoldnegative_body_terminal + S (dst_negative_sum_sum_zero_excludedfold) = S ((S (S (0))) * fs_v_dst_sum_zero_excludedfoldnegative)) /\ exists fs_q_dst_sum_zero_excludedfoldnegative_body_terminal. fs_u_dst_sum_zero_excludedfoldnegative = fs_q_dst_sum_zero_excludedfoldnegative_body_terminal * S ((S (S (0))) * fs_v_dst_sum_zero_excludedfoldnegative) + (dst_negative_sum_sum_zero_excludedfold))) /\ forall fs_i_dst_sum_zero_excludedfoldnegative_body_steps. (exists fs_lt_dst_sum_zero_excludedfoldnegative_body_steps_bound. fs_lt_dst_sum_zero_excludedfoldnegative_body_steps_bound + S fs_i_dst_sum_zero_excludedfoldnegative_body_steps = S (0)) -> exists fs_a_dst_sum_zero_excludedfoldnegative_body_steps fs_r_dst_sum_zero_excludedfoldnegative_body_steps fs_s_dst_sum_zero_excludedfoldnegative_body_steps. ((((exists fs_h_dst_sum_zero_excludedfoldnegative_body_steps_summand. fs_h_dst_sum_zero_excludedfoldnegative_body_steps_summand + S (fs_a_dst_sum_zero_excludedfoldnegative_body_steps) = S ((S (fs_i_dst_sum_zero_excludedfoldnegative_body_steps)) * dst_negative_scale_sum_zero_excludedfold)) /\ exists fs_q_dst_sum_zero_excludedfoldnegative_body_steps_summand. dst_negative_code_sum_zero_excludedfold = fs_q_dst_sum_zero_excludedfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_zero_excludedfoldnegative_body_steps)) * dst_negative_scale_sum_zero_excludedfold) + (fs_a_dst_sum_zero_excludedfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_zero_excludedfoldnegative_body_steps_partial. fs_h_dst_sum_zero_excludedfoldnegative_body_steps_partial + S (fs_r_dst_sum_zero_excludedfoldnegative_body_steps) = S ((S (fs_i_dst_sum_zero_excludedfoldnegative_body_steps)) * fs_v_dst_sum_zero_excludedfoldnegative)) /\ exists fs_q_dst_sum_zero_excludedfoldnegative_body_steps_partial. fs_u_dst_sum_zero_excludedfoldnegative = fs_q_dst_sum_zero_excludedfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_zero_excludedfoldnegative_body_steps)) * fs_v_dst_sum_zero_excludedfoldnegative) + (fs_r_dst_sum_zero_excludedfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_zero_excludedfoldnegative_body_steps_successor. fs_h_dst_sum_zero_excludedfoldnegative_body_steps_successor + S (fs_s_dst_sum_zero_excludedfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_zero_excludedfoldnegative_body_steps)) * fs_v_dst_sum_zero_excludedfoldnegative)) /\ exists fs_q_dst_sum_zero_excludedfoldnegative_body_steps_successor. fs_u_dst_sum_zero_excludedfoldnegative = fs_q_dst_sum_zero_excludedfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_zero_excludedfoldnegative_body_steps)) * fs_v_dst_sum_zero_excludedfoldnegative) + (fs_s_dst_sum_zero_excludedfoldnegative_body_steps))) /\ fs_s_dst_sum_zero_excludedfoldnegative_body_steps = fs_r_dst_sum_zero_excludedfoldnegative_body_steps + fs_a_dst_sum_zero_excludedfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_zero_excludedfoldresult ge_balance_negative_sum_zero_excludedfoldresult. (((((z) = 2 * (ge_balance_positive_sum_zero_excludedfoldresult) /\ (ge_balance_negative_sum_zero_excludedfoldresult) = 0) \/ exists ge_signed_half_sum_zero_excludedfoldresultdecode. (((z) = 2 * ge_signed_half_sum_zero_excludedfoldresultdecode + 1 /\ (ge_balance_positive_sum_zero_excludedfoldresult) = 0) /\ (ge_balance_negative_sum_zero_excludedfoldresult) = S ge_signed_half_sum_zero_excludedfoldresultdecode))) /\ ((dst_positive_sum_sum_zero_excludedfold) + ge_balance_negative_sum_zero_excludedfoldresult = (dst_negative_sum_sum_zero_excludedfold) + ge_balance_positive_sum_zero_excludedfoldresult))))))))))))) -> false

signed_divisor_sum_one

new owned theorem · read exact theorem evidence

Bundle node 312; exact statement SHA-256 80e2388674be08dcb59e48394c33b1adc1102799ef6af5761365dc465afdce0c

Exact first-order statement

forall N F a. (exists dst_positive_code_sum_one_input dst_positive_scale_sum_one_input dst_negative_code_sum_one_input dst_negative_scale_sum_one_input. (((F) = (((((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) * S ((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) + ((dst_positive_scale_sum_one_input) + (dst_positive_scale_sum_one_input))) + (((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input)))) * S ((((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) * S ((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) + ((dst_positive_scale_sum_one_input) + (dst_positive_scale_sum_one_input))) + (((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input)))) + ((((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input))) + (((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input)))))) /\ (forall dst_index_sum_one_input. (exists pvs_le_gap_sum_one_inputdomain. pvs_le_gap_sum_one_inputdomain + (dst_index_sum_one_input) = (N)) -> exists dst_positive_sum_one_input dst_negative_sum_one_input dst_value_sum_one_input. ((((exists ff_h_pvs_sum_one_inputentrypositive. ff_h_pvs_sum_one_inputentrypositive + S (dst_positive_sum_one_input) = S ((S (dst_index_sum_one_input)) * dst_positive_scale_sum_one_input)) /\ exists ff_q_pvs_sum_one_inputentrypositive. dst_positive_code_sum_one_input = ff_q_pvs_sum_one_inputentrypositive * S ((S (dst_index_sum_one_input)) * dst_positive_scale_sum_one_input) + (dst_positive_sum_one_input))) /\ (((((exists ff_h_pvs_sum_one_inputentrynegative. ff_h_pvs_sum_one_inputentrynegative + S (dst_negative_sum_one_input) = S ((S (dst_index_sum_one_input)) * dst_negative_scale_sum_one_input)) /\ exists ff_q_pvs_sum_one_inputentrynegative. dst_negative_code_sum_one_input = ff_q_pvs_sum_one_inputentrynegative * S ((S (dst_index_sum_one_input)) * dst_negative_scale_sum_one_input) + (dst_negative_sum_one_input))) /\ (exists ge_balance_positive_sum_one_inputentryvalue ge_balance_negative_sum_one_inputentryvalue. (((((dst_value_sum_one_input) = 2 * (ge_balance_positive_sum_one_inputentryvalue) /\ (ge_balance_negative_sum_one_inputentryvalue) = 0) \/ exists ge_signed_half_sum_one_inputentryvaluedecode. (((dst_value_sum_one_input) = 2 * ge_signed_half_sum_one_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_one_inputentryvalue) = 0) /\ (ge_balance_negative_sum_one_inputentryvalue) = S ge_signed_half_sum_one_inputentryvaluedecode))) /\ ((dst_positive_sum_one_input) + ge_balance_negative_sum_one_inputentryvalue = (dst_negative_sum_one_input) + ge_balance_positive_sum_one_inputentryvalue))))))))) -> (exists pvs_le_gap_sum_one_bound. pvs_le_gap_sum_one_bound + (1) = (N)) -> (exists dst_positive_code_sum_one_entry dst_positive_scale_sum_one_entry dst_negative_code_sum_one_entry dst_negative_scale_sum_one_entry dst_positive_sum_one_entry dst_negative_sum_one_entry. (((F) = (((((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) * S ((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) + ((dst_positive_scale_sum_one_entry) + (dst_positive_scale_sum_one_entry))) + (((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry)))) * S ((((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) * S ((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) + ((dst_positive_scale_sum_one_entry) + (dst_positive_scale_sum_one_entry))) + (((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry)))) + ((((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry))) + (((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry)))))) /\ (((((exists ff_h_pvs_sum_one_entrypositive. ff_h_pvs_sum_one_entrypositive + S (dst_positive_sum_one_entry) = S ((S (1)) * dst_positive_scale_sum_one_entry)) /\ exists ff_q_pvs_sum_one_entrypositive. dst_positive_code_sum_one_entry = ff_q_pvs_sum_one_entrypositive * S ((S (1)) * dst_positive_scale_sum_one_entry) + (dst_positive_sum_one_entry))) /\ (((((exists ff_h_pvs_sum_one_entrynegative. ff_h_pvs_sum_one_entrynegative + S (dst_negative_sum_one_entry) = S ((S (1)) * dst_negative_scale_sum_one_entry)) /\ exists ff_q_pvs_sum_one_entrynegative. dst_negative_code_sum_one_entry = ff_q_pvs_sum_one_entrynegative * S ((S (1)) * dst_negative_scale_sum_one_entry) + (dst_negative_sum_one_entry))) /\ (exists ge_balance_positive_sum_one_entryvalue ge_balance_negative_sum_one_entryvalue. (((((a) = 2 * (ge_balance_positive_sum_one_entryvalue) /\ (ge_balance_negative_sum_one_entryvalue) = 0) \/ exists ge_signed_half_sum_one_entryvaluedecode. (((a) = 2 * ge_signed_half_sum_one_entryvaluedecode + 1 /\ (ge_balance_positive_sum_one_entryvalue) = 0) /\ (ge_balance_negative_sum_one_entryvalue) = S ge_signed_half_sum_one_entryvaluedecode))) /\ ((dst_positive_sum_one_entry) + ge_balance_negative_sum_one_entryvalue = (dst_negative_sum_one_entry) + ge_balance_positive_sum_one_entryvalue))))))))) -> (((~((1)=0)) /\ (exists dm_mask_table_sum_one_result. ((((exists dst_positive_code_sum_one_resultmasktable dst_positive_scale_sum_one_resultmasktable dst_negative_code_sum_one_resultmasktable dst_negative_scale_sum_one_resultmasktable. (((dm_mask_table_sum_one_result) = (((((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) * S ((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) + ((dst_positive_scale_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable))) + (((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)))) * S ((((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) * S ((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) + ((dst_positive_scale_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable))) + (((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)))) + ((((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable))) + (((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)))))) /\ (forall dst_index_sum_one_resultmasktable. (exists pvs_le_gap_sum_one_resultmasktabledomain. pvs_le_gap_sum_one_resultmasktabledomain + (dst_index_sum_one_resultmasktable) = (1)) -> exists dst_positive_sum_one_resultmasktable dst_negative_sum_one_resultmasktable dst_value_sum_one_resultmasktable. ((((exists ff_h_pvs_sum_one_resultmasktableentrypositive. ff_h_pvs_sum_one_resultmasktableentrypositive + S (dst_positive_sum_one_resultmasktable) = S ((S (dst_index_sum_one_resultmasktable)) * dst_positive_scale_sum_one_resultmasktable)) /\ exists ff_q_pvs_sum_one_resultmasktableentrypositive. dst_positive_code_sum_one_resultmasktable = ff_q_pvs_sum_one_resultmasktableentrypositive * S ((S (dst_index_sum_one_resultmasktable)) * dst_positive_scale_sum_one_resultmasktable) + (dst_positive_sum_one_resultmasktable))) /\ (((((exists ff_h_pvs_sum_one_resultmasktableentrynegative. ff_h_pvs_sum_one_resultmasktableentrynegative + S (dst_negative_sum_one_resultmasktable) = S ((S (dst_index_sum_one_resultmasktable)) * dst_negative_scale_sum_one_resultmasktable)) /\ exists ff_q_pvs_sum_one_resultmasktableentrynegative. dst_negative_code_sum_one_resultmasktable = ff_q_pvs_sum_one_resultmasktableentrynegative * S ((S (dst_index_sum_one_resultmasktable)) * dst_negative_scale_sum_one_resultmasktable) + (dst_negative_sum_one_resultmasktable))) /\ (exists ge_balance_positive_sum_one_resultmasktableentryvalue ge_balance_negative_sum_one_resultmasktableentryvalue. (((((dst_value_sum_one_resultmasktable) = 2 * (ge_balance_positive_sum_one_resultmasktableentryvalue) /\ (ge_balance_negative_sum_one_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_one_resultmasktableentryvaluedecode. (((dst_value_sum_one_resultmasktable) = 2 * ge_signed_half_sum_one_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_one_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_one_resultmasktableentryvalue) = S ge_signed_half_sum_one_resultmasktableentryvaluedecode))) /\ ((dst_positive_sum_one_resultmasktable) + ge_balance_negative_sum_one_resultmasktableentryvalue = (dst_negative_sum_one_resultmasktable) + ge_balance_positive_sum_one_resultmasktableentryvalue))))))))) /\ (forall dm_index_sum_one_resultmask dm_value_sum_one_resultmask. (exists pvs_le_gap_sum_one_resultmaskdomain. pvs_le_gap_sum_one_resultmaskdomain + (dm_index_sum_one_resultmask) = (1)) -> (exists dst_positive_code_sum_one_resultmasklookup dst_positive_scale_sum_one_resultmasklookup dst_negative_code_sum_one_resultmasklookup dst_negative_scale_sum_one_resultmasklookup dst_positive_sum_one_resultmasklookup dst_negative_sum_one_resultmasklookup. (((dm_mask_table_sum_one_result) = (((((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) * S ((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) + ((dst_positive_scale_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup))) + (((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)))) * S ((((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) * S ((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) + ((dst_positive_scale_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup))) + (((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)))) + ((((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup))) + (((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)))))) /\ (((((exists ff_h_pvs_sum_one_resultmasklookuppositive. ff_h_pvs_sum_one_resultmasklookuppositive + S (dst_positive_sum_one_resultmasklookup) = S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmasklookup)) /\ exists ff_q_pvs_sum_one_resultmasklookuppositive. dst_positive_code_sum_one_resultmasklookup = ff_q_pvs_sum_one_resultmasklookuppositive * S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmasklookup) + (dst_positive_sum_one_resultmasklookup))) /\ (((((exists ff_h_pvs_sum_one_resultmasklookupnegative. ff_h_pvs_sum_one_resultmasklookupnegative + S (dst_negative_sum_one_resultmasklookup) = S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmasklookup)) /\ exists ff_q_pvs_sum_one_resultmasklookupnegative. dst_negative_code_sum_one_resultmasklookup = ff_q_pvs_sum_one_resultmasklookupnegative * S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_sum_one_resultmasklookup))) /\ (exists ge_balance_positive_sum_one_resultmasklookupvalue ge_balance_negative_sum_one_resultmasklookupvalue. (((((dm_value_sum_one_resultmask) = 2 * (ge_balance_positive_sum_one_resultmasklookupvalue) /\ (ge_balance_negative_sum_one_resultmasklookupvalue) = 0) \/ exists ge_signed_half_sum_one_resultmasklookupvaluedecode. (((dm_value_sum_one_resultmask) = 2 * ge_signed_half_sum_one_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_one_resultmasklookupvalue) = 0) /\ (ge_balance_negative_sum_one_resultmasklookupvalue) = S ge_signed_half_sum_one_resultmasklookupvaluedecode))) /\ ((dst_positive_sum_one_resultmasklookup) + ge_balance_negative_sum_one_resultmasklookupvalue = (dst_negative_sum_one_resultmasklookup) + ge_balance_positive_sum_one_resultmasklookupvalue))))))))) -> ((((~((dm_index_sum_one_resultmask)=0)) /\ (exists dm_quotient_sum_one_resultmaskentry. (((1)=(dm_index_sum_one_resultmask)*dm_quotient_sum_one_resultmaskentry) /\ (exists dst_positive_code_sum_one_resultmaskentryinput dst_positive_scale_sum_one_resultmaskentryinput dst_negative_code_sum_one_resultmaskentryinput dst_negative_scale_sum_one_resultmaskentryinput dst_positive_sum_one_resultmaskentryinput dst_negative_sum_one_resultmaskentryinput. (((F) = (((((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) * S ((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) + ((dst_positive_scale_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput))) + (((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)))) * S ((((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) * S ((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) + ((dst_positive_scale_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput))) + (((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)))) + ((((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput))) + (((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_one_resultmaskentryinputpositive. ff_h_pvs_sum_one_resultmaskentryinputpositive + S (dst_positive_sum_one_resultmaskentryinput) = S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmaskentryinput)) /\ exists ff_q_pvs_sum_one_resultmaskentryinputpositive. dst_positive_code_sum_one_resultmaskentryinput = ff_q_pvs_sum_one_resultmaskentryinputpositive * S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmaskentryinput) + (dst_positive_sum_one_resultmaskentryinput))) /\ (((((exists ff_h_pvs_sum_one_resultmaskentryinputnegative. ff_h_pvs_sum_one_resultmaskentryinputnegative + S (dst_negative_sum_one_resultmaskentryinput) = S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmaskentryinput)) /\ exists ff_q_pvs_sum_one_resultmaskentryinputnegative. dst_negative_code_sum_one_resultmaskentryinput = ff_q_pvs_sum_one_resultmaskentryinputnegative * S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_sum_one_resultmaskentryinput))) /\ (exists ge_balance_positive_sum_one_resultmaskentryinputvalue ge_balance_negative_sum_one_resultmaskentryinputvalue. (((((dm_value_sum_one_resultmask) = 2 * (ge_balance_positive_sum_one_resultmaskentryinputvalue) /\ (ge_balance_negative_sum_one_resultmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_one_resultmaskentryinputvaluedecode. (((dm_value_sum_one_resultmask) = 2 * ge_signed_half_sum_one_resultmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_one_resultmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_one_resultmaskentryinputvalue) = S ge_signed_half_sum_one_resultmaskentryinputvaluedecode))) /\ ((dst_positive_sum_one_resultmaskentryinput) + ge_balance_negative_sum_one_resultmaskentryinputvalue = (dst_negative_sum_one_resultmaskentryinput) + ge_balance_positive_sum_one_resultmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_one_resultmask)=0 \/ ~(exists pvs_factor_sum_one_resultmaskentrynondivisor. (1) = (dm_index_sum_one_resultmask) * pvs_factor_sum_one_resultmaskentrynondivisor)) /\ ((dm_value_sum_one_resultmask)=0))))))) /\ (exists dst_positive_code_sum_one_resultfold dst_positive_scale_sum_one_resultfold dst_negative_code_sum_one_resultfold dst_negative_scale_sum_one_resultfold dst_positive_sum_sum_one_resultfold dst_negative_sum_sum_one_resultfold. (((dm_mask_table_sum_one_result) = (((((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) * S ((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) + ((dst_positive_scale_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold))) + (((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)))) * S ((((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) * S ((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) + ((dst_positive_scale_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold))) + (((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)))) + ((((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold))) + (((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)))))) /\ (((exists fs_u_dst_sum_one_resultfoldpositive fs_v_dst_sum_one_resultfoldpositive. ((((exists fs_h_dst_sum_one_resultfoldpositive_body_start. fs_h_dst_sum_one_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_start. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_one_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_one_resultfoldpositive_body_terminal. fs_h_dst_sum_one_resultfoldpositive_body_terminal + S (dst_positive_sum_sum_one_resultfold) = S ((S (S (1))) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_terminal. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_terminal * S ((S (S (1))) * fs_v_dst_sum_one_resultfoldpositive) + (dst_positive_sum_sum_one_resultfold))) /\ forall fs_i_dst_sum_one_resultfoldpositive_body_steps. (exists fs_lt_dst_sum_one_resultfoldpositive_body_steps_bound. fs_lt_dst_sum_one_resultfoldpositive_body_steps_bound + S fs_i_dst_sum_one_resultfoldpositive_body_steps = S (1)) -> exists fs_a_dst_sum_one_resultfoldpositive_body_steps fs_r_dst_sum_one_resultfoldpositive_body_steps fs_s_dst_sum_one_resultfoldpositive_body_steps. ((((exists fs_h_dst_sum_one_resultfoldpositive_body_steps_summand. fs_h_dst_sum_one_resultfoldpositive_body_steps_summand + S (fs_a_dst_sum_one_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * dst_positive_scale_sum_one_resultfold)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_steps_summand. dst_positive_code_sum_one_resultfold = fs_q_dst_sum_one_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * dst_positive_scale_sum_one_resultfold) + (fs_a_dst_sum_one_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldpositive_body_steps_partial. fs_h_dst_sum_one_resultfoldpositive_body_steps_partial + S (fs_r_dst_sum_one_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_steps_partial. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive) + (fs_r_dst_sum_one_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldpositive_body_steps_successor. fs_h_dst_sum_one_resultfoldpositive_body_steps_successor + S (fs_s_dst_sum_one_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_steps_successor. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive) + (fs_s_dst_sum_one_resultfoldpositive_body_steps))) /\ fs_s_dst_sum_one_resultfoldpositive_body_steps = fs_r_dst_sum_one_resultfoldpositive_body_steps + fs_a_dst_sum_one_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_one_resultfoldnegative fs_v_dst_sum_one_resultfoldnegative. ((((exists fs_h_dst_sum_one_resultfoldnegative_body_start. fs_h_dst_sum_one_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_start. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_one_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_one_resultfoldnegative_body_terminal. fs_h_dst_sum_one_resultfoldnegative_body_terminal + S (dst_negative_sum_sum_one_resultfold) = S ((S (S (1))) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_terminal. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_terminal * S ((S (S (1))) * fs_v_dst_sum_one_resultfoldnegative) + (dst_negative_sum_sum_one_resultfold))) /\ forall fs_i_dst_sum_one_resultfoldnegative_body_steps. (exists fs_lt_dst_sum_one_resultfoldnegative_body_steps_bound. fs_lt_dst_sum_one_resultfoldnegative_body_steps_bound + S fs_i_dst_sum_one_resultfoldnegative_body_steps = S (1)) -> exists fs_a_dst_sum_one_resultfoldnegative_body_steps fs_r_dst_sum_one_resultfoldnegative_body_steps fs_s_dst_sum_one_resultfoldnegative_body_steps. ((((exists fs_h_dst_sum_one_resultfoldnegative_body_steps_summand. fs_h_dst_sum_one_resultfoldnegative_body_steps_summand + S (fs_a_dst_sum_one_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * dst_negative_scale_sum_one_resultfold)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_steps_summand. dst_negative_code_sum_one_resultfold = fs_q_dst_sum_one_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * dst_negative_scale_sum_one_resultfold) + (fs_a_dst_sum_one_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldnegative_body_steps_partial. fs_h_dst_sum_one_resultfoldnegative_body_steps_partial + S (fs_r_dst_sum_one_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_steps_partial. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative) + (fs_r_dst_sum_one_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldnegative_body_steps_successor. fs_h_dst_sum_one_resultfoldnegative_body_steps_successor + S (fs_s_dst_sum_one_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_steps_successor. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative) + (fs_s_dst_sum_one_resultfoldnegative_body_steps))) /\ fs_s_dst_sum_one_resultfoldnegative_body_steps = fs_r_dst_sum_one_resultfoldnegative_body_steps + fs_a_dst_sum_one_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_one_resultfoldresult ge_balance_negative_sum_one_resultfoldresult. (((((a) = 2 * (ge_balance_positive_sum_one_resultfoldresult) /\ (ge_balance_negative_sum_one_resultfoldresult) = 0) \/ exists ge_signed_half_sum_one_resultfoldresultdecode. (((a) = 2 * ge_signed_half_sum_one_resultfoldresultdecode + 1 /\ (ge_balance_positive_sum_one_resultfoldresult) = 0) /\ (ge_balance_negative_sum_one_resultfoldresult) = S ge_signed_half_sum_one_resultfoldresultdecode))) /\ ((dst_positive_sum_sum_one_resultfold) + ge_balance_negative_sum_one_resultfoldresult = (dst_negative_sum_sum_one_resultfold) + ge_balance_positive_sum_one_resultfoldresult)))))))))))))

signed_divisor_sum_positive_source_extensional

new owned theorem · read exact theorem evidence

Bundle node 313; exact statement SHA-256 5db775338790a36cdffa83a65f52f26d244827ba90942feb09600b9f5a202672

Exact first-order statement

forall F G n a b. (forall dm_index_sum_source_equal dm_first_value_sum_source_equal dm_second_value_sum_source_equal. ~(dm_index_sum_source_equal=0) -> (exists pvs_le_gap_sum_source_equaldomain. pvs_le_gap_sum_source_equaldomain + (dm_index_sum_source_equal) = (n)) -> (exists dst_positive_code_sum_source_equalfirst dst_positive_scale_sum_source_equalfirst dst_negative_code_sum_source_equalfirst dst_negative_scale_sum_source_equalfirst dst_positive_sum_source_equalfirst dst_negative_sum_source_equalfirst. (((F) = (((((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) * S ((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) + ((dst_positive_scale_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst))) + (((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)))) * S ((((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) * S ((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) + ((dst_positive_scale_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst))) + (((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)))) + ((((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst))) + (((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)))))) /\ (((((exists ff_h_pvs_sum_source_equalfirstpositive. ff_h_pvs_sum_source_equalfirstpositive + S (dst_positive_sum_source_equalfirst) = S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalfirst)) /\ exists ff_q_pvs_sum_source_equalfirstpositive. dst_positive_code_sum_source_equalfirst = ff_q_pvs_sum_source_equalfirstpositive * S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalfirst) + (dst_positive_sum_source_equalfirst))) /\ (((((exists ff_h_pvs_sum_source_equalfirstnegative. ff_h_pvs_sum_source_equalfirstnegative + S (dst_negative_sum_source_equalfirst) = S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalfirst)) /\ exists ff_q_pvs_sum_source_equalfirstnegative. dst_negative_code_sum_source_equalfirst = ff_q_pvs_sum_source_equalfirstnegative * S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalfirst) + (dst_negative_sum_source_equalfirst))) /\ (exists ge_balance_positive_sum_source_equalfirstvalue ge_balance_negative_sum_source_equalfirstvalue. (((((dm_first_value_sum_source_equal) = 2 * (ge_balance_positive_sum_source_equalfirstvalue) /\ (ge_balance_negative_sum_source_equalfirstvalue) = 0) \/ exists ge_signed_half_sum_source_equalfirstvaluedecode. (((dm_first_value_sum_source_equal) = 2 * ge_signed_half_sum_source_equalfirstvaluedecode + 1 /\ (ge_balance_positive_sum_source_equalfirstvalue) = 0) /\ (ge_balance_negative_sum_source_equalfirstvalue) = S ge_signed_half_sum_source_equalfirstvaluedecode))) /\ ((dst_positive_sum_source_equalfirst) + ge_balance_negative_sum_source_equalfirstvalue = (dst_negative_sum_source_equalfirst) + ge_balance_positive_sum_source_equalfirstvalue))))))))) -> (exists dst_positive_code_sum_source_equalsecond dst_positive_scale_sum_source_equalsecond dst_negative_code_sum_source_equalsecond dst_negative_scale_sum_source_equalsecond dst_positive_sum_source_equalsecond dst_negative_sum_source_equalsecond. (((G) = (((((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) * S ((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) + ((dst_positive_scale_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond))) + (((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)))) * S ((((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) * S ((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) + ((dst_positive_scale_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond))) + (((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)))) + ((((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond))) + (((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)))))) /\ (((((exists ff_h_pvs_sum_source_equalsecondpositive. ff_h_pvs_sum_source_equalsecondpositive + S (dst_positive_sum_source_equalsecond) = S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalsecond)) /\ exists ff_q_pvs_sum_source_equalsecondpositive. dst_positive_code_sum_source_equalsecond = ff_q_pvs_sum_source_equalsecondpositive * S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalsecond) + (dst_positive_sum_source_equalsecond))) /\ (((((exists ff_h_pvs_sum_source_equalsecondnegative. ff_h_pvs_sum_source_equalsecondnegative + S (dst_negative_sum_source_equalsecond) = S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalsecond)) /\ exists ff_q_pvs_sum_source_equalsecondnegative. dst_negative_code_sum_source_equalsecond = ff_q_pvs_sum_source_equalsecondnegative * S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalsecond) + (dst_negative_sum_source_equalsecond))) /\ (exists ge_balance_positive_sum_source_equalsecondvalue ge_balance_negative_sum_source_equalsecondvalue. (((((dm_second_value_sum_source_equal) = 2 * (ge_balance_positive_sum_source_equalsecondvalue) /\ (ge_balance_negative_sum_source_equalsecondvalue) = 0) \/ exists ge_signed_half_sum_source_equalsecondvaluedecode. (((dm_second_value_sum_source_equal) = 2 * ge_signed_half_sum_source_equalsecondvaluedecode + 1 /\ (ge_balance_positive_sum_source_equalsecondvalue) = 0) /\ (ge_balance_negative_sum_source_equalsecondvalue) = S ge_signed_half_sum_source_equalsecondvaluedecode))) /\ ((dst_positive_sum_source_equalsecond) + ge_balance_negative_sum_source_equalsecondvalue = (dst_negative_sum_source_equalsecond) + ge_balance_positive_sum_source_equalsecondvalue))))))))) -> dm_first_value_sum_source_equal=dm_second_value_sum_source_equal) -> (((~((n)=0)) /\ (exists dm_mask_table_sum_source_first. ((((exists dst_positive_code_sum_source_firstmasktable dst_positive_scale_sum_source_firstmasktable dst_negative_code_sum_source_firstmasktable dst_negative_scale_sum_source_firstmasktable. (((dm_mask_table_sum_source_first) = (((((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) * S ((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) + ((dst_positive_scale_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable))) + (((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)))) * S ((((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) * S ((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) + ((dst_positive_scale_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable))) + (((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)))) + ((((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable))) + (((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)))))) /\ (forall dst_index_sum_source_firstmasktable. (exists pvs_le_gap_sum_source_firstmasktabledomain. pvs_le_gap_sum_source_firstmasktabledomain + (dst_index_sum_source_firstmasktable) = (n)) -> exists dst_positive_sum_source_firstmasktable dst_negative_sum_source_firstmasktable dst_value_sum_source_firstmasktable. ((((exists ff_h_pvs_sum_source_firstmasktableentrypositive. ff_h_pvs_sum_source_firstmasktableentrypositive + S (dst_positive_sum_source_firstmasktable) = S ((S (dst_index_sum_source_firstmasktable)) * dst_positive_scale_sum_source_firstmasktable)) /\ exists ff_q_pvs_sum_source_firstmasktableentrypositive. dst_positive_code_sum_source_firstmasktable = ff_q_pvs_sum_source_firstmasktableentrypositive * S ((S (dst_index_sum_source_firstmasktable)) * dst_positive_scale_sum_source_firstmasktable) + (dst_positive_sum_source_firstmasktable))) /\ (((((exists ff_h_pvs_sum_source_firstmasktableentrynegative. ff_h_pvs_sum_source_firstmasktableentrynegative + S (dst_negative_sum_source_firstmasktable) = S ((S (dst_index_sum_source_firstmasktable)) * dst_negative_scale_sum_source_firstmasktable)) /\ exists ff_q_pvs_sum_source_firstmasktableentrynegative. dst_negative_code_sum_source_firstmasktable = ff_q_pvs_sum_source_firstmasktableentrynegative * S ((S (dst_index_sum_source_firstmasktable)) * dst_negative_scale_sum_source_firstmasktable) + (dst_negative_sum_source_firstmasktable))) /\ (exists ge_balance_positive_sum_source_firstmasktableentryvalue ge_balance_negative_sum_source_firstmasktableentryvalue. (((((dst_value_sum_source_firstmasktable) = 2 * (ge_balance_positive_sum_source_firstmasktableentryvalue) /\ (ge_balance_negative_sum_source_firstmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_source_firstmasktableentryvaluedecode. (((dst_value_sum_source_firstmasktable) = 2 * ge_signed_half_sum_source_firstmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_source_firstmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_source_firstmasktableentryvalue) = S ge_signed_half_sum_source_firstmasktableentryvaluedecode))) /\ ((dst_positive_sum_source_firstmasktable) + ge_balance_negative_sum_source_firstmasktableentryvalue = (dst_negative_sum_source_firstmasktable) + ge_balance_positive_sum_source_firstmasktableentryvalue))))))))) /\ (forall dm_index_sum_source_firstmask dm_value_sum_source_firstmask. (exists pvs_le_gap_sum_source_firstmaskdomain. pvs_le_gap_sum_source_firstmaskdomain + (dm_index_sum_source_firstmask) = (n)) -> (exists dst_positive_code_sum_source_firstmasklookup dst_positive_scale_sum_source_firstmasklookup dst_negative_code_sum_source_firstmasklookup dst_negative_scale_sum_source_firstmasklookup dst_positive_sum_source_firstmasklookup dst_negative_sum_source_firstmasklookup. (((dm_mask_table_sum_source_first) = (((((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) * S ((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) + ((dst_positive_scale_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup))) + (((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)))) * S ((((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) * S ((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) + ((dst_positive_scale_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup))) + (((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)))) + ((((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup))) + (((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)))))) /\ (((((exists ff_h_pvs_sum_source_firstmasklookuppositive. ff_h_pvs_sum_source_firstmasklookuppositive + S (dst_positive_sum_source_firstmasklookup) = S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmasklookup)) /\ exists ff_q_pvs_sum_source_firstmasklookuppositive. dst_positive_code_sum_source_firstmasklookup = ff_q_pvs_sum_source_firstmasklookuppositive * S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmasklookup) + (dst_positive_sum_source_firstmasklookup))) /\ (((((exists ff_h_pvs_sum_source_firstmasklookupnegative. ff_h_pvs_sum_source_firstmasklookupnegative + S (dst_negative_sum_source_firstmasklookup) = S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmasklookup)) /\ exists ff_q_pvs_sum_source_firstmasklookupnegative. dst_negative_code_sum_source_firstmasklookup = ff_q_pvs_sum_source_firstmasklookupnegative * S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_sum_source_firstmasklookup))) /\ (exists ge_balance_positive_sum_source_firstmasklookupvalue ge_balance_negative_sum_source_firstmasklookupvalue. (((((dm_value_sum_source_firstmask) = 2 * (ge_balance_positive_sum_source_firstmasklookupvalue) /\ (ge_balance_negative_sum_source_firstmasklookupvalue) = 0) \/ exists ge_signed_half_sum_source_firstmasklookupvaluedecode. (((dm_value_sum_source_firstmask) = 2 * ge_signed_half_sum_source_firstmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_source_firstmasklookupvalue) = 0) /\ (ge_balance_negative_sum_source_firstmasklookupvalue) = S ge_signed_half_sum_source_firstmasklookupvaluedecode))) /\ ((dst_positive_sum_source_firstmasklookup) + ge_balance_negative_sum_source_firstmasklookupvalue = (dst_negative_sum_source_firstmasklookup) + ge_balance_positive_sum_source_firstmasklookupvalue))))))))) -> ((((~((dm_index_sum_source_firstmask)=0)) /\ (exists dm_quotient_sum_source_firstmaskentry. (((n)=(dm_index_sum_source_firstmask)*dm_quotient_sum_source_firstmaskentry) /\ (exists dst_positive_code_sum_source_firstmaskentryinput dst_positive_scale_sum_source_firstmaskentryinput dst_negative_code_sum_source_firstmaskentryinput dst_negative_scale_sum_source_firstmaskentryinput dst_positive_sum_source_firstmaskentryinput dst_negative_sum_source_firstmaskentryinput. (((F) = (((((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) * S ((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) + ((dst_positive_scale_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput))) + (((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)))) * S ((((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) * S ((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) + ((dst_positive_scale_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput))) + (((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)))) + ((((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput))) + (((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_source_firstmaskentryinputpositive. ff_h_pvs_sum_source_firstmaskentryinputpositive + S (dst_positive_sum_source_firstmaskentryinput) = S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmaskentryinput)) /\ exists ff_q_pvs_sum_source_firstmaskentryinputpositive. dst_positive_code_sum_source_firstmaskentryinput = ff_q_pvs_sum_source_firstmaskentryinputpositive * S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmaskentryinput) + (dst_positive_sum_source_firstmaskentryinput))) /\ (((((exists ff_h_pvs_sum_source_firstmaskentryinputnegative. ff_h_pvs_sum_source_firstmaskentryinputnegative + S (dst_negative_sum_source_firstmaskentryinput) = S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmaskentryinput)) /\ exists ff_q_pvs_sum_source_firstmaskentryinputnegative. dst_negative_code_sum_source_firstmaskentryinput = ff_q_pvs_sum_source_firstmaskentryinputnegative * S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_sum_source_firstmaskentryinput))) /\ (exists ge_balance_positive_sum_source_firstmaskentryinputvalue ge_balance_negative_sum_source_firstmaskentryinputvalue. (((((dm_value_sum_source_firstmask) = 2 * (ge_balance_positive_sum_source_firstmaskentryinputvalue) /\ (ge_balance_negative_sum_source_firstmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_source_firstmaskentryinputvaluedecode. (((dm_value_sum_source_firstmask) = 2 * ge_signed_half_sum_source_firstmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_source_firstmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_source_firstmaskentryinputvalue) = S ge_signed_half_sum_source_firstmaskentryinputvaluedecode))) /\ ((dst_positive_sum_source_firstmaskentryinput) + ge_balance_negative_sum_source_firstmaskentryinputvalue = (dst_negative_sum_source_firstmaskentryinput) + ge_balance_positive_sum_source_firstmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_source_firstmask)=0 \/ ~(exists pvs_factor_sum_source_firstmaskentrynondivisor. (n) = (dm_index_sum_source_firstmask) * pvs_factor_sum_source_firstmaskentrynondivisor)) /\ ((dm_value_sum_source_firstmask)=0))))))) /\ (exists dst_positive_code_sum_source_firstfold dst_positive_scale_sum_source_firstfold dst_negative_code_sum_source_firstfold dst_negative_scale_sum_source_firstfold dst_positive_sum_sum_source_firstfold dst_negative_sum_sum_source_firstfold. (((dm_mask_table_sum_source_first) = (((((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) * S ((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) + ((dst_positive_scale_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold))) + (((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)))) * S ((((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) * S ((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) + ((dst_positive_scale_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold))) + (((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)))) + ((((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold))) + (((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)))))) /\ (((exists fs_u_dst_sum_source_firstfoldpositive fs_v_dst_sum_source_firstfoldpositive. ((((exists fs_h_dst_sum_source_firstfoldpositive_body_start. fs_h_dst_sum_source_firstfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_start. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_source_firstfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_source_firstfoldpositive_body_terminal. fs_h_dst_sum_source_firstfoldpositive_body_terminal + S (dst_positive_sum_sum_source_firstfold) = S ((S (S (n))) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_terminal. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_firstfoldpositive) + (dst_positive_sum_sum_source_firstfold))) /\ forall fs_i_dst_sum_source_firstfoldpositive_body_steps. (exists fs_lt_dst_sum_source_firstfoldpositive_body_steps_bound. fs_lt_dst_sum_source_firstfoldpositive_body_steps_bound + S fs_i_dst_sum_source_firstfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_source_firstfoldpositive_body_steps fs_r_dst_sum_source_firstfoldpositive_body_steps fs_s_dst_sum_source_firstfoldpositive_body_steps. ((((exists fs_h_dst_sum_source_firstfoldpositive_body_steps_summand. fs_h_dst_sum_source_firstfoldpositive_body_steps_summand + S (fs_a_dst_sum_source_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * dst_positive_scale_sum_source_firstfold)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_steps_summand. dst_positive_code_sum_source_firstfold = fs_q_dst_sum_source_firstfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * dst_positive_scale_sum_source_firstfold) + (fs_a_dst_sum_source_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldpositive_body_steps_partial. fs_h_dst_sum_source_firstfoldpositive_body_steps_partial + S (fs_r_dst_sum_source_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_steps_partial. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive) + (fs_r_dst_sum_source_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldpositive_body_steps_successor. fs_h_dst_sum_source_firstfoldpositive_body_steps_successor + S (fs_s_dst_sum_source_firstfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_steps_successor. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive) + (fs_s_dst_sum_source_firstfoldpositive_body_steps))) /\ fs_s_dst_sum_source_firstfoldpositive_body_steps = fs_r_dst_sum_source_firstfoldpositive_body_steps + fs_a_dst_sum_source_firstfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_source_firstfoldnegative fs_v_dst_sum_source_firstfoldnegative. ((((exists fs_h_dst_sum_source_firstfoldnegative_body_start. fs_h_dst_sum_source_firstfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_start. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_source_firstfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_source_firstfoldnegative_body_terminal. fs_h_dst_sum_source_firstfoldnegative_body_terminal + S (dst_negative_sum_sum_source_firstfold) = S ((S (S (n))) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_terminal. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_firstfoldnegative) + (dst_negative_sum_sum_source_firstfold))) /\ forall fs_i_dst_sum_source_firstfoldnegative_body_steps. (exists fs_lt_dst_sum_source_firstfoldnegative_body_steps_bound. fs_lt_dst_sum_source_firstfoldnegative_body_steps_bound + S fs_i_dst_sum_source_firstfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_source_firstfoldnegative_body_steps fs_r_dst_sum_source_firstfoldnegative_body_steps fs_s_dst_sum_source_firstfoldnegative_body_steps. ((((exists fs_h_dst_sum_source_firstfoldnegative_body_steps_summand. fs_h_dst_sum_source_firstfoldnegative_body_steps_summand + S (fs_a_dst_sum_source_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * dst_negative_scale_sum_source_firstfold)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_steps_summand. dst_negative_code_sum_source_firstfold = fs_q_dst_sum_source_firstfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * dst_negative_scale_sum_source_firstfold) + (fs_a_dst_sum_source_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldnegative_body_steps_partial. fs_h_dst_sum_source_firstfoldnegative_body_steps_partial + S (fs_r_dst_sum_source_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_steps_partial. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative) + (fs_r_dst_sum_source_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldnegative_body_steps_successor. fs_h_dst_sum_source_firstfoldnegative_body_steps_successor + S (fs_s_dst_sum_source_firstfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_steps_successor. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative) + (fs_s_dst_sum_source_firstfoldnegative_body_steps))) /\ fs_s_dst_sum_source_firstfoldnegative_body_steps = fs_r_dst_sum_source_firstfoldnegative_body_steps + fs_a_dst_sum_source_firstfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_source_firstfoldresult ge_balance_negative_sum_source_firstfoldresult. (((((a) = 2 * (ge_balance_positive_sum_source_firstfoldresult) /\ (ge_balance_negative_sum_source_firstfoldresult) = 0) \/ exists ge_signed_half_sum_source_firstfoldresultdecode. (((a) = 2 * ge_signed_half_sum_source_firstfoldresultdecode + 1 /\ (ge_balance_positive_sum_source_firstfoldresult) = 0) /\ (ge_balance_negative_sum_source_firstfoldresult) = S ge_signed_half_sum_source_firstfoldresultdecode))) /\ ((dst_positive_sum_sum_source_firstfold) + ge_balance_negative_sum_source_firstfoldresult = (dst_negative_sum_sum_source_firstfold) + ge_balance_positive_sum_source_firstfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dm_mask_table_sum_source_second. ((((exists dst_positive_code_sum_source_secondmasktable dst_positive_scale_sum_source_secondmasktable dst_negative_code_sum_source_secondmasktable dst_negative_scale_sum_source_secondmasktable. (((dm_mask_table_sum_source_second) = (((((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) * S ((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) + ((dst_positive_scale_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable))) + (((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)))) * S ((((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) * S ((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) + ((dst_positive_scale_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable))) + (((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)))) + ((((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable))) + (((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)))))) /\ (forall dst_index_sum_source_secondmasktable. (exists pvs_le_gap_sum_source_secondmasktabledomain. pvs_le_gap_sum_source_secondmasktabledomain + (dst_index_sum_source_secondmasktable) = (n)) -> exists dst_positive_sum_source_secondmasktable dst_negative_sum_source_secondmasktable dst_value_sum_source_secondmasktable. ((((exists ff_h_pvs_sum_source_secondmasktableentrypositive. ff_h_pvs_sum_source_secondmasktableentrypositive + S (dst_positive_sum_source_secondmasktable) = S ((S (dst_index_sum_source_secondmasktable)) * dst_positive_scale_sum_source_secondmasktable)) /\ exists ff_q_pvs_sum_source_secondmasktableentrypositive. dst_positive_code_sum_source_secondmasktable = ff_q_pvs_sum_source_secondmasktableentrypositive * S ((S (dst_index_sum_source_secondmasktable)) * dst_positive_scale_sum_source_secondmasktable) + (dst_positive_sum_source_secondmasktable))) /\ (((((exists ff_h_pvs_sum_source_secondmasktableentrynegative. ff_h_pvs_sum_source_secondmasktableentrynegative + S (dst_negative_sum_source_secondmasktable) = S ((S (dst_index_sum_source_secondmasktable)) * dst_negative_scale_sum_source_secondmasktable)) /\ exists ff_q_pvs_sum_source_secondmasktableentrynegative. dst_negative_code_sum_source_secondmasktable = ff_q_pvs_sum_source_secondmasktableentrynegative * S ((S (dst_index_sum_source_secondmasktable)) * dst_negative_scale_sum_source_secondmasktable) + (dst_negative_sum_source_secondmasktable))) /\ (exists ge_balance_positive_sum_source_secondmasktableentryvalue ge_balance_negative_sum_source_secondmasktableentryvalue. (((((dst_value_sum_source_secondmasktable) = 2 * (ge_balance_positive_sum_source_secondmasktableentryvalue) /\ (ge_balance_negative_sum_source_secondmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_source_secondmasktableentryvaluedecode. (((dst_value_sum_source_secondmasktable) = 2 * ge_signed_half_sum_source_secondmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_source_secondmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_source_secondmasktableentryvalue) = S ge_signed_half_sum_source_secondmasktableentryvaluedecode))) /\ ((dst_positive_sum_source_secondmasktable) + ge_balance_negative_sum_source_secondmasktableentryvalue = (dst_negative_sum_source_secondmasktable) + ge_balance_positive_sum_source_secondmasktableentryvalue))))))))) /\ (forall dm_index_sum_source_secondmask dm_value_sum_source_secondmask. (exists pvs_le_gap_sum_source_secondmaskdomain. pvs_le_gap_sum_source_secondmaskdomain + (dm_index_sum_source_secondmask) = (n)) -> (exists dst_positive_code_sum_source_secondmasklookup dst_positive_scale_sum_source_secondmasklookup dst_negative_code_sum_source_secondmasklookup dst_negative_scale_sum_source_secondmasklookup dst_positive_sum_source_secondmasklookup dst_negative_sum_source_secondmasklookup. (((dm_mask_table_sum_source_second) = (((((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) * S ((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) + ((dst_positive_scale_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup))) + (((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)))) * S ((((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) * S ((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) + ((dst_positive_scale_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup))) + (((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)))) + ((((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup))) + (((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)))))) /\ (((((exists ff_h_pvs_sum_source_secondmasklookuppositive. ff_h_pvs_sum_source_secondmasklookuppositive + S (dst_positive_sum_source_secondmasklookup) = S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmasklookup)) /\ exists ff_q_pvs_sum_source_secondmasklookuppositive. dst_positive_code_sum_source_secondmasklookup = ff_q_pvs_sum_source_secondmasklookuppositive * S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmasklookup) + (dst_positive_sum_source_secondmasklookup))) /\ (((((exists ff_h_pvs_sum_source_secondmasklookupnegative. ff_h_pvs_sum_source_secondmasklookupnegative + S (dst_negative_sum_source_secondmasklookup) = S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmasklookup)) /\ exists ff_q_pvs_sum_source_secondmasklookupnegative. dst_negative_code_sum_source_secondmasklookup = ff_q_pvs_sum_source_secondmasklookupnegative * S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_sum_source_secondmasklookup))) /\ (exists ge_balance_positive_sum_source_secondmasklookupvalue ge_balance_negative_sum_source_secondmasklookupvalue. (((((dm_value_sum_source_secondmask) = 2 * (ge_balance_positive_sum_source_secondmasklookupvalue) /\ (ge_balance_negative_sum_source_secondmasklookupvalue) = 0) \/ exists ge_signed_half_sum_source_secondmasklookupvaluedecode. (((dm_value_sum_source_secondmask) = 2 * ge_signed_half_sum_source_secondmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_source_secondmasklookupvalue) = 0) /\ (ge_balance_negative_sum_source_secondmasklookupvalue) = S ge_signed_half_sum_source_secondmasklookupvaluedecode))) /\ ((dst_positive_sum_source_secondmasklookup) + ge_balance_negative_sum_source_secondmasklookupvalue = (dst_negative_sum_source_secondmasklookup) + ge_balance_positive_sum_source_secondmasklookupvalue))))))))) -> ((((~((dm_index_sum_source_secondmask)=0)) /\ (exists dm_quotient_sum_source_secondmaskentry. (((n)=(dm_index_sum_source_secondmask)*dm_quotient_sum_source_secondmaskentry) /\ (exists dst_positive_code_sum_source_secondmaskentryinput dst_positive_scale_sum_source_secondmaskentryinput dst_negative_code_sum_source_secondmaskentryinput dst_negative_scale_sum_source_secondmaskentryinput dst_positive_sum_source_secondmaskentryinput dst_negative_sum_source_secondmaskentryinput. (((G) = (((((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) * S ((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) + ((dst_positive_scale_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput))) + (((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)))) * S ((((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) * S ((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) + ((dst_positive_scale_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput))) + (((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)))) + ((((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput))) + (((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_source_secondmaskentryinputpositive. ff_h_pvs_sum_source_secondmaskentryinputpositive + S (dst_positive_sum_source_secondmaskentryinput) = S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmaskentryinput)) /\ exists ff_q_pvs_sum_source_secondmaskentryinputpositive. dst_positive_code_sum_source_secondmaskentryinput = ff_q_pvs_sum_source_secondmaskentryinputpositive * S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmaskentryinput) + (dst_positive_sum_source_secondmaskentryinput))) /\ (((((exists ff_h_pvs_sum_source_secondmaskentryinputnegative. ff_h_pvs_sum_source_secondmaskentryinputnegative + S (dst_negative_sum_source_secondmaskentryinput) = S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmaskentryinput)) /\ exists ff_q_pvs_sum_source_secondmaskentryinputnegative. dst_negative_code_sum_source_secondmaskentryinput = ff_q_pvs_sum_source_secondmaskentryinputnegative * S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_sum_source_secondmaskentryinput))) /\ (exists ge_balance_positive_sum_source_secondmaskentryinputvalue ge_balance_negative_sum_source_secondmaskentryinputvalue. (((((dm_value_sum_source_secondmask) = 2 * (ge_balance_positive_sum_source_secondmaskentryinputvalue) /\ (ge_balance_negative_sum_source_secondmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_source_secondmaskentryinputvaluedecode. (((dm_value_sum_source_secondmask) = 2 * ge_signed_half_sum_source_secondmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_source_secondmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_source_secondmaskentryinputvalue) = S ge_signed_half_sum_source_secondmaskentryinputvaluedecode))) /\ ((dst_positive_sum_source_secondmaskentryinput) + ge_balance_negative_sum_source_secondmaskentryinputvalue = (dst_negative_sum_source_secondmaskentryinput) + ge_balance_positive_sum_source_secondmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_source_secondmask)=0 \/ ~(exists pvs_factor_sum_source_secondmaskentrynondivisor. (n) = (dm_index_sum_source_secondmask) * pvs_factor_sum_source_secondmaskentrynondivisor)) /\ ((dm_value_sum_source_secondmask)=0))))))) /\ (exists dst_positive_code_sum_source_secondfold dst_positive_scale_sum_source_secondfold dst_negative_code_sum_source_secondfold dst_negative_scale_sum_source_secondfold dst_positive_sum_sum_source_secondfold dst_negative_sum_sum_source_secondfold. (((dm_mask_table_sum_source_second) = (((((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) * S ((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) + ((dst_positive_scale_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold))) + (((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)))) * S ((((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) * S ((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) + ((dst_positive_scale_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold))) + (((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)))) + ((((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold))) + (((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)))))) /\ (((exists fs_u_dst_sum_source_secondfoldpositive fs_v_dst_sum_source_secondfoldpositive. ((((exists fs_h_dst_sum_source_secondfoldpositive_body_start. fs_h_dst_sum_source_secondfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_start. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_source_secondfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_source_secondfoldpositive_body_terminal. fs_h_dst_sum_source_secondfoldpositive_body_terminal + S (dst_positive_sum_sum_source_secondfold) = S ((S (S (n))) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_terminal. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_secondfoldpositive) + (dst_positive_sum_sum_source_secondfold))) /\ forall fs_i_dst_sum_source_secondfoldpositive_body_steps. (exists fs_lt_dst_sum_source_secondfoldpositive_body_steps_bound. fs_lt_dst_sum_source_secondfoldpositive_body_steps_bound + S fs_i_dst_sum_source_secondfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_source_secondfoldpositive_body_steps fs_r_dst_sum_source_secondfoldpositive_body_steps fs_s_dst_sum_source_secondfoldpositive_body_steps. ((((exists fs_h_dst_sum_source_secondfoldpositive_body_steps_summand. fs_h_dst_sum_source_secondfoldpositive_body_steps_summand + S (fs_a_dst_sum_source_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * dst_positive_scale_sum_source_secondfold)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_steps_summand. dst_positive_code_sum_source_secondfold = fs_q_dst_sum_source_secondfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * dst_positive_scale_sum_source_secondfold) + (fs_a_dst_sum_source_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldpositive_body_steps_partial. fs_h_dst_sum_source_secondfoldpositive_body_steps_partial + S (fs_r_dst_sum_source_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_steps_partial. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive) + (fs_r_dst_sum_source_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldpositive_body_steps_successor. fs_h_dst_sum_source_secondfoldpositive_body_steps_successor + S (fs_s_dst_sum_source_secondfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_steps_successor. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive) + (fs_s_dst_sum_source_secondfoldpositive_body_steps))) /\ fs_s_dst_sum_source_secondfoldpositive_body_steps = fs_r_dst_sum_source_secondfoldpositive_body_steps + fs_a_dst_sum_source_secondfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_source_secondfoldnegative fs_v_dst_sum_source_secondfoldnegative. ((((exists fs_h_dst_sum_source_secondfoldnegative_body_start. fs_h_dst_sum_source_secondfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_start. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_source_secondfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_source_secondfoldnegative_body_terminal. fs_h_dst_sum_source_secondfoldnegative_body_terminal + S (dst_negative_sum_sum_source_secondfold) = S ((S (S (n))) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_terminal. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_secondfoldnegative) + (dst_negative_sum_sum_source_secondfold))) /\ forall fs_i_dst_sum_source_secondfoldnegative_body_steps. (exists fs_lt_dst_sum_source_secondfoldnegative_body_steps_bound. fs_lt_dst_sum_source_secondfoldnegative_body_steps_bound + S fs_i_dst_sum_source_secondfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_source_secondfoldnegative_body_steps fs_r_dst_sum_source_secondfoldnegative_body_steps fs_s_dst_sum_source_secondfoldnegative_body_steps. ((((exists fs_h_dst_sum_source_secondfoldnegative_body_steps_summand. fs_h_dst_sum_source_secondfoldnegative_body_steps_summand + S (fs_a_dst_sum_source_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * dst_negative_scale_sum_source_secondfold)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_steps_summand. dst_negative_code_sum_source_secondfold = fs_q_dst_sum_source_secondfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * dst_negative_scale_sum_source_secondfold) + (fs_a_dst_sum_source_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldnegative_body_steps_partial. fs_h_dst_sum_source_secondfoldnegative_body_steps_partial + S (fs_r_dst_sum_source_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_steps_partial. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative) + (fs_r_dst_sum_source_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldnegative_body_steps_successor. fs_h_dst_sum_source_secondfoldnegative_body_steps_successor + S (fs_s_dst_sum_source_secondfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_steps_successor. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative) + (fs_s_dst_sum_source_secondfoldnegative_body_steps))) /\ fs_s_dst_sum_source_secondfoldnegative_body_steps = fs_r_dst_sum_source_secondfoldnegative_body_steps + fs_a_dst_sum_source_secondfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_source_secondfoldresult ge_balance_negative_sum_source_secondfoldresult. (((((b) = 2 * (ge_balance_positive_sum_source_secondfoldresult) /\ (ge_balance_negative_sum_source_secondfoldresult) = 0) \/ exists ge_signed_half_sum_source_secondfoldresultdecode. (((b) = 2 * ge_signed_half_sum_source_secondfoldresultdecode + 1 /\ (ge_balance_positive_sum_source_secondfoldresult) = 0) /\ (ge_balance_negative_sum_source_secondfoldresult) = S ge_signed_half_sum_source_secondfoldresultdecode))) /\ ((dst_positive_sum_sum_source_secondfold) + ge_balance_negative_sum_source_secondfoldresult = (dst_negative_sum_sum_source_secondfold) + ge_balance_positive_sum_source_secondfoldresult))))))))))))) -> a=b

add_comm

inherited alpha v30 · read exact theorem evidence

Bundle node 2; exact statement SHA-256 d0964c9be754ff543a32b916d0b2a1bc278f849ba40378004f32a397d83a168c

Exact first-order statement

forall n m. n + m = m + n

beta_prefix_extend

inherited alpha v30 · read exact theorem evidence

Bundle node 129; exact statement SHA-256 292c7a2a1abbf591e9a3cfd77ad0533f12761f691460fca7a20f413c6f66a1e0

Exact first-order statement

forall k b e s. exists z c. (((exists h. h + S s = S ((S k) * c)) /\ exists q. z = q * S ((S k) * c) + s) /\ forall i a. (exists h. h + S i = k) -> ((exists h. h + S a = S ((S i) * e)) /\ exists q. b = q * S ((S i) * e) + a) -> ((exists h. h + S a = S ((S i) * c)) /\ exists q. z = q * S ((S i) * c) + a))

divisor_signed_sum_empty_value

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 272; exact statement SHA-256 e8642c62a9360306119f85a4f994cd94861c3c685d27204f53ada36b6dd45bcd

Exact first-order statement

forall F z. (exists dst_positive_code_empty_sum dst_positive_scale_empty_sum dst_negative_code_empty_sum dst_negative_scale_empty_sum dst_positive_sum_empty_sum dst_negative_sum_empty_sum. (((F) = (((((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) * S ((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) + ((dst_positive_scale_empty_sum) + (dst_positive_scale_empty_sum))) + (((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum)))) * S ((((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) * S ((dst_positive_code_empty_sum) + (dst_positive_scale_empty_sum)) + ((dst_positive_scale_empty_sum) + (dst_positive_scale_empty_sum))) + (((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum)))) + ((((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum))) + (((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) * S ((dst_negative_code_empty_sum) + (dst_negative_scale_empty_sum)) + ((dst_negative_scale_empty_sum) + (dst_negative_scale_empty_sum)))))) /\ (((exists fs_u_dst_empty_sumpositive fs_v_dst_empty_sumpositive. ((((exists fs_h_dst_empty_sumpositive_body_start. fs_h_dst_empty_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_start. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_start * S ((S (0)) * fs_v_dst_empty_sumpositive) + (0))) /\ ((((exists fs_h_dst_empty_sumpositive_body_terminal. fs_h_dst_empty_sumpositive_body_terminal + S (dst_positive_sum_empty_sum) = S ((S (0)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_terminal. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_terminal * S ((S (0)) * fs_v_dst_empty_sumpositive) + (dst_positive_sum_empty_sum))) /\ forall fs_i_dst_empty_sumpositive_body_steps. (exists fs_lt_dst_empty_sumpositive_body_steps_bound. fs_lt_dst_empty_sumpositive_body_steps_bound + S fs_i_dst_empty_sumpositive_body_steps = 0) -> exists fs_a_dst_empty_sumpositive_body_steps fs_r_dst_empty_sumpositive_body_steps fs_s_dst_empty_sumpositive_body_steps. ((((exists fs_h_dst_empty_sumpositive_body_steps_summand. fs_h_dst_empty_sumpositive_body_steps_summand + S (fs_a_dst_empty_sumpositive_body_steps) = S ((S (fs_i_dst_empty_sumpositive_body_steps)) * dst_positive_scale_empty_sum)) /\ exists fs_q_dst_empty_sumpositive_body_steps_summand. dst_positive_code_empty_sum = fs_q_dst_empty_sumpositive_body_steps_summand * S ((S (fs_i_dst_empty_sumpositive_body_steps)) * dst_positive_scale_empty_sum) + (fs_a_dst_empty_sumpositive_body_steps))) /\ ((((exists fs_h_dst_empty_sumpositive_body_steps_partial. fs_h_dst_empty_sumpositive_body_steps_partial + S (fs_r_dst_empty_sumpositive_body_steps) = S ((S (fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_steps_partial. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_steps_partial * S ((S (fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive) + (fs_r_dst_empty_sumpositive_body_steps))) /\ ((((exists fs_h_dst_empty_sumpositive_body_steps_successor. fs_h_dst_empty_sumpositive_body_steps_successor + S (fs_s_dst_empty_sumpositive_body_steps) = S ((S (S fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive)) /\ exists fs_q_dst_empty_sumpositive_body_steps_successor. fs_u_dst_empty_sumpositive = fs_q_dst_empty_sumpositive_body_steps_successor * S ((S (S fs_i_dst_empty_sumpositive_body_steps)) * fs_v_dst_empty_sumpositive) + (fs_s_dst_empty_sumpositive_body_steps))) /\ fs_s_dst_empty_sumpositive_body_steps = fs_r_dst_empty_sumpositive_body_steps + fs_a_dst_empty_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_empty_sumnegative fs_v_dst_empty_sumnegative. ((((exists fs_h_dst_empty_sumnegative_body_start. fs_h_dst_empty_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_start. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_start * S ((S (0)) * fs_v_dst_empty_sumnegative) + (0))) /\ ((((exists fs_h_dst_empty_sumnegative_body_terminal. fs_h_dst_empty_sumnegative_body_terminal + S (dst_negative_sum_empty_sum) = S ((S (0)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_terminal. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_terminal * S ((S (0)) * fs_v_dst_empty_sumnegative) + (dst_negative_sum_empty_sum))) /\ forall fs_i_dst_empty_sumnegative_body_steps. (exists fs_lt_dst_empty_sumnegative_body_steps_bound. fs_lt_dst_empty_sumnegative_body_steps_bound + S fs_i_dst_empty_sumnegative_body_steps = 0) -> exists fs_a_dst_empty_sumnegative_body_steps fs_r_dst_empty_sumnegative_body_steps fs_s_dst_empty_sumnegative_body_steps. ((((exists fs_h_dst_empty_sumnegative_body_steps_summand. fs_h_dst_empty_sumnegative_body_steps_summand + S (fs_a_dst_empty_sumnegative_body_steps) = S ((S (fs_i_dst_empty_sumnegative_body_steps)) * dst_negative_scale_empty_sum)) /\ exists fs_q_dst_empty_sumnegative_body_steps_summand. dst_negative_code_empty_sum = fs_q_dst_empty_sumnegative_body_steps_summand * S ((S (fs_i_dst_empty_sumnegative_body_steps)) * dst_negative_scale_empty_sum) + (fs_a_dst_empty_sumnegative_body_steps))) /\ ((((exists fs_h_dst_empty_sumnegative_body_steps_partial. fs_h_dst_empty_sumnegative_body_steps_partial + S (fs_r_dst_empty_sumnegative_body_steps) = S ((S (fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_steps_partial. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_steps_partial * S ((S (fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative) + (fs_r_dst_empty_sumnegative_body_steps))) /\ ((((exists fs_h_dst_empty_sumnegative_body_steps_successor. fs_h_dst_empty_sumnegative_body_steps_successor + S (fs_s_dst_empty_sumnegative_body_steps) = S ((S (S fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative)) /\ exists fs_q_dst_empty_sumnegative_body_steps_successor. fs_u_dst_empty_sumnegative = fs_q_dst_empty_sumnegative_body_steps_successor * S ((S (S fs_i_dst_empty_sumnegative_body_steps)) * fs_v_dst_empty_sumnegative) + (fs_s_dst_empty_sumnegative_body_steps))) /\ fs_s_dst_empty_sumnegative_body_steps = fs_r_dst_empty_sumnegative_body_steps + fs_a_dst_empty_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_empty_sumresult ge_balance_negative_empty_sumresult. (((((z) = 2 * (ge_balance_positive_empty_sumresult) /\ (ge_balance_negative_empty_sumresult) = 0) \/ exists ge_signed_half_empty_sumresultdecode. (((z) = 2 * ge_signed_half_empty_sumresultdecode + 1 /\ (ge_balance_positive_empty_sumresult) = 0) /\ (ge_balance_negative_empty_sumresult) = S ge_signed_half_empty_sumresultdecode))) /\ ((dst_positive_sum_empty_sum) + ge_balance_negative_empty_sumresult = (dst_negative_sum_empty_sum) + ge_balance_positive_empty_sumresult))))))))) -> z = 0

divisor_signed_sum_exists_from_components

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 271; exact statement SHA-256 dc8a67265f62df88cc20398fae6101b8f7708646af331e0efbb077fb07fde474

Exact first-order statement

forall F pb pc nb nc l. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> exists z. (exists dst_positive_code_sum_exists_result dst_positive_scale_sum_exists_result dst_negative_code_sum_exists_result dst_negative_scale_sum_exists_result dst_positive_sum_sum_exists_result dst_negative_sum_sum_exists_result. (((F) = (((((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) * S ((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) + ((dst_positive_scale_sum_exists_result) + (dst_positive_scale_sum_exists_result))) + (((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result)))) * S ((((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) * S ((dst_positive_code_sum_exists_result) + (dst_positive_scale_sum_exists_result)) + ((dst_positive_scale_sum_exists_result) + (dst_positive_scale_sum_exists_result))) + (((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result)))) + ((((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result))) + (((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) * S ((dst_negative_code_sum_exists_result) + (dst_negative_scale_sum_exists_result)) + ((dst_negative_scale_sum_exists_result) + (dst_negative_scale_sum_exists_result)))))) /\ (((exists fs_u_dst_sum_exists_resultpositive fs_v_dst_sum_exists_resultpositive. ((((exists fs_h_dst_sum_exists_resultpositive_body_start. fs_h_dst_sum_exists_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_start. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_start * S ((S (0)) * fs_v_dst_sum_exists_resultpositive) + (0))) /\ ((((exists fs_h_dst_sum_exists_resultpositive_body_terminal. fs_h_dst_sum_exists_resultpositive_body_terminal + S (dst_positive_sum_sum_exists_result) = S ((S (l)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_terminal. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_resultpositive) + (dst_positive_sum_sum_exists_result))) /\ forall fs_i_dst_sum_exists_resultpositive_body_steps. (exists fs_lt_dst_sum_exists_resultpositive_body_steps_bound. fs_lt_dst_sum_exists_resultpositive_body_steps_bound + S fs_i_dst_sum_exists_resultpositive_body_steps = l) -> exists fs_a_dst_sum_exists_resultpositive_body_steps fs_r_dst_sum_exists_resultpositive_body_steps fs_s_dst_sum_exists_resultpositive_body_steps. ((((exists fs_h_dst_sum_exists_resultpositive_body_steps_summand. fs_h_dst_sum_exists_resultpositive_body_steps_summand + S (fs_a_dst_sum_exists_resultpositive_body_steps) = S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * dst_positive_scale_sum_exists_result)) /\ exists fs_q_dst_sum_exists_resultpositive_body_steps_summand. dst_positive_code_sum_exists_result = fs_q_dst_sum_exists_resultpositive_body_steps_summand * S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * dst_positive_scale_sum_exists_result) + (fs_a_dst_sum_exists_resultpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultpositive_body_steps_partial. fs_h_dst_sum_exists_resultpositive_body_steps_partial + S (fs_r_dst_sum_exists_resultpositive_body_steps) = S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_steps_partial. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_steps_partial * S ((S (fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive) + (fs_r_dst_sum_exists_resultpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultpositive_body_steps_successor. fs_h_dst_sum_exists_resultpositive_body_steps_successor + S (fs_s_dst_sum_exists_resultpositive_body_steps) = S ((S (S fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive)) /\ exists fs_q_dst_sum_exists_resultpositive_body_steps_successor. fs_u_dst_sum_exists_resultpositive = fs_q_dst_sum_exists_resultpositive_body_steps_successor * S ((S (S fs_i_dst_sum_exists_resultpositive_body_steps)) * fs_v_dst_sum_exists_resultpositive) + (fs_s_dst_sum_exists_resultpositive_body_steps))) /\ fs_s_dst_sum_exists_resultpositive_body_steps = fs_r_dst_sum_exists_resultpositive_body_steps + fs_a_dst_sum_exists_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_exists_resultnegative fs_v_dst_sum_exists_resultnegative. ((((exists fs_h_dst_sum_exists_resultnegative_body_start. fs_h_dst_sum_exists_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_start. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_start * S ((S (0)) * fs_v_dst_sum_exists_resultnegative) + (0))) /\ ((((exists fs_h_dst_sum_exists_resultnegative_body_terminal. fs_h_dst_sum_exists_resultnegative_body_terminal + S (dst_negative_sum_sum_exists_result) = S ((S (l)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_terminal. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_resultnegative) + (dst_negative_sum_sum_exists_result))) /\ forall fs_i_dst_sum_exists_resultnegative_body_steps. (exists fs_lt_dst_sum_exists_resultnegative_body_steps_bound. fs_lt_dst_sum_exists_resultnegative_body_steps_bound + S fs_i_dst_sum_exists_resultnegative_body_steps = l) -> exists fs_a_dst_sum_exists_resultnegative_body_steps fs_r_dst_sum_exists_resultnegative_body_steps fs_s_dst_sum_exists_resultnegative_body_steps. ((((exists fs_h_dst_sum_exists_resultnegative_body_steps_summand. fs_h_dst_sum_exists_resultnegative_body_steps_summand + S (fs_a_dst_sum_exists_resultnegative_body_steps) = S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * dst_negative_scale_sum_exists_result)) /\ exists fs_q_dst_sum_exists_resultnegative_body_steps_summand. dst_negative_code_sum_exists_result = fs_q_dst_sum_exists_resultnegative_body_steps_summand * S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * dst_negative_scale_sum_exists_result) + (fs_a_dst_sum_exists_resultnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultnegative_body_steps_partial. fs_h_dst_sum_exists_resultnegative_body_steps_partial + S (fs_r_dst_sum_exists_resultnegative_body_steps) = S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_steps_partial. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_steps_partial * S ((S (fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative) + (fs_r_dst_sum_exists_resultnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_resultnegative_body_steps_successor. fs_h_dst_sum_exists_resultnegative_body_steps_successor + S (fs_s_dst_sum_exists_resultnegative_body_steps) = S ((S (S fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative)) /\ exists fs_q_dst_sum_exists_resultnegative_body_steps_successor. fs_u_dst_sum_exists_resultnegative = fs_q_dst_sum_exists_resultnegative_body_steps_successor * S ((S (S fs_i_dst_sum_exists_resultnegative_body_steps)) * fs_v_dst_sum_exists_resultnegative) + (fs_s_dst_sum_exists_resultnegative_body_steps))) /\ fs_s_dst_sum_exists_resultnegative_body_steps = fs_r_dst_sum_exists_resultnegative_body_steps + fs_a_dst_sum_exists_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_exists_resultresult ge_balance_negative_sum_exists_resultresult. (((((z) = 2 * (ge_balance_positive_sum_exists_resultresult) /\ (ge_balance_negative_sum_exists_resultresult) = 0) \/ exists ge_signed_half_sum_exists_resultresultdecode. (((z) = 2 * ge_signed_half_sum_exists_resultresultdecode + 1 /\ (ge_balance_positive_sum_exists_resultresult) = 0) /\ (ge_balance_negative_sum_exists_resultresult) = S ge_signed_half_sum_exists_resultresultdecode))) /\ ((dst_positive_sum_sum_exists_result) + ge_balance_negative_sum_exists_resultresult = (dst_negative_sum_sum_exists_result) + ge_balance_positive_sum_exists_resultresult)))))))))

divisor_signed_sum_extensional

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 275; exact statement SHA-256 b5d76a97376567d4d2e34212f1172b134f14781a661d76925a3615f38065c348

Exact first-order statement

forall F G l a b. (forall dst_index_sum_ext_entries dst_first_sum_ext_entries dst_second_sum_ext_entries. (exists pvs_gap_sum_ext_entriesbound. pvs_gap_sum_ext_entriesbound + S (dst_index_sum_ext_entries) = (l)) -> (exists dst_positive_code_sum_ext_entriesfirst dst_positive_scale_sum_ext_entriesfirst dst_negative_code_sum_ext_entriesfirst dst_negative_scale_sum_ext_entriesfirst dst_positive_sum_ext_entriesfirst dst_negative_sum_ext_entriesfirst. (((F) = (((((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) * S ((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) + ((dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))) * S ((((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) * S ((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) + ((dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))) + ((((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))))) /\ (((((exists ff_h_pvs_sum_ext_entriesfirstpositive. ff_h_pvs_sum_ext_entriesfirstpositive + S (dst_positive_sum_ext_entriesfirst) = S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriesfirst)) /\ exists ff_q_pvs_sum_ext_entriesfirstpositive. dst_positive_code_sum_ext_entriesfirst = ff_q_pvs_sum_ext_entriesfirstpositive * S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_sum_ext_entriesfirst))) /\ (((((exists ff_h_pvs_sum_ext_entriesfirstnegative. ff_h_pvs_sum_ext_entriesfirstnegative + S (dst_negative_sum_ext_entriesfirst) = S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriesfirst)) /\ exists ff_q_pvs_sum_ext_entriesfirstnegative. dst_negative_code_sum_ext_entriesfirst = ff_q_pvs_sum_ext_entriesfirstnegative * S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_sum_ext_entriesfirst))) /\ (exists ge_balance_positive_sum_ext_entriesfirstvalue ge_balance_negative_sum_ext_entriesfirstvalue. (((((dst_first_sum_ext_entries) = 2 * (ge_balance_positive_sum_ext_entriesfirstvalue) /\ (ge_balance_negative_sum_ext_entriesfirstvalue) = 0) \/ exists ge_signed_half_sum_ext_entriesfirstvaluedecode. (((dst_first_sum_ext_entries) = 2 * ge_signed_half_sum_ext_entriesfirstvaluedecode + 1 /\ (ge_balance_positive_sum_ext_entriesfirstvalue) = 0) /\ (ge_balance_negative_sum_ext_entriesfirstvalue) = S ge_signed_half_sum_ext_entriesfirstvaluedecode))) /\ ((dst_positive_sum_ext_entriesfirst) + ge_balance_negative_sum_ext_entriesfirstvalue = (dst_negative_sum_ext_entriesfirst) + ge_balance_positive_sum_ext_entriesfirstvalue))))))))) -> (exists dst_positive_code_sum_ext_entriessecond dst_positive_scale_sum_ext_entriessecond dst_negative_code_sum_ext_entriessecond dst_negative_scale_sum_ext_entriessecond dst_positive_sum_ext_entriessecond dst_negative_sum_ext_entriessecond. (((G) = (((((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) * S ((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) + ((dst_positive_scale_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))) * S ((((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) * S ((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) + ((dst_positive_scale_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))) + ((((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))))) /\ (((((exists ff_h_pvs_sum_ext_entriessecondpositive. ff_h_pvs_sum_ext_entriessecondpositive + S (dst_positive_sum_ext_entriessecond) = S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriessecond)) /\ exists ff_q_pvs_sum_ext_entriessecondpositive. dst_positive_code_sum_ext_entriessecond = ff_q_pvs_sum_ext_entriessecondpositive * S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriessecond) + (dst_positive_sum_ext_entriessecond))) /\ (((((exists ff_h_pvs_sum_ext_entriessecondnegative. ff_h_pvs_sum_ext_entriessecondnegative + S (dst_negative_sum_ext_entriessecond) = S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriessecond)) /\ exists ff_q_pvs_sum_ext_entriessecondnegative. dst_negative_code_sum_ext_entriessecond = ff_q_pvs_sum_ext_entriessecondnegative * S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriessecond) + (dst_negative_sum_ext_entriessecond))) /\ (exists ge_balance_positive_sum_ext_entriessecondvalue ge_balance_negative_sum_ext_entriessecondvalue. (((((dst_second_sum_ext_entries) = 2 * (ge_balance_positive_sum_ext_entriessecondvalue) /\ (ge_balance_negative_sum_ext_entriessecondvalue) = 0) \/ exists ge_signed_half_sum_ext_entriessecondvaluedecode. (((dst_second_sum_ext_entries) = 2 * ge_signed_half_sum_ext_entriessecondvaluedecode + 1 /\ (ge_balance_positive_sum_ext_entriessecondvalue) = 0) /\ (ge_balance_negative_sum_ext_entriessecondvalue) = S ge_signed_half_sum_ext_entriessecondvaluedecode))) /\ ((dst_positive_sum_ext_entriessecond) + ge_balance_negative_sum_ext_entriessecondvalue = (dst_negative_sum_ext_entriessecond) + ge_balance_positive_sum_ext_entriessecondvalue))))))))) -> dst_first_sum_ext_entries = dst_second_sum_ext_entries) -> (exists dst_positive_code_sum_ext_first dst_positive_scale_sum_ext_first dst_negative_code_sum_ext_first dst_negative_scale_sum_ext_first dst_positive_sum_sum_ext_first dst_negative_sum_sum_ext_first. (((F) = (((((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) * S ((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) + ((dst_positive_scale_sum_ext_first) + (dst_positive_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))) * S ((((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) * S ((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) + ((dst_positive_scale_sum_ext_first) + (dst_positive_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))) + ((((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))))) /\ (((exists fs_u_dst_sum_ext_firstpositive fs_v_dst_sum_ext_firstpositive. ((((exists fs_h_dst_sum_ext_firstpositive_body_start. fs_h_dst_sum_ext_firstpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_start. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_start * S ((S (0)) * fs_v_dst_sum_ext_firstpositive) + (0))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_terminal. fs_h_dst_sum_ext_firstpositive_body_terminal + S (dst_positive_sum_sum_ext_first) = S ((S (l)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_terminal. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_firstpositive) + (dst_positive_sum_sum_ext_first))) /\ forall fs_i_dst_sum_ext_firstpositive_body_steps. (exists fs_lt_dst_sum_ext_firstpositive_body_steps_bound. fs_lt_dst_sum_ext_firstpositive_body_steps_bound + S fs_i_dst_sum_ext_firstpositive_body_steps = l) -> exists fs_a_dst_sum_ext_firstpositive_body_steps fs_r_dst_sum_ext_firstpositive_body_steps fs_s_dst_sum_ext_firstpositive_body_steps. ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_summand. fs_h_dst_sum_ext_firstpositive_body_steps_summand + S (fs_a_dst_sum_ext_firstpositive_body_steps) = S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * dst_positive_scale_sum_ext_first)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_summand. dst_positive_code_sum_ext_first = fs_q_dst_sum_ext_firstpositive_body_steps_summand * S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * dst_positive_scale_sum_ext_first) + (fs_a_dst_sum_ext_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_partial. fs_h_dst_sum_ext_firstpositive_body_steps_partial + S (fs_r_dst_sum_ext_firstpositive_body_steps) = S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_partial. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_steps_partial * S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive) + (fs_r_dst_sum_ext_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_successor. fs_h_dst_sum_ext_firstpositive_body_steps_successor + S (fs_s_dst_sum_ext_firstpositive_body_steps) = S ((S (S fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_successor. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_steps_successor * S ((S (S fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive) + (fs_s_dst_sum_ext_firstpositive_body_steps))) /\ fs_s_dst_sum_ext_firstpositive_body_steps = fs_r_dst_sum_ext_firstpositive_body_steps + fs_a_dst_sum_ext_firstpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_ext_firstnegative fs_v_dst_sum_ext_firstnegative. ((((exists fs_h_dst_sum_ext_firstnegative_body_start. fs_h_dst_sum_ext_firstnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_start. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_start * S ((S (0)) * fs_v_dst_sum_ext_firstnegative) + (0))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_terminal. fs_h_dst_sum_ext_firstnegative_body_terminal + S (dst_negative_sum_sum_ext_first) = S ((S (l)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_terminal. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_firstnegative) + (dst_negative_sum_sum_ext_first))) /\ forall fs_i_dst_sum_ext_firstnegative_body_steps. (exists fs_lt_dst_sum_ext_firstnegative_body_steps_bound. fs_lt_dst_sum_ext_firstnegative_body_steps_bound + S fs_i_dst_sum_ext_firstnegative_body_steps = l) -> exists fs_a_dst_sum_ext_firstnegative_body_steps fs_r_dst_sum_ext_firstnegative_body_steps fs_s_dst_sum_ext_firstnegative_body_steps. ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_summand. fs_h_dst_sum_ext_firstnegative_body_steps_summand + S (fs_a_dst_sum_ext_firstnegative_body_steps) = S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * dst_negative_scale_sum_ext_first)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_summand. dst_negative_code_sum_ext_first = fs_q_dst_sum_ext_firstnegative_body_steps_summand * S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * dst_negative_scale_sum_ext_first) + (fs_a_dst_sum_ext_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_partial. fs_h_dst_sum_ext_firstnegative_body_steps_partial + S (fs_r_dst_sum_ext_firstnegative_body_steps) = S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_partial. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_steps_partial * S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative) + (fs_r_dst_sum_ext_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_successor. fs_h_dst_sum_ext_firstnegative_body_steps_successor + S (fs_s_dst_sum_ext_firstnegative_body_steps) = S ((S (S fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_successor. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_steps_successor * S ((S (S fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative) + (fs_s_dst_sum_ext_firstnegative_body_steps))) /\ fs_s_dst_sum_ext_firstnegative_body_steps = fs_r_dst_sum_ext_firstnegative_body_steps + fs_a_dst_sum_ext_firstnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_ext_firstresult ge_balance_negative_sum_ext_firstresult. (((((a) = 2 * (ge_balance_positive_sum_ext_firstresult) /\ (ge_balance_negative_sum_ext_firstresult) = 0) \/ exists ge_signed_half_sum_ext_firstresultdecode. (((a) = 2 * ge_signed_half_sum_ext_firstresultdecode + 1 /\ (ge_balance_positive_sum_ext_firstresult) = 0) /\ (ge_balance_negative_sum_ext_firstresult) = S ge_signed_half_sum_ext_firstresultdecode))) /\ ((dst_positive_sum_sum_ext_first) + ge_balance_negative_sum_ext_firstresult = (dst_negative_sum_sum_ext_first) + ge_balance_positive_sum_ext_firstresult))))))))) -> (exists dst_positive_code_sum_ext_second dst_positive_scale_sum_ext_second dst_negative_code_sum_ext_second dst_negative_scale_sum_ext_second dst_positive_sum_sum_ext_second dst_negative_sum_sum_ext_second. (((G) = (((((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) * S ((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) + ((dst_positive_scale_sum_ext_second) + (dst_positive_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))) * S ((((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) * S ((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) + ((dst_positive_scale_sum_ext_second) + (dst_positive_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))) + ((((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))))) /\ (((exists fs_u_dst_sum_ext_secondpositive fs_v_dst_sum_ext_secondpositive. ((((exists fs_h_dst_sum_ext_secondpositive_body_start. fs_h_dst_sum_ext_secondpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_start. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_start * S ((S (0)) * fs_v_dst_sum_ext_secondpositive) + (0))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_terminal. fs_h_dst_sum_ext_secondpositive_body_terminal + S (dst_positive_sum_sum_ext_second) = S ((S (l)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_terminal. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_secondpositive) + (dst_positive_sum_sum_ext_second))) /\ forall fs_i_dst_sum_ext_secondpositive_body_steps. (exists fs_lt_dst_sum_ext_secondpositive_body_steps_bound. fs_lt_dst_sum_ext_secondpositive_body_steps_bound + S fs_i_dst_sum_ext_secondpositive_body_steps = l) -> exists fs_a_dst_sum_ext_secondpositive_body_steps fs_r_dst_sum_ext_secondpositive_body_steps fs_s_dst_sum_ext_secondpositive_body_steps. ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_summand. fs_h_dst_sum_ext_secondpositive_body_steps_summand + S (fs_a_dst_sum_ext_secondpositive_body_steps) = S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * dst_positive_scale_sum_ext_second)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_summand. dst_positive_code_sum_ext_second = fs_q_dst_sum_ext_secondpositive_body_steps_summand * S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * dst_positive_scale_sum_ext_second) + (fs_a_dst_sum_ext_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_partial. fs_h_dst_sum_ext_secondpositive_body_steps_partial + S (fs_r_dst_sum_ext_secondpositive_body_steps) = S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_partial. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_steps_partial * S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive) + (fs_r_dst_sum_ext_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_successor. fs_h_dst_sum_ext_secondpositive_body_steps_successor + S (fs_s_dst_sum_ext_secondpositive_body_steps) = S ((S (S fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_successor. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_steps_successor * S ((S (S fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive) + (fs_s_dst_sum_ext_secondpositive_body_steps))) /\ fs_s_dst_sum_ext_secondpositive_body_steps = fs_r_dst_sum_ext_secondpositive_body_steps + fs_a_dst_sum_ext_secondpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_ext_secondnegative fs_v_dst_sum_ext_secondnegative. ((((exists fs_h_dst_sum_ext_secondnegative_body_start. fs_h_dst_sum_ext_secondnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_start. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_start * S ((S (0)) * fs_v_dst_sum_ext_secondnegative) + (0))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_terminal. fs_h_dst_sum_ext_secondnegative_body_terminal + S (dst_negative_sum_sum_ext_second) = S ((S (l)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_terminal. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_secondnegative) + (dst_negative_sum_sum_ext_second))) /\ forall fs_i_dst_sum_ext_secondnegative_body_steps. (exists fs_lt_dst_sum_ext_secondnegative_body_steps_bound. fs_lt_dst_sum_ext_secondnegative_body_steps_bound + S fs_i_dst_sum_ext_secondnegative_body_steps = l) -> exists fs_a_dst_sum_ext_secondnegative_body_steps fs_r_dst_sum_ext_secondnegative_body_steps fs_s_dst_sum_ext_secondnegative_body_steps. ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_summand. fs_h_dst_sum_ext_secondnegative_body_steps_summand + S (fs_a_dst_sum_ext_secondnegative_body_steps) = S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * dst_negative_scale_sum_ext_second)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_summand. dst_negative_code_sum_ext_second = fs_q_dst_sum_ext_secondnegative_body_steps_summand * S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * dst_negative_scale_sum_ext_second) + (fs_a_dst_sum_ext_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_partial. fs_h_dst_sum_ext_secondnegative_body_steps_partial + S (fs_r_dst_sum_ext_secondnegative_body_steps) = S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_partial. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_steps_partial * S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative) + (fs_r_dst_sum_ext_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_successor. fs_h_dst_sum_ext_secondnegative_body_steps_successor + S (fs_s_dst_sum_ext_secondnegative_body_steps) = S ((S (S fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_successor. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_steps_successor * S ((S (S fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative) + (fs_s_dst_sum_ext_secondnegative_body_steps))) /\ fs_s_dst_sum_ext_secondnegative_body_steps = fs_r_dst_sum_ext_secondnegative_body_steps + fs_a_dst_sum_ext_secondnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_ext_secondresult ge_balance_negative_sum_ext_secondresult. (((((b) = 2 * (ge_balance_positive_sum_ext_secondresult) /\ (ge_balance_negative_sum_ext_secondresult) = 0) \/ exists ge_signed_half_sum_ext_secondresultdecode. (((b) = 2 * ge_signed_half_sum_ext_secondresultdecode + 1 /\ (ge_balance_positive_sum_ext_secondresult) = 0) /\ (ge_balance_negative_sum_ext_secondresult) = S ge_signed_half_sum_ext_secondresultdecode))) /\ ((dst_positive_sum_sum_ext_second) + ge_balance_negative_sum_ext_secondresult = (dst_negative_sum_sum_ext_second) + ge_balance_positive_sum_ext_secondresult))))))))) -> a = b

divisor_signed_sum_successor_intro

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 276; exact statement SHA-256 67f6acbf8ddd9dc6d4963b7ee11403c734e768abd48aad9d04dbd11d69c4b5c5

Exact first-order statement

forall F l a b c. (exists dst_positive_code_step_sum dst_positive_scale_step_sum dst_negative_code_step_sum dst_negative_scale_step_sum dst_positive_sum_step_sum dst_negative_sum_step_sum. (((F) = (((((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) * S ((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) + ((dst_positive_scale_step_sum) + (dst_positive_scale_step_sum))) + (((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum)))) * S ((((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) * S ((dst_positive_code_step_sum) + (dst_positive_scale_step_sum)) + ((dst_positive_scale_step_sum) + (dst_positive_scale_step_sum))) + (((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum)))) + ((((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum))) + (((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) * S ((dst_negative_code_step_sum) + (dst_negative_scale_step_sum)) + ((dst_negative_scale_step_sum) + (dst_negative_scale_step_sum)))))) /\ (((exists fs_u_dst_step_sumpositive fs_v_dst_step_sumpositive. ((((exists fs_h_dst_step_sumpositive_body_start. fs_h_dst_step_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_start. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_start * S ((S (0)) * fs_v_dst_step_sumpositive) + (0))) /\ ((((exists fs_h_dst_step_sumpositive_body_terminal. fs_h_dst_step_sumpositive_body_terminal + S (dst_positive_sum_step_sum) = S ((S (l)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_terminal. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_step_sumpositive) + (dst_positive_sum_step_sum))) /\ forall fs_i_dst_step_sumpositive_body_steps. (exists fs_lt_dst_step_sumpositive_body_steps_bound. fs_lt_dst_step_sumpositive_body_steps_bound + S fs_i_dst_step_sumpositive_body_steps = l) -> exists fs_a_dst_step_sumpositive_body_steps fs_r_dst_step_sumpositive_body_steps fs_s_dst_step_sumpositive_body_steps. ((((exists fs_h_dst_step_sumpositive_body_steps_summand. fs_h_dst_step_sumpositive_body_steps_summand + S (fs_a_dst_step_sumpositive_body_steps) = S ((S (fs_i_dst_step_sumpositive_body_steps)) * dst_positive_scale_step_sum)) /\ exists fs_q_dst_step_sumpositive_body_steps_summand. dst_positive_code_step_sum = fs_q_dst_step_sumpositive_body_steps_summand * S ((S (fs_i_dst_step_sumpositive_body_steps)) * dst_positive_scale_step_sum) + (fs_a_dst_step_sumpositive_body_steps))) /\ ((((exists fs_h_dst_step_sumpositive_body_steps_partial. fs_h_dst_step_sumpositive_body_steps_partial + S (fs_r_dst_step_sumpositive_body_steps) = S ((S (fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_steps_partial. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_steps_partial * S ((S (fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive) + (fs_r_dst_step_sumpositive_body_steps))) /\ ((((exists fs_h_dst_step_sumpositive_body_steps_successor. fs_h_dst_step_sumpositive_body_steps_successor + S (fs_s_dst_step_sumpositive_body_steps) = S ((S (S fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive)) /\ exists fs_q_dst_step_sumpositive_body_steps_successor. fs_u_dst_step_sumpositive = fs_q_dst_step_sumpositive_body_steps_successor * S ((S (S fs_i_dst_step_sumpositive_body_steps)) * fs_v_dst_step_sumpositive) + (fs_s_dst_step_sumpositive_body_steps))) /\ fs_s_dst_step_sumpositive_body_steps = fs_r_dst_step_sumpositive_body_steps + fs_a_dst_step_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_step_sumnegative fs_v_dst_step_sumnegative. ((((exists fs_h_dst_step_sumnegative_body_start. fs_h_dst_step_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_start. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_start * S ((S (0)) * fs_v_dst_step_sumnegative) + (0))) /\ ((((exists fs_h_dst_step_sumnegative_body_terminal. fs_h_dst_step_sumnegative_body_terminal + S (dst_negative_sum_step_sum) = S ((S (l)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_terminal. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_step_sumnegative) + (dst_negative_sum_step_sum))) /\ forall fs_i_dst_step_sumnegative_body_steps. (exists fs_lt_dst_step_sumnegative_body_steps_bound. fs_lt_dst_step_sumnegative_body_steps_bound + S fs_i_dst_step_sumnegative_body_steps = l) -> exists fs_a_dst_step_sumnegative_body_steps fs_r_dst_step_sumnegative_body_steps fs_s_dst_step_sumnegative_body_steps. ((((exists fs_h_dst_step_sumnegative_body_steps_summand. fs_h_dst_step_sumnegative_body_steps_summand + S (fs_a_dst_step_sumnegative_body_steps) = S ((S (fs_i_dst_step_sumnegative_body_steps)) * dst_negative_scale_step_sum)) /\ exists fs_q_dst_step_sumnegative_body_steps_summand. dst_negative_code_step_sum = fs_q_dst_step_sumnegative_body_steps_summand * S ((S (fs_i_dst_step_sumnegative_body_steps)) * dst_negative_scale_step_sum) + (fs_a_dst_step_sumnegative_body_steps))) /\ ((((exists fs_h_dst_step_sumnegative_body_steps_partial. fs_h_dst_step_sumnegative_body_steps_partial + S (fs_r_dst_step_sumnegative_body_steps) = S ((S (fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_steps_partial. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_steps_partial * S ((S (fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative) + (fs_r_dst_step_sumnegative_body_steps))) /\ ((((exists fs_h_dst_step_sumnegative_body_steps_successor. fs_h_dst_step_sumnegative_body_steps_successor + S (fs_s_dst_step_sumnegative_body_steps) = S ((S (S fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative)) /\ exists fs_q_dst_step_sumnegative_body_steps_successor. fs_u_dst_step_sumnegative = fs_q_dst_step_sumnegative_body_steps_successor * S ((S (S fs_i_dst_step_sumnegative_body_steps)) * fs_v_dst_step_sumnegative) + (fs_s_dst_step_sumnegative_body_steps))) /\ fs_s_dst_step_sumnegative_body_steps = fs_r_dst_step_sumnegative_body_steps + fs_a_dst_step_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_step_sumresult ge_balance_negative_step_sumresult. (((((a) = 2 * (ge_balance_positive_step_sumresult) /\ (ge_balance_negative_step_sumresult) = 0) \/ exists ge_signed_half_step_sumresultdecode. (((a) = 2 * ge_signed_half_step_sumresultdecode + 1 /\ (ge_balance_positive_step_sumresult) = 0) /\ (ge_balance_negative_step_sumresult) = S ge_signed_half_step_sumresultdecode))) /\ ((dst_positive_sum_step_sum) + ge_balance_negative_step_sumresult = (dst_negative_sum_step_sum) + ge_balance_positive_step_sumresult))))))))) -> (exists dst_positive_code_step_entry dst_positive_scale_step_entry dst_negative_code_step_entry dst_negative_scale_step_entry dst_positive_step_entry dst_negative_step_entry. (((F) = (((((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) * S ((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) + ((dst_positive_scale_step_entry) + (dst_positive_scale_step_entry))) + (((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry)))) * S ((((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) * S ((dst_positive_code_step_entry) + (dst_positive_scale_step_entry)) + ((dst_positive_scale_step_entry) + (dst_positive_scale_step_entry))) + (((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry)))) + ((((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry))) + (((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) * S ((dst_negative_code_step_entry) + (dst_negative_scale_step_entry)) + ((dst_negative_scale_step_entry) + (dst_negative_scale_step_entry)))))) /\ (((((exists ff_h_pvs_step_entrypositive. ff_h_pvs_step_entrypositive + S (dst_positive_step_entry) = S ((S (l)) * dst_positive_scale_step_entry)) /\ exists ff_q_pvs_step_entrypositive. dst_positive_code_step_entry = ff_q_pvs_step_entrypositive * S ((S (l)) * dst_positive_scale_step_entry) + (dst_positive_step_entry))) /\ (((((exists ff_h_pvs_step_entrynegative. ff_h_pvs_step_entrynegative + S (dst_negative_step_entry) = S ((S (l)) * dst_negative_scale_step_entry)) /\ exists ff_q_pvs_step_entrynegative. dst_negative_code_step_entry = ff_q_pvs_step_entrynegative * S ((S (l)) * dst_negative_scale_step_entry) + (dst_negative_step_entry))) /\ (exists ge_balance_positive_step_entryvalue ge_balance_negative_step_entryvalue. (((((b) = 2 * (ge_balance_positive_step_entryvalue) /\ (ge_balance_negative_step_entryvalue) = 0) \/ exists ge_signed_half_step_entryvaluedecode. (((b) = 2 * ge_signed_half_step_entryvaluedecode + 1 /\ (ge_balance_positive_step_entryvalue) = 0) /\ (ge_balance_negative_step_entryvalue) = S ge_signed_half_step_entryvaluedecode))) /\ ((dst_positive_step_entry) + ge_balance_negative_step_entryvalue = (dst_negative_step_entry) + ge_balance_positive_step_entryvalue))))))))) -> (exists dsa_ap_step_add dsa_an_step_add dsa_bp_step_add dsa_bn_step_add dsa_cp_step_add dsa_cn_step_add. (((((a) = 2 * (dsa_ap_step_add) /\ (dsa_an_step_add) = 0) \/ exists ge_signed_half_step_addleft. (((a) = 2 * ge_signed_half_step_addleft + 1 /\ (dsa_ap_step_add) = 0) /\ (dsa_an_step_add) = S ge_signed_half_step_addleft))) /\ ((((((b) = 2 * (dsa_bp_step_add) /\ (dsa_bn_step_add) = 0) \/ exists ge_signed_half_step_addright. (((b) = 2 * ge_signed_half_step_addright + 1 /\ (dsa_bp_step_add) = 0) /\ (dsa_bn_step_add) = S ge_signed_half_step_addright))) /\ ((((((c) = 2 * (dsa_cp_step_add) /\ (dsa_cn_step_add) = 0) \/ exists ge_signed_half_step_addoutput. (((c) = 2 * ge_signed_half_step_addoutput + 1 /\ (dsa_cp_step_add) = 0) /\ (dsa_cn_step_add) = S ge_signed_half_step_addoutput))) /\ ((dsa_ap_step_add + dsa_bp_step_add) + dsa_cn_step_add = (dsa_an_step_add + dsa_bn_step_add) + dsa_cp_step_add))))))) -> (exists dst_positive_code_step_result dst_positive_scale_step_result dst_negative_code_step_result dst_negative_scale_step_result dst_positive_sum_step_result dst_negative_sum_step_result. (((F) = (((((dst_positive_code_step_result) + (dst_positive_scale_step_result)) * S ((dst_positive_code_step_result) + (dst_positive_scale_step_result)) + ((dst_positive_scale_step_result) + (dst_positive_scale_step_result))) + (((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result)))) * S ((((dst_positive_code_step_result) + (dst_positive_scale_step_result)) * S ((dst_positive_code_step_result) + (dst_positive_scale_step_result)) + ((dst_positive_scale_step_result) + (dst_positive_scale_step_result))) + (((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result)))) + ((((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result))) + (((dst_negative_code_step_result) + (dst_negative_scale_step_result)) * S ((dst_negative_code_step_result) + (dst_negative_scale_step_result)) + ((dst_negative_scale_step_result) + (dst_negative_scale_step_result)))))) /\ (((exists fs_u_dst_step_resultpositive fs_v_dst_step_resultpositive. ((((exists fs_h_dst_step_resultpositive_body_start. fs_h_dst_step_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_start. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_start * S ((S (0)) * fs_v_dst_step_resultpositive) + (0))) /\ ((((exists fs_h_dst_step_resultpositive_body_terminal. fs_h_dst_step_resultpositive_body_terminal + S (dst_positive_sum_step_result) = S ((S (S l)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_terminal. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_terminal * S ((S (S l)) * fs_v_dst_step_resultpositive) + (dst_positive_sum_step_result))) /\ forall fs_i_dst_step_resultpositive_body_steps. (exists fs_lt_dst_step_resultpositive_body_steps_bound. fs_lt_dst_step_resultpositive_body_steps_bound + S fs_i_dst_step_resultpositive_body_steps = S l) -> exists fs_a_dst_step_resultpositive_body_steps fs_r_dst_step_resultpositive_body_steps fs_s_dst_step_resultpositive_body_steps. ((((exists fs_h_dst_step_resultpositive_body_steps_summand. fs_h_dst_step_resultpositive_body_steps_summand + S (fs_a_dst_step_resultpositive_body_steps) = S ((S (fs_i_dst_step_resultpositive_body_steps)) * dst_positive_scale_step_result)) /\ exists fs_q_dst_step_resultpositive_body_steps_summand. dst_positive_code_step_result = fs_q_dst_step_resultpositive_body_steps_summand * S ((S (fs_i_dst_step_resultpositive_body_steps)) * dst_positive_scale_step_result) + (fs_a_dst_step_resultpositive_body_steps))) /\ ((((exists fs_h_dst_step_resultpositive_body_steps_partial. fs_h_dst_step_resultpositive_body_steps_partial + S (fs_r_dst_step_resultpositive_body_steps) = S ((S (fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_steps_partial. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_steps_partial * S ((S (fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive) + (fs_r_dst_step_resultpositive_body_steps))) /\ ((((exists fs_h_dst_step_resultpositive_body_steps_successor. fs_h_dst_step_resultpositive_body_steps_successor + S (fs_s_dst_step_resultpositive_body_steps) = S ((S (S fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive)) /\ exists fs_q_dst_step_resultpositive_body_steps_successor. fs_u_dst_step_resultpositive = fs_q_dst_step_resultpositive_body_steps_successor * S ((S (S fs_i_dst_step_resultpositive_body_steps)) * fs_v_dst_step_resultpositive) + (fs_s_dst_step_resultpositive_body_steps))) /\ fs_s_dst_step_resultpositive_body_steps = fs_r_dst_step_resultpositive_body_steps + fs_a_dst_step_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_step_resultnegative fs_v_dst_step_resultnegative. ((((exists fs_h_dst_step_resultnegative_body_start. fs_h_dst_step_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_start. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_start * S ((S (0)) * fs_v_dst_step_resultnegative) + (0))) /\ ((((exists fs_h_dst_step_resultnegative_body_terminal. fs_h_dst_step_resultnegative_body_terminal + S (dst_negative_sum_step_result) = S ((S (S l)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_terminal. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_terminal * S ((S (S l)) * fs_v_dst_step_resultnegative) + (dst_negative_sum_step_result))) /\ forall fs_i_dst_step_resultnegative_body_steps. (exists fs_lt_dst_step_resultnegative_body_steps_bound. fs_lt_dst_step_resultnegative_body_steps_bound + S fs_i_dst_step_resultnegative_body_steps = S l) -> exists fs_a_dst_step_resultnegative_body_steps fs_r_dst_step_resultnegative_body_steps fs_s_dst_step_resultnegative_body_steps. ((((exists fs_h_dst_step_resultnegative_body_steps_summand. fs_h_dst_step_resultnegative_body_steps_summand + S (fs_a_dst_step_resultnegative_body_steps) = S ((S (fs_i_dst_step_resultnegative_body_steps)) * dst_negative_scale_step_result)) /\ exists fs_q_dst_step_resultnegative_body_steps_summand. dst_negative_code_step_result = fs_q_dst_step_resultnegative_body_steps_summand * S ((S (fs_i_dst_step_resultnegative_body_steps)) * dst_negative_scale_step_result) + (fs_a_dst_step_resultnegative_body_steps))) /\ ((((exists fs_h_dst_step_resultnegative_body_steps_partial. fs_h_dst_step_resultnegative_body_steps_partial + S (fs_r_dst_step_resultnegative_body_steps) = S ((S (fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_steps_partial. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_steps_partial * S ((S (fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative) + (fs_r_dst_step_resultnegative_body_steps))) /\ ((((exists fs_h_dst_step_resultnegative_body_steps_successor. fs_h_dst_step_resultnegative_body_steps_successor + S (fs_s_dst_step_resultnegative_body_steps) = S ((S (S fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative)) /\ exists fs_q_dst_step_resultnegative_body_steps_successor. fs_u_dst_step_resultnegative = fs_q_dst_step_resultnegative_body_steps_successor * S ((S (S fs_i_dst_step_resultnegative_body_steps)) * fs_v_dst_step_resultnegative) + (fs_s_dst_step_resultnegative_body_steps))) /\ fs_s_dst_step_resultnegative_body_steps = fs_r_dst_step_resultnegative_body_steps + fs_a_dst_step_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_step_resultresult ge_balance_negative_step_resultresult. (((((c) = 2 * (ge_balance_positive_step_resultresult) /\ (ge_balance_negative_step_resultresult) = 0) \/ exists ge_signed_half_step_resultresultdecode. (((c) = 2 * ge_signed_half_step_resultresultdecode + 1 /\ (ge_balance_positive_step_resultresult) = 0) /\ (ge_balance_negative_step_resultresult) = S ge_signed_half_step_resultresultdecode))) /\ ((dst_positive_sum_step_result) + ge_balance_negative_step_resultresult = (dst_negative_sum_step_result) + ge_balance_positive_step_resultresult)))))))))

divisor_signed_table_at_from_components

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 263; exact statement SHA-256 6b292868fda937823a4dfc13fe3f5577a2f91913c3ff758e7ad9032e0af31ce3

Exact first-order statement

forall F pb pc nb nc i p n z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (((exists ff_h_pvs_entry_positive. ff_h_pvs_entry_positive + S (p) = S ((S (i)) * pc)) /\ exists ff_q_pvs_entry_positive. pb = ff_q_pvs_entry_positive * S ((S (i)) * pc) + (p))) -> (((exists ff_h_pvs_entry_negative. ff_h_pvs_entry_negative + S (n) = S ((S (i)) * nc)) /\ exists ff_q_pvs_entry_negative. nb = ff_q_pvs_entry_negative * S ((S (i)) * nc) + (n))) -> (exists ge_balance_positive_entry_balance ge_balance_negative_entry_balance. (((((z) = 2 * (ge_balance_positive_entry_balance) /\ (ge_balance_negative_entry_balance) = 0) \/ exists ge_signed_half_entry_balancedecode. (((z) = 2 * ge_signed_half_entry_balancedecode + 1 /\ (ge_balance_positive_entry_balance) = 0) /\ (ge_balance_negative_entry_balance) = S ge_signed_half_entry_balancedecode))) /\ ((p) + ge_balance_negative_entry_balance = (n) + ge_balance_positive_entry_balance))) -> (exists dst_positive_code_entry_result dst_positive_scale_entry_result dst_negative_code_entry_result dst_negative_scale_entry_result dst_positive_entry_result dst_negative_entry_result. (((F) = (((((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) * S ((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) + ((dst_positive_scale_entry_result) + (dst_positive_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))) * S ((((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) * S ((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) + ((dst_positive_scale_entry_result) + (dst_positive_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))) + ((((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))))) /\ (((((exists ff_h_pvs_entry_resultpositive. ff_h_pvs_entry_resultpositive + S (dst_positive_entry_result) = S ((S (i)) * dst_positive_scale_entry_result)) /\ exists ff_q_pvs_entry_resultpositive. dst_positive_code_entry_result = ff_q_pvs_entry_resultpositive * S ((S (i)) * dst_positive_scale_entry_result) + (dst_positive_entry_result))) /\ (((((exists ff_h_pvs_entry_resultnegative. ff_h_pvs_entry_resultnegative + S (dst_negative_entry_result) = S ((S (i)) * dst_negative_scale_entry_result)) /\ exists ff_q_pvs_entry_resultnegative. dst_negative_code_entry_result = ff_q_pvs_entry_resultnegative * S ((S (i)) * dst_negative_scale_entry_result) + (dst_negative_entry_result))) /\ (exists ge_balance_positive_entry_resultvalue ge_balance_negative_entry_resultvalue. (((((z) = 2 * (ge_balance_positive_entry_resultvalue) /\ (ge_balance_negative_entry_resultvalue) = 0) \/ exists ge_signed_half_entry_resultvaluedecode. (((z) = 2 * ge_signed_half_entry_resultvaluedecode + 1 /\ (ge_balance_positive_entry_resultvalue) = 0) /\ (ge_balance_negative_entry_resultvalue) = S ge_signed_half_entry_resultvaluedecode))) /\ ((dst_positive_entry_result) + ge_balance_negative_entry_resultvalue = (dst_negative_entry_result) + ge_balance_positive_entry_resultvalue)))))))))

divisor_signed_table_at_functional

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 268; exact statement SHA-256 c47babd7207da358b0bfd877418fabee735ca070824b94fcbfdd81eb07957575

Exact first-order statement

forall F i a b. (exists dst_positive_code_functional_first dst_positive_scale_functional_first dst_negative_code_functional_first dst_negative_scale_functional_first dst_positive_functional_first dst_negative_functional_first. (((F) = (((((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) * S ((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) + ((dst_positive_scale_functional_first) + (dst_positive_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))) * S ((((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) * S ((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) + ((dst_positive_scale_functional_first) + (dst_positive_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))) + ((((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))))) /\ (((((exists ff_h_pvs_functional_firstpositive. ff_h_pvs_functional_firstpositive + S (dst_positive_functional_first) = S ((S (i)) * dst_positive_scale_functional_first)) /\ exists ff_q_pvs_functional_firstpositive. dst_positive_code_functional_first = ff_q_pvs_functional_firstpositive * S ((S (i)) * dst_positive_scale_functional_first) + (dst_positive_functional_first))) /\ (((((exists ff_h_pvs_functional_firstnegative. ff_h_pvs_functional_firstnegative + S (dst_negative_functional_first) = S ((S (i)) * dst_negative_scale_functional_first)) /\ exists ff_q_pvs_functional_firstnegative. dst_negative_code_functional_first = ff_q_pvs_functional_firstnegative * S ((S (i)) * dst_negative_scale_functional_first) + (dst_negative_functional_first))) /\ (exists ge_balance_positive_functional_firstvalue ge_balance_negative_functional_firstvalue. (((((a) = 2 * (ge_balance_positive_functional_firstvalue) /\ (ge_balance_negative_functional_firstvalue) = 0) \/ exists ge_signed_half_functional_firstvaluedecode. (((a) = 2 * ge_signed_half_functional_firstvaluedecode + 1 /\ (ge_balance_positive_functional_firstvalue) = 0) /\ (ge_balance_negative_functional_firstvalue) = S ge_signed_half_functional_firstvaluedecode))) /\ ((dst_positive_functional_first) + ge_balance_negative_functional_firstvalue = (dst_negative_functional_first) + ge_balance_positive_functional_firstvalue))))))))) -> (exists dst_positive_code_functional_second dst_positive_scale_functional_second dst_negative_code_functional_second dst_negative_scale_functional_second dst_positive_functional_second dst_negative_functional_second. (((F) = (((((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) * S ((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) + ((dst_positive_scale_functional_second) + (dst_positive_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))) * S ((((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) * S ((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) + ((dst_positive_scale_functional_second) + (dst_positive_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))) + ((((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))))) /\ (((((exists ff_h_pvs_functional_secondpositive. ff_h_pvs_functional_secondpositive + S (dst_positive_functional_second) = S ((S (i)) * dst_positive_scale_functional_second)) /\ exists ff_q_pvs_functional_secondpositive. dst_positive_code_functional_second = ff_q_pvs_functional_secondpositive * S ((S (i)) * dst_positive_scale_functional_second) + (dst_positive_functional_second))) /\ (((((exists ff_h_pvs_functional_secondnegative. ff_h_pvs_functional_secondnegative + S (dst_negative_functional_second) = S ((S (i)) * dst_negative_scale_functional_second)) /\ exists ff_q_pvs_functional_secondnegative. dst_negative_code_functional_second = ff_q_pvs_functional_secondnegative * S ((S (i)) * dst_negative_scale_functional_second) + (dst_negative_functional_second))) /\ (exists ge_balance_positive_functional_secondvalue ge_balance_negative_functional_secondvalue. (((((b) = 2 * (ge_balance_positive_functional_secondvalue) /\ (ge_balance_negative_functional_secondvalue) = 0) \/ exists ge_signed_half_functional_secondvaluedecode. (((b) = 2 * ge_signed_half_functional_secondvaluedecode + 1 /\ (ge_balance_positive_functional_secondvalue) = 0) /\ (ge_balance_negative_functional_secondvalue) = S ge_signed_half_functional_secondvaluedecode))) /\ ((dst_positive_functional_second) + ge_balance_negative_functional_secondvalue = (dst_negative_functional_second) + ge_balance_positive_functional_secondvalue))))))))) -> a = b

divisor_signed_table_at_to_components

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 264; exact statement SHA-256 3b275347602b0aa7fa93ed2d78491dda483509d0d7de3147c8eb924c0ee89ab7

Exact first-order statement

forall F pb pc nb nc i z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_unpack_entry dst_positive_scale_unpack_entry dst_negative_code_unpack_entry dst_negative_scale_unpack_entry dst_positive_unpack_entry dst_negative_unpack_entry. (((F) = (((((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) * S ((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) + ((dst_positive_scale_unpack_entry) + (dst_positive_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))) * S ((((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) * S ((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) + ((dst_positive_scale_unpack_entry) + (dst_positive_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))) + ((((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))))) /\ (((((exists ff_h_pvs_unpack_entrypositive. ff_h_pvs_unpack_entrypositive + S (dst_positive_unpack_entry) = S ((S (i)) * dst_positive_scale_unpack_entry)) /\ exists ff_q_pvs_unpack_entrypositive. dst_positive_code_unpack_entry = ff_q_pvs_unpack_entrypositive * S ((S (i)) * dst_positive_scale_unpack_entry) + (dst_positive_unpack_entry))) /\ (((((exists ff_h_pvs_unpack_entrynegative. ff_h_pvs_unpack_entrynegative + S (dst_negative_unpack_entry) = S ((S (i)) * dst_negative_scale_unpack_entry)) /\ exists ff_q_pvs_unpack_entrynegative. dst_negative_code_unpack_entry = ff_q_pvs_unpack_entrynegative * S ((S (i)) * dst_negative_scale_unpack_entry) + (dst_negative_unpack_entry))) /\ (exists ge_balance_positive_unpack_entryvalue ge_balance_negative_unpack_entryvalue. (((((z) = 2 * (ge_balance_positive_unpack_entryvalue) /\ (ge_balance_negative_unpack_entryvalue) = 0) \/ exists ge_signed_half_unpack_entryvaluedecode. (((z) = 2 * ge_signed_half_unpack_entryvaluedecode + 1 /\ (ge_balance_positive_unpack_entryvalue) = 0) /\ (ge_balance_negative_unpack_entryvalue) = S ge_signed_half_unpack_entryvaluedecode))) /\ ((dst_positive_unpack_entry) + ge_balance_negative_unpack_entryvalue = (dst_negative_unpack_entry) + ge_balance_positive_unpack_entryvalue))))))))) -> exists p n. (((((exists ff_h_pvs_unpack_resultpositive. ff_h_pvs_unpack_resultpositive + S (p) = S ((S (i)) * pc)) /\ exists ff_q_pvs_unpack_resultpositive. pb = ff_q_pvs_unpack_resultpositive * S ((S (i)) * pc) + (p))) /\ (((((exists ff_h_pvs_unpack_resultnegative. ff_h_pvs_unpack_resultnegative + S (n) = S ((S (i)) * nc)) /\ exists ff_q_pvs_unpack_resultnegative. nb = ff_q_pvs_unpack_resultnegative * S ((S (i)) * nc) + (n))) /\ (exists ge_balance_positive_unpack_resultvalue ge_balance_negative_unpack_resultvalue. (((((z) = 2 * (ge_balance_positive_unpack_resultvalue) /\ (ge_balance_negative_unpack_resultvalue) = 0) \/ exists ge_signed_half_unpack_resultvaluedecode. (((z) = 2 * ge_signed_half_unpack_resultvaluedecode + 1 /\ (ge_balance_positive_unpack_resultvalue) = 0) /\ (ge_balance_negative_unpack_resultvalue) = S ge_signed_half_unpack_resultvaluedecode))) /\ ((p) + ge_balance_negative_unpack_resultvalue = (n) + ge_balance_positive_unpack_resultvalue)))))))

divisor_signed_table_components

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 266; exact statement SHA-256 48ef6e47809edda57f20ad719e0cab9f9c6da9a366b156fe2f68f04d931a8142

Exact first-order statement

forall N F. (exists dst_positive_code_extract_table dst_positive_scale_extract_table dst_negative_code_extract_table dst_negative_scale_extract_table. (((F) = (((((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) * S ((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) + ((dst_positive_scale_extract_table) + (dst_positive_scale_extract_table))) + (((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table)))) * S ((((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) * S ((dst_positive_code_extract_table) + (dst_positive_scale_extract_table)) + ((dst_positive_scale_extract_table) + (dst_positive_scale_extract_table))) + (((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table)))) + ((((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table))) + (((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) * S ((dst_negative_code_extract_table) + (dst_negative_scale_extract_table)) + ((dst_negative_scale_extract_table) + (dst_negative_scale_extract_table)))))) /\ (forall dst_index_extract_table. (exists pvs_le_gap_extract_tabledomain. pvs_le_gap_extract_tabledomain + (dst_index_extract_table) = (N)) -> exists dst_positive_extract_table dst_negative_extract_table dst_value_extract_table. ((((exists ff_h_pvs_extract_tableentrypositive. ff_h_pvs_extract_tableentrypositive + S (dst_positive_extract_table) = S ((S (dst_index_extract_table)) * dst_positive_scale_extract_table)) /\ exists ff_q_pvs_extract_tableentrypositive. dst_positive_code_extract_table = ff_q_pvs_extract_tableentrypositive * S ((S (dst_index_extract_table)) * dst_positive_scale_extract_table) + (dst_positive_extract_table))) /\ (((((exists ff_h_pvs_extract_tableentrynegative. ff_h_pvs_extract_tableentrynegative + S (dst_negative_extract_table) = S ((S (dst_index_extract_table)) * dst_negative_scale_extract_table)) /\ exists ff_q_pvs_extract_tableentrynegative. dst_negative_code_extract_table = ff_q_pvs_extract_tableentrynegative * S ((S (dst_index_extract_table)) * dst_negative_scale_extract_table) + (dst_negative_extract_table))) /\ (exists ge_balance_positive_extract_tableentryvalue ge_balance_negative_extract_tableentryvalue. (((((dst_value_extract_table) = 2 * (ge_balance_positive_extract_tableentryvalue) /\ (ge_balance_negative_extract_tableentryvalue) = 0) \/ exists ge_signed_half_extract_tableentryvaluedecode. (((dst_value_extract_table) = 2 * ge_signed_half_extract_tableentryvaluedecode + 1 /\ (ge_balance_positive_extract_tableentryvalue) = 0) /\ (ge_balance_negative_extract_tableentryvalue) = S ge_signed_half_extract_tableentryvaluedecode))) /\ ((dst_positive_extract_table) + ge_balance_negative_extract_tableentryvalue = (dst_negative_extract_table) + ge_balance_positive_extract_tableentryvalue))))))))) -> exists pb pc nb nc. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))))))

divisor_signed_table_from_components

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 265; exact statement SHA-256 5fd017177babe11d163fc123d3f4e63c6e2f654c82c3f81765194d6e14cfd98d

Exact first-order statement

forall N F pb pc nb nc. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_constructor_table dst_positive_scale_constructor_table dst_negative_code_constructor_table dst_negative_scale_constructor_table. (((F) = (((((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) * S ((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) + ((dst_positive_scale_constructor_table) + (dst_positive_scale_constructor_table))) + (((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table)))) * S ((((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) * S ((dst_positive_code_constructor_table) + (dst_positive_scale_constructor_table)) + ((dst_positive_scale_constructor_table) + (dst_positive_scale_constructor_table))) + (((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table)))) + ((((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table))) + (((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) * S ((dst_negative_code_constructor_table) + (dst_negative_scale_constructor_table)) + ((dst_negative_scale_constructor_table) + (dst_negative_scale_constructor_table)))))) /\ (forall dst_index_constructor_table. (exists pvs_le_gap_constructor_tabledomain. pvs_le_gap_constructor_tabledomain + (dst_index_constructor_table) = (N)) -> exists dst_positive_constructor_table dst_negative_constructor_table dst_value_constructor_table. ((((exists ff_h_pvs_constructor_tableentrypositive. ff_h_pvs_constructor_tableentrypositive + S (dst_positive_constructor_table) = S ((S (dst_index_constructor_table)) * dst_positive_scale_constructor_table)) /\ exists ff_q_pvs_constructor_tableentrypositive. dst_positive_code_constructor_table = ff_q_pvs_constructor_tableentrypositive * S ((S (dst_index_constructor_table)) * dst_positive_scale_constructor_table) + (dst_positive_constructor_table))) /\ (((((exists ff_h_pvs_constructor_tableentrynegative. ff_h_pvs_constructor_tableentrynegative + S (dst_negative_constructor_table) = S ((S (dst_index_constructor_table)) * dst_negative_scale_constructor_table)) /\ exists ff_q_pvs_constructor_tableentrynegative. dst_negative_code_constructor_table = ff_q_pvs_constructor_tableentrynegative * S ((S (dst_index_constructor_table)) * dst_negative_scale_constructor_table) + (dst_negative_constructor_table))) /\ (exists ge_balance_positive_constructor_tableentryvalue ge_balance_negative_constructor_tableentryvalue. (((((dst_value_constructor_table) = 2 * (ge_balance_positive_constructor_tableentryvalue) /\ (ge_balance_negative_constructor_tableentryvalue) = 0) \/ exists ge_signed_half_constructor_tableentryvaluedecode. (((dst_value_constructor_table) = 2 * ge_signed_half_constructor_tableentryvaluedecode + 1 /\ (ge_balance_positive_constructor_tableentryvalue) = 0) /\ (ge_balance_negative_constructor_tableentryvalue) = S ge_signed_half_constructor_tableentryvaluedecode))) /\ ((dst_positive_constructor_table) + ge_balance_negative_constructor_tableentryvalue = (dst_negative_constructor_table) + ge_balance_positive_constructor_tableentryvalue)))))))))

divisor_signed_table_lookup

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 267; exact statement SHA-256 6cf135d9868dc10b2399e4768deccbcb2fc7ca1ae34e9c4258c3c8713b67feab

Exact first-order statement

forall N F i. (exists dst_positive_code_lookup_table dst_positive_scale_lookup_table dst_negative_code_lookup_table dst_negative_scale_lookup_table. (((F) = (((((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) * S ((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) + ((dst_positive_scale_lookup_table) + (dst_positive_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))) * S ((((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) * S ((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) + ((dst_positive_scale_lookup_table) + (dst_positive_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))) + ((((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))))) /\ (forall dst_index_lookup_table. (exists pvs_le_gap_lookup_tabledomain. pvs_le_gap_lookup_tabledomain + (dst_index_lookup_table) = (N)) -> exists dst_positive_lookup_table dst_negative_lookup_table dst_value_lookup_table. ((((exists ff_h_pvs_lookup_tableentrypositive. ff_h_pvs_lookup_tableentrypositive + S (dst_positive_lookup_table) = S ((S (dst_index_lookup_table)) * dst_positive_scale_lookup_table)) /\ exists ff_q_pvs_lookup_tableentrypositive. dst_positive_code_lookup_table = ff_q_pvs_lookup_tableentrypositive * S ((S (dst_index_lookup_table)) * dst_positive_scale_lookup_table) + (dst_positive_lookup_table))) /\ (((((exists ff_h_pvs_lookup_tableentrynegative. ff_h_pvs_lookup_tableentrynegative + S (dst_negative_lookup_table) = S ((S (dst_index_lookup_table)) * dst_negative_scale_lookup_table)) /\ exists ff_q_pvs_lookup_tableentrynegative. dst_negative_code_lookup_table = ff_q_pvs_lookup_tableentrynegative * S ((S (dst_index_lookup_table)) * dst_negative_scale_lookup_table) + (dst_negative_lookup_table))) /\ (exists ge_balance_positive_lookup_tableentryvalue ge_balance_negative_lookup_tableentryvalue. (((((dst_value_lookup_table) = 2 * (ge_balance_positive_lookup_tableentryvalue) /\ (ge_balance_negative_lookup_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_tableentryvaluedecode. (((dst_value_lookup_table) = 2 * ge_signed_half_lookup_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_tableentryvalue) = S ge_signed_half_lookup_tableentryvaluedecode))) /\ ((dst_positive_lookup_table) + ge_balance_negative_lookup_tableentryvalue = (dst_negative_lookup_table) + ge_balance_positive_lookup_tableentryvalue))))))))) -> (exists pvs_le_gap_lookup_domain. pvs_le_gap_lookup_domain + (i) = (N)) -> exists z. (exists dst_positive_code_lookup_result dst_positive_scale_lookup_result dst_negative_code_lookup_result dst_negative_scale_lookup_result dst_positive_lookup_result dst_negative_lookup_result. (((F) = (((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) * S ((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) + ((((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))))) /\ (((((exists ff_h_pvs_lookup_resultpositive. ff_h_pvs_lookup_resultpositive + S (dst_positive_lookup_result) = S ((S (i)) * dst_positive_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultpositive. dst_positive_code_lookup_result = ff_q_pvs_lookup_resultpositive * S ((S (i)) * dst_positive_scale_lookup_result) + (dst_positive_lookup_result))) /\ (((((exists ff_h_pvs_lookup_resultnegative. ff_h_pvs_lookup_resultnegative + S (dst_negative_lookup_result) = S ((S (i)) * dst_negative_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultnegative. dst_negative_code_lookup_result = ff_q_pvs_lookup_resultnegative * S ((S (i)) * dst_negative_scale_lookup_result) + (dst_negative_lookup_result))) /\ (exists ge_balance_positive_lookup_resultvalue ge_balance_negative_lookup_resultvalue. (((((z) = 2 * (ge_balance_positive_lookup_resultvalue) /\ (ge_balance_negative_lookup_resultvalue) = 0) \/ exists ge_signed_half_lookup_resultvaluedecode. (((z) = 2 * ge_signed_half_lookup_resultvaluedecode + 1 /\ (ge_balance_positive_lookup_resultvalue) = 0) /\ (ge_balance_negative_lookup_resultvalue) = S ge_signed_half_lookup_resultvaluedecode))) /\ ((dst_positive_lookup_result) + ge_balance_negative_lookup_resultvalue = (dst_negative_lookup_result) + ge_balance_positive_lookup_resultvalue)))))))))

divisor_signed_table_restrict

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 269; exact statement SHA-256 3e56a4039f59b96cf697e14e305740fdfe11d7f1667875630c1d79b09d2c54dc

Exact first-order statement

forall N K F. (exists dst_positive_code_restriction_source dst_positive_scale_restriction_source dst_negative_code_restriction_source dst_negative_scale_restriction_source. (((F) = (((((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) * S ((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) + ((dst_positive_scale_restriction_source) + (dst_positive_scale_restriction_source))) + (((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source)))) * S ((((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) * S ((dst_positive_code_restriction_source) + (dst_positive_scale_restriction_source)) + ((dst_positive_scale_restriction_source) + (dst_positive_scale_restriction_source))) + (((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source)))) + ((((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source))) + (((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) * S ((dst_negative_code_restriction_source) + (dst_negative_scale_restriction_source)) + ((dst_negative_scale_restriction_source) + (dst_negative_scale_restriction_source)))))) /\ (forall dst_index_restriction_source. (exists pvs_le_gap_restriction_sourcedomain. pvs_le_gap_restriction_sourcedomain + (dst_index_restriction_source) = (N)) -> exists dst_positive_restriction_source dst_negative_restriction_source dst_value_restriction_source. ((((exists ff_h_pvs_restriction_sourceentrypositive. ff_h_pvs_restriction_sourceentrypositive + S (dst_positive_restriction_source) = S ((S (dst_index_restriction_source)) * dst_positive_scale_restriction_source)) /\ exists ff_q_pvs_restriction_sourceentrypositive. dst_positive_code_restriction_source = ff_q_pvs_restriction_sourceentrypositive * S ((S (dst_index_restriction_source)) * dst_positive_scale_restriction_source) + (dst_positive_restriction_source))) /\ (((((exists ff_h_pvs_restriction_sourceentrynegative. ff_h_pvs_restriction_sourceentrynegative + S (dst_negative_restriction_source) = S ((S (dst_index_restriction_source)) * dst_negative_scale_restriction_source)) /\ exists ff_q_pvs_restriction_sourceentrynegative. dst_negative_code_restriction_source = ff_q_pvs_restriction_sourceentrynegative * S ((S (dst_index_restriction_source)) * dst_negative_scale_restriction_source) + (dst_negative_restriction_source))) /\ (exists ge_balance_positive_restriction_sourceentryvalue ge_balance_negative_restriction_sourceentryvalue. (((((dst_value_restriction_source) = 2 * (ge_balance_positive_restriction_sourceentryvalue) /\ (ge_balance_negative_restriction_sourceentryvalue) = 0) \/ exists ge_signed_half_restriction_sourceentryvaluedecode. (((dst_value_restriction_source) = 2 * ge_signed_half_restriction_sourceentryvaluedecode + 1 /\ (ge_balance_positive_restriction_sourceentryvalue) = 0) /\ (ge_balance_negative_restriction_sourceentryvalue) = S ge_signed_half_restriction_sourceentryvaluedecode))) /\ ((dst_positive_restriction_source) + ge_balance_negative_restriction_sourceentryvalue = (dst_negative_restriction_source) + ge_balance_positive_restriction_sourceentryvalue))))))))) -> (exists pvs_le_gap_restriction_bound. pvs_le_gap_restriction_bound + (K) = (N)) -> (exists dst_positive_code_restriction_target dst_positive_scale_restriction_target dst_negative_code_restriction_target dst_negative_scale_restriction_target. (((F) = (((((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) * S ((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) + ((dst_positive_scale_restriction_target) + (dst_positive_scale_restriction_target))) + (((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target)))) * S ((((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) * S ((dst_positive_code_restriction_target) + (dst_positive_scale_restriction_target)) + ((dst_positive_scale_restriction_target) + (dst_positive_scale_restriction_target))) + (((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target)))) + ((((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target))) + (((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) * S ((dst_negative_code_restriction_target) + (dst_negative_scale_restriction_target)) + ((dst_negative_scale_restriction_target) + (dst_negative_scale_restriction_target)))))) /\ (forall dst_index_restriction_target. (exists pvs_le_gap_restriction_targetdomain. pvs_le_gap_restriction_targetdomain + (dst_index_restriction_target) = (K)) -> exists dst_positive_restriction_target dst_negative_restriction_target dst_value_restriction_target. ((((exists ff_h_pvs_restriction_targetentrypositive. ff_h_pvs_restriction_targetentrypositive + S (dst_positive_restriction_target) = S ((S (dst_index_restriction_target)) * dst_positive_scale_restriction_target)) /\ exists ff_q_pvs_restriction_targetentrypositive. dst_positive_code_restriction_target = ff_q_pvs_restriction_targetentrypositive * S ((S (dst_index_restriction_target)) * dst_positive_scale_restriction_target) + (dst_positive_restriction_target))) /\ (((((exists ff_h_pvs_restriction_targetentrynegative. ff_h_pvs_restriction_targetentrynegative + S (dst_negative_restriction_target) = S ((S (dst_index_restriction_target)) * dst_negative_scale_restriction_target)) /\ exists ff_q_pvs_restriction_targetentrynegative. dst_negative_code_restriction_target = ff_q_pvs_restriction_targetentrynegative * S ((S (dst_index_restriction_target)) * dst_negative_scale_restriction_target) + (dst_negative_restriction_target))) /\ (exists ge_balance_positive_restriction_targetentryvalue ge_balance_negative_restriction_targetentryvalue. (((((dst_value_restriction_target) = 2 * (ge_balance_positive_restriction_targetentryvalue) /\ (ge_balance_negative_restriction_targetentryvalue) = 0) \/ exists ge_signed_half_restriction_targetentryvaluedecode. (((dst_value_restriction_target) = 2 * ge_signed_half_restriction_targetentryvaluedecode + 1 /\ (ge_balance_positive_restriction_targetentryvalue) = 0) /\ (ge_balance_negative_restriction_targetentryvalue) = S ge_signed_half_restriction_targetentryvaluedecode))) /\ ((dst_positive_restriction_target) + ge_balance_negative_restriction_targetentryvalue = (dst_negative_restriction_target) + ge_balance_positive_restriction_targetentryvalue)))))))))

eq_decidable

inherited alpha v30 · read exact theorem evidence

Bundle node 77; exact statement SHA-256 c13a817645afe596d7f55f88eb9400073ae742c17213dfbf907f4c497aa1aca1

Exact first-order statement

forall a b. a = b \/ ~(a = b)

le_eq_or_lt

inherited alpha v30 · read exact theorem evidence

Bundle node 38; exact statement SHA-256 c62d7d9dd2e202f7ef167c085afae1c16f5ee96d7d8269234b68249f5038f72a

Exact first-order statement

forall a b. (exists k. k + a = b) -> a = b \/ exists k. k + S a = b

le_of_succ_le_succ

inherited alpha v30 · read exact theorem evidence

Bundle node 34; exact statement SHA-256 bfa8be55903d6a037b942f30e28a0606ad55956d00b47532ab2c1cadb87d9a2a

Exact first-order statement

forall a b. (exists k. k + S a = S b) -> exists r. r + a = b

le_succ_self

inherited alpha v30 · read exact theorem evidence

Bundle node 26; exact statement SHA-256 60174e116dc1779726af5ab6335933bf94a1278b174352205c842e300e570651

Exact first-order statement

forall n. n <= S n

le_trans

inherited alpha v30 · read exact theorem evidence

Bundle node 14; exact statement SHA-256 9283783a3d2617190746cb05073cdf1f8a1b90c1a6bbdd640a26e28eb44b887d

Exact first-order statement

forall n m k. n <= m -> m <= k -> n <= k

le_zero

inherited alpha v30 · read exact theorem evidence

Bundle node 27; exact statement SHA-256 f9c4e4faa5263ab84d5c6221a21f22a3a581de21585d30f87fe8e24fcb81faef

Exact first-order statement

forall n. n <= 0 -> n = 0

mobius_one

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 262; exact statement SHA-256 7e25b6ee50f327823f711ec20cfbd25178b198c7210f11bc73f08441e73273e6

Exact first-order statement

((~((1) = 0)) /\ ((((exists mv_square_prime_one_valuesquare. ((~((mv_square_prime_one_valuesquare) = 1) /\ forall pvs_left_one_valuesquareprime pvs_right_one_valuesquareprime. (mv_square_prime_one_valuesquare) = pvs_left_one_valuesquareprime * pvs_right_one_valuesquareprime -> pvs_left_one_valuesquareprime = 1 \/ pvs_right_one_valuesquareprime = 1) /\ (exists pvs_factor_one_valuesquaredivisor. (1) = (mv_square_prime_one_valuesquare * mv_square_prime_one_valuesquare) * pvs_factor_one_valuesquaredivisor))) /\ ((2) = 0))) \/ (((((~((1) = 0)) /\ (forall sfd_prime_one_valuesquarefree. (~((sfd_prime_one_valuesquarefree) = 1) /\ forall pvs_left_one_valuesquarefreedomain pvs_right_one_valuesquarefreedomain. (sfd_prime_one_valuesquarefree) = pvs_left_one_valuesquarefreedomain * pvs_right_one_valuesquarefreedomain -> pvs_left_one_valuesquarefreedomain = 1 \/ pvs_right_one_valuesquarefreedomain = 1) -> (exists pvs_le_gap_one_valuesquarefreebound. pvs_le_gap_one_valuesquarefreebound + (sfd_prime_one_valuesquarefree) = (1)) -> ~(exists pvs_factor_one_valuesquarefreesquare. (1) = (sfd_prime_one_valuesquarefree * sfd_prime_one_valuesquarefree) * pvs_factor_one_valuesquarefreesquare)))) /\ (exists mv_factor_code_one_valuefactors mv_factor_scale_one_valuefactors mv_factor_count_one_valuefactors. (((~(1 = 0) /\ ((exists ff_u_fsat_one_valuefactorsfactorization_product ff_v_fsat_one_valuefactorsfactorization_product. ((((exists ff_h_fsat_one_valuefactorsfactorization_product_start. ff_h_fsat_one_valuefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_one_valuefactorsfactorization_product)) /\ exists ff_q_fsat_one_valuefactorsfactorization_product_start. ff_u_fsat_one_valuefactorsfactorization_product = ff_q_fsat_one_valuefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_one_valuefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_one_valuefactorsfactorization_product_terminal. ff_h_fsat_one_valuefactorsfactorization_product_terminal + S (1) = S ((S (mv_factor_count_one_valuefactors)) * ff_v_fsat_one_valuefactorsfactorization_product)) /\ exists ff_q_fsat_one_valuefactorsfactorization_product_terminal. ff_u_fsat_one_valuefactorsfactorization_product = ff_q_fsat_one_valuefactorsfactorization_product_terminal * S ((S (mv_factor_count_one_valuefactors)) * ff_v_fsat_one_valuefactorsfactorization_product) + (1))) /\ forall ff_i_fsat_one_valuefactorsfactorization_product. (exists ff_lt_fsat_one_valuefactorsfactorization_product_bound. ff_lt_fsat_one_valuefactorsfactorization_product_bound + S ff_i_fsat_one_valuefactorsfactorization_product = mv_factor_count_one_valuefactors) -> exists ff_p_fsat_one_valuefactorsfactorization_product ff_r_fsat_one_valuefactorsfactorization_product ff_s_fsat_one_valuefactorsfactorization_product. ((((exists ff_h_fsat_one_valuefactorsfactorization_product_factor. ff_h_fsat_one_valuefactorsfactorization_product_factor + S (ff_p_fsat_one_valuefactorsfactorization_product) = S ((S (ff_i_fsat_one_valuefactorsfactorization_product)) * mv_factor_scale_one_valuefactors)) /\ exists ff_q_fsat_one_valuefactorsfactorization_product_factor. mv_factor_code_one_valuefactors = ff_q_fsat_one_valuefactorsfactorization_product_factor * S ((S (ff_i_fsat_one_valuefactorsfactorization_product)) * mv_factor_scale_one_valuefactors) + (ff_p_fsat_one_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_one_valuefactorsfactorization_product_partial. ff_h_fsat_one_valuefactorsfactorization_product_partial + S (ff_r_fsat_one_valuefactorsfactorization_product) = S ((S (ff_i_fsat_one_valuefactorsfactorization_product)) * ff_v_fsat_one_valuefactorsfactorization_product)) /\ exists ff_q_fsat_one_valuefactorsfactorization_product_partial. ff_u_fsat_one_valuefactorsfactorization_product = ff_q_fsat_one_valuefactorsfactorization_product_partial * S ((S (ff_i_fsat_one_valuefactorsfactorization_product)) * ff_v_fsat_one_valuefactorsfactorization_product) + (ff_r_fsat_one_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_one_valuefactorsfactorization_product_successor. ff_h_fsat_one_valuefactorsfactorization_product_successor + S (ff_s_fsat_one_valuefactorsfactorization_product) = S ((S (S ff_i_fsat_one_valuefactorsfactorization_product)) * ff_v_fsat_one_valuefactorsfactorization_product)) /\ exists ff_q_fsat_one_valuefactorsfactorization_product_successor. ff_u_fsat_one_valuefactorsfactorization_product = ff_q_fsat_one_valuefactorsfactorization_product_successor * S ((S (S ff_i_fsat_one_valuefactorsfactorization_product)) * ff_v_fsat_one_valuefactorsfactorization_product) + (ff_s_fsat_one_valuefactorsfactorization_product))) /\ ff_s_fsat_one_valuefactorsfactorization_product = ff_r_fsat_one_valuefactorsfactorization_product * ff_p_fsat_one_valuefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_one_valuefactorsfactorization_primes. (exists ftsf_gap_fsat_one_valuefactorsfactorization_primes_bound. ftsf_gap_fsat_one_valuefactorsfactorization_primes_bound + S ftsf_index_fsat_one_valuefactorsfactorization_primes = (mv_factor_count_one_valuefactors)) -> exists ftsf_factor_fsat_one_valuefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_one_valuefactorsfactorization_primes_entry. ff_h_ftsf_fsat_one_valuefactorsfactorization_primes_entry + S (ftsf_factor_fsat_one_valuefactorsfactorization_primes) = S ((S (ftsf_index_fsat_one_valuefactorsfactorization_primes)) * mv_factor_scale_one_valuefactors)) /\ exists ff_q_ftsf_fsat_one_valuefactorsfactorization_primes_entry. mv_factor_code_one_valuefactors = ff_q_ftsf_fsat_one_valuefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_one_valuefactorsfactorization_primes)) * mv_factor_scale_one_valuefactors) + (ftsf_factor_fsat_one_valuefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_one_valuefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_one_valuefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_one_valuefactorsfactorization_primes_prime. ftsf_factor_fsat_one_valuefactorsfactorization_primes = frm_prime_left_ftsf_fsat_one_valuefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_one_valuefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_one_valuefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_one_valuefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_one_valuefactorsparityeven. (mv_factor_count_one_valuefactors) = 2 * mv_even_half_one_valuefactorsparityeven) /\ ((2) = 2))) \/ (((exists mv_odd_half_one_valuefactorsparityodd. (mv_factor_count_one_valuefactors) = 2 * mv_odd_half_one_valuefactorsparityodd + 1) /\ ((2) = 1))))))))))

mobius_value_exists

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 259; exact statement SHA-256 66d70409d9b65a8d69997c5ed6ccb6e002ae29046eb3d1dd1e563685fc4897da

Exact first-order statement

forall n. ~(n = 0) -> exists z. (((~((n) = 0)) /\ ((((exists mv_square_prime_exists_valuesquare. ((~((mv_square_prime_exists_valuesquare) = 1) /\ forall pvs_left_exists_valuesquareprime pvs_right_exists_valuesquareprime. (mv_square_prime_exists_valuesquare) = pvs_left_exists_valuesquareprime * pvs_right_exists_valuesquareprime -> pvs_left_exists_valuesquareprime = 1 \/ pvs_right_exists_valuesquareprime = 1) /\ (exists pvs_factor_exists_valuesquaredivisor. (n) = (mv_square_prime_exists_valuesquare * mv_square_prime_exists_valuesquare) * pvs_factor_exists_valuesquaredivisor))) /\ ((z) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_exists_valuesquarefree. (~((sfd_prime_exists_valuesquarefree) = 1) /\ forall pvs_left_exists_valuesquarefreedomain pvs_right_exists_valuesquarefreedomain. (sfd_prime_exists_valuesquarefree) = pvs_left_exists_valuesquarefreedomain * pvs_right_exists_valuesquarefreedomain -> pvs_left_exists_valuesquarefreedomain = 1 \/ pvs_right_exists_valuesquarefreedomain = 1) -> (exists pvs_le_gap_exists_valuesquarefreebound. pvs_le_gap_exists_valuesquarefreebound + (sfd_prime_exists_valuesquarefree) = (n)) -> ~(exists pvs_factor_exists_valuesquarefreesquare. (n) = (sfd_prime_exists_valuesquarefree * sfd_prime_exists_valuesquarefree) * pvs_factor_exists_valuesquarefreesquare)))) /\ (exists mv_factor_code_exists_valuefactors mv_factor_scale_exists_valuefactors mv_factor_count_exists_valuefactors. (((~(n = 0) /\ ((exists ff_u_fsat_exists_valuefactorsfactorization_product ff_v_fsat_exists_valuefactorsfactorization_product. ((((exists ff_h_fsat_exists_valuefactorsfactorization_product_start. ff_h_fsat_exists_valuefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_exists_valuefactorsfactorization_product)) /\ exists ff_q_fsat_exists_valuefactorsfactorization_product_start. ff_u_fsat_exists_valuefactorsfactorization_product = ff_q_fsat_exists_valuefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_exists_valuefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_exists_valuefactorsfactorization_product_terminal. ff_h_fsat_exists_valuefactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_exists_valuefactors)) * ff_v_fsat_exists_valuefactorsfactorization_product)) /\ exists ff_q_fsat_exists_valuefactorsfactorization_product_terminal. ff_u_fsat_exists_valuefactorsfactorization_product = ff_q_fsat_exists_valuefactorsfactorization_product_terminal * S ((S (mv_factor_count_exists_valuefactors)) * ff_v_fsat_exists_valuefactorsfactorization_product) + (n))) /\ forall ff_i_fsat_exists_valuefactorsfactorization_product. (exists ff_lt_fsat_exists_valuefactorsfactorization_product_bound. ff_lt_fsat_exists_valuefactorsfactorization_product_bound + S ff_i_fsat_exists_valuefactorsfactorization_product = mv_factor_count_exists_valuefactors) -> exists ff_p_fsat_exists_valuefactorsfactorization_product ff_r_fsat_exists_valuefactorsfactorization_product ff_s_fsat_exists_valuefactorsfactorization_product. ((((exists ff_h_fsat_exists_valuefactorsfactorization_product_factor. ff_h_fsat_exists_valuefactorsfactorization_product_factor + S (ff_p_fsat_exists_valuefactorsfactorization_product) = S ((S (ff_i_fsat_exists_valuefactorsfactorization_product)) * mv_factor_scale_exists_valuefactors)) /\ exists ff_q_fsat_exists_valuefactorsfactorization_product_factor. mv_factor_code_exists_valuefactors = ff_q_fsat_exists_valuefactorsfactorization_product_factor * S ((S (ff_i_fsat_exists_valuefactorsfactorization_product)) * mv_factor_scale_exists_valuefactors) + (ff_p_fsat_exists_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_exists_valuefactorsfactorization_product_partial. ff_h_fsat_exists_valuefactorsfactorization_product_partial + S (ff_r_fsat_exists_valuefactorsfactorization_product) = S ((S (ff_i_fsat_exists_valuefactorsfactorization_product)) * ff_v_fsat_exists_valuefactorsfactorization_product)) /\ exists ff_q_fsat_exists_valuefactorsfactorization_product_partial. ff_u_fsat_exists_valuefactorsfactorization_product = ff_q_fsat_exists_valuefactorsfactorization_product_partial * S ((S (ff_i_fsat_exists_valuefactorsfactorization_product)) * ff_v_fsat_exists_valuefactorsfactorization_product) + (ff_r_fsat_exists_valuefactorsfactorization_product))) /\ ((((exists ff_h_fsat_exists_valuefactorsfactorization_product_successor. ff_h_fsat_exists_valuefactorsfactorization_product_successor + S (ff_s_fsat_exists_valuefactorsfactorization_product) = S ((S (S ff_i_fsat_exists_valuefactorsfactorization_product)) * ff_v_fsat_exists_valuefactorsfactorization_product)) /\ exists ff_q_fsat_exists_valuefactorsfactorization_product_successor. ff_u_fsat_exists_valuefactorsfactorization_product = ff_q_fsat_exists_valuefactorsfactorization_product_successor * S ((S (S ff_i_fsat_exists_valuefactorsfactorization_product)) * ff_v_fsat_exists_valuefactorsfactorization_product) + (ff_s_fsat_exists_valuefactorsfactorization_product))) /\ ff_s_fsat_exists_valuefactorsfactorization_product = ff_r_fsat_exists_valuefactorsfactorization_product * ff_p_fsat_exists_valuefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_exists_valuefactorsfactorization_primes. (exists ftsf_gap_fsat_exists_valuefactorsfactorization_primes_bound. ftsf_gap_fsat_exists_valuefactorsfactorization_primes_bound + S ftsf_index_fsat_exists_valuefactorsfactorization_primes = (mv_factor_count_exists_valuefactors)) -> exists ftsf_factor_fsat_exists_valuefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_exists_valuefactorsfactorization_primes_entry. ff_h_ftsf_fsat_exists_valuefactorsfactorization_primes_entry + S (ftsf_factor_fsat_exists_valuefactorsfactorization_primes) = S ((S (ftsf_index_fsat_exists_valuefactorsfactorization_primes)) * mv_factor_scale_exists_valuefactors)) /\ exists ff_q_ftsf_fsat_exists_valuefactorsfactorization_primes_entry. mv_factor_code_exists_valuefactors = ff_q_ftsf_fsat_exists_valuefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_exists_valuefactorsfactorization_primes)) * mv_factor_scale_exists_valuefactors) + (ftsf_factor_fsat_exists_valuefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_exists_valuefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_exists_valuefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_exists_valuefactorsfactorization_primes_prime. ftsf_factor_fsat_exists_valuefactorsfactorization_primes = frm_prime_left_ftsf_fsat_exists_valuefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_exists_valuefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_exists_valuefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_exists_valuefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_exists_valuefactorsparityeven. (mv_factor_count_exists_valuefactors) = 2 * mv_even_half_exists_valuefactorsparityeven) /\ ((z) = 2))) \/ (((exists mv_odd_half_exists_valuefactorsparityodd. (mv_factor_count_exists_valuefactors) = 2 * mv_odd_half_exists_valuefactorsparityodd + 1) /\ ((z) = 1)))))))))))

mobius_value_functional

inherited published non admitted checkpoint · read exact theorem evidence

Bundle node 261; exact statement SHA-256 d6bf764d3fcc08f8b8f2294fb16cb0d1fb91dc58b9563920db33dc522b7e4eb3

Exact first-order statement

forall n a b. (((~((n) = 0)) /\ ((((exists mv_square_prime_functional_firstsquare. ((~((mv_square_prime_functional_firstsquare) = 1) /\ forall pvs_left_functional_firstsquareprime pvs_right_functional_firstsquareprime. (mv_square_prime_functional_firstsquare) = pvs_left_functional_firstsquareprime * pvs_right_functional_firstsquareprime -> pvs_left_functional_firstsquareprime = 1 \/ pvs_right_functional_firstsquareprime = 1) /\ (exists pvs_factor_functional_firstsquaredivisor. (n) = (mv_square_prime_functional_firstsquare * mv_square_prime_functional_firstsquare) * pvs_factor_functional_firstsquaredivisor))) /\ ((a) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_functional_firstsquarefree. (~((sfd_prime_functional_firstsquarefree) = 1) /\ forall pvs_left_functional_firstsquarefreedomain pvs_right_functional_firstsquarefreedomain. (sfd_prime_functional_firstsquarefree) = pvs_left_functional_firstsquarefreedomain * pvs_right_functional_firstsquarefreedomain -> pvs_left_functional_firstsquarefreedomain = 1 \/ pvs_right_functional_firstsquarefreedomain = 1) -> (exists pvs_le_gap_functional_firstsquarefreebound. pvs_le_gap_functional_firstsquarefreebound + (sfd_prime_functional_firstsquarefree) = (n)) -> ~(exists pvs_factor_functional_firstsquarefreesquare. (n) = (sfd_prime_functional_firstsquarefree * sfd_prime_functional_firstsquarefree) * pvs_factor_functional_firstsquarefreesquare)))) /\ (exists mv_factor_code_functional_firstfactors mv_factor_scale_functional_firstfactors mv_factor_count_functional_firstfactors. (((~(n = 0) /\ ((exists ff_u_fsat_functional_firstfactorsfactorization_product ff_v_fsat_functional_firstfactorsfactorization_product. ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_start. ff_h_fsat_functional_firstfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_start. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_terminal. ff_h_fsat_functional_firstfactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_functional_firstfactors)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_terminal. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_terminal * S ((S (mv_factor_count_functional_firstfactors)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (n))) /\ forall ff_i_fsat_functional_firstfactorsfactorization_product. (exists ff_lt_fsat_functional_firstfactorsfactorization_product_bound. ff_lt_fsat_functional_firstfactorsfactorization_product_bound + S ff_i_fsat_functional_firstfactorsfactorization_product = mv_factor_count_functional_firstfactors) -> exists ff_p_fsat_functional_firstfactorsfactorization_product ff_r_fsat_functional_firstfactorsfactorization_product ff_s_fsat_functional_firstfactorsfactorization_product. ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_factor. ff_h_fsat_functional_firstfactorsfactorization_product_factor + S (ff_p_fsat_functional_firstfactorsfactorization_product) = S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * mv_factor_scale_functional_firstfactors)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_factor. mv_factor_code_functional_firstfactors = ff_q_fsat_functional_firstfactorsfactorization_product_factor * S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * mv_factor_scale_functional_firstfactors) + (ff_p_fsat_functional_firstfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_partial. ff_h_fsat_functional_firstfactorsfactorization_product_partial + S (ff_r_fsat_functional_firstfactorsfactorization_product) = S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_partial. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_partial * S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (ff_r_fsat_functional_firstfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_successor. ff_h_fsat_functional_firstfactorsfactorization_product_successor + S (ff_s_fsat_functional_firstfactorsfactorization_product) = S ((S (S ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_successor. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_successor * S ((S (S ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (ff_s_fsat_functional_firstfactorsfactorization_product))) /\ ff_s_fsat_functional_firstfactorsfactorization_product = ff_r_fsat_functional_firstfactorsfactorization_product * ff_p_fsat_functional_firstfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_functional_firstfactorsfactorization_primes. (exists ftsf_gap_fsat_functional_firstfactorsfactorization_primes_bound. ftsf_gap_fsat_functional_firstfactorsfactorization_primes_bound + S ftsf_index_fsat_functional_firstfactorsfactorization_primes = (mv_factor_count_functional_firstfactors)) -> exists ftsf_factor_fsat_functional_firstfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_functional_firstfactorsfactorization_primes_entry. ff_h_ftsf_fsat_functional_firstfactorsfactorization_primes_entry + S (ftsf_factor_fsat_functional_firstfactorsfactorization_primes) = S ((S (ftsf_index_fsat_functional_firstfactorsfactorization_primes)) * mv_factor_scale_functional_firstfactors)) /\ exists ff_q_ftsf_fsat_functional_firstfactorsfactorization_primes_entry. mv_factor_code_functional_firstfactors = ff_q_ftsf_fsat_functional_firstfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_functional_firstfactorsfactorization_primes)) * mv_factor_scale_functional_firstfactors) + (ftsf_factor_fsat_functional_firstfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_functional_firstfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_functional_firstfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_functional_firstfactorsfactorization_primes_prime. ftsf_factor_fsat_functional_firstfactorsfactorization_primes = frm_prime_left_ftsf_fsat_functional_firstfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_functional_firstfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_functional_firstfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_functional_firstfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_functional_firstfactorsparityeven. (mv_factor_count_functional_firstfactors) = 2 * mv_even_half_functional_firstfactorsparityeven) /\ ((a) = 2))) \/ (((exists mv_odd_half_functional_firstfactorsparityodd. (mv_factor_count_functional_firstfactors) = 2 * mv_odd_half_functional_firstfactorsparityodd + 1) /\ ((a) = 1))))))))))) -> (((~((n) = 0)) /\ ((((exists mv_square_prime_functional_secondsquare. ((~((mv_square_prime_functional_secondsquare) = 1) /\ forall pvs_left_functional_secondsquareprime pvs_right_functional_secondsquareprime. (mv_square_prime_functional_secondsquare) = pvs_left_functional_secondsquareprime * pvs_right_functional_secondsquareprime -> pvs_left_functional_secondsquareprime = 1 \/ pvs_right_functional_secondsquareprime = 1) /\ (exists pvs_factor_functional_secondsquaredivisor. (n) = (mv_square_prime_functional_secondsquare * mv_square_prime_functional_secondsquare) * pvs_factor_functional_secondsquaredivisor))) /\ ((b) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_functional_secondsquarefree. (~((sfd_prime_functional_secondsquarefree) = 1) /\ forall pvs_left_functional_secondsquarefreedomain pvs_right_functional_secondsquarefreedomain. (sfd_prime_functional_secondsquarefree) = pvs_left_functional_secondsquarefreedomain * pvs_right_functional_secondsquarefreedomain -> pvs_left_functional_secondsquarefreedomain = 1 \/ pvs_right_functional_secondsquarefreedomain = 1) -> (exists pvs_le_gap_functional_secondsquarefreebound. pvs_le_gap_functional_secondsquarefreebound + (sfd_prime_functional_secondsquarefree) = (n)) -> ~(exists pvs_factor_functional_secondsquarefreesquare. (n) = (sfd_prime_functional_secondsquarefree * sfd_prime_functional_secondsquarefree) * pvs_factor_functional_secondsquarefreesquare)))) /\ (exists mv_factor_code_functional_secondfactors mv_factor_scale_functional_secondfactors mv_factor_count_functional_secondfactors. (((~(n = 0) /\ ((exists ff_u_fsat_functional_secondfactorsfactorization_product ff_v_fsat_functional_secondfactorsfactorization_product. ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_start. ff_h_fsat_functional_secondfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_start. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_terminal. ff_h_fsat_functional_secondfactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_functional_secondfactors)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_terminal. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_terminal * S ((S (mv_factor_count_functional_secondfactors)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (n))) /\ forall ff_i_fsat_functional_secondfactorsfactorization_product. (exists ff_lt_fsat_functional_secondfactorsfactorization_product_bound. ff_lt_fsat_functional_secondfactorsfactorization_product_bound + S ff_i_fsat_functional_secondfactorsfactorization_product = mv_factor_count_functional_secondfactors) -> exists ff_p_fsat_functional_secondfactorsfactorization_product ff_r_fsat_functional_secondfactorsfactorization_product ff_s_fsat_functional_secondfactorsfactorization_product. ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_factor. ff_h_fsat_functional_secondfactorsfactorization_product_factor + S (ff_p_fsat_functional_secondfactorsfactorization_product) = S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * mv_factor_scale_functional_secondfactors)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_factor. mv_factor_code_functional_secondfactors = ff_q_fsat_functional_secondfactorsfactorization_product_factor * S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * mv_factor_scale_functional_secondfactors) + (ff_p_fsat_functional_secondfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_partial. ff_h_fsat_functional_secondfactorsfactorization_product_partial + S (ff_r_fsat_functional_secondfactorsfactorization_product) = S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_partial. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_partial * S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (ff_r_fsat_functional_secondfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_successor. ff_h_fsat_functional_secondfactorsfactorization_product_successor + S (ff_s_fsat_functional_secondfactorsfactorization_product) = S ((S (S ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_successor. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_successor * S ((S (S ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (ff_s_fsat_functional_secondfactorsfactorization_product))) /\ ff_s_fsat_functional_secondfactorsfactorization_product = ff_r_fsat_functional_secondfactorsfactorization_product * ff_p_fsat_functional_secondfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_functional_secondfactorsfactorization_primes. (exists ftsf_gap_fsat_functional_secondfactorsfactorization_primes_bound. ftsf_gap_fsat_functional_secondfactorsfactorization_primes_bound + S ftsf_index_fsat_functional_secondfactorsfactorization_primes = (mv_factor_count_functional_secondfactors)) -> exists ftsf_factor_fsat_functional_secondfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_functional_secondfactorsfactorization_primes_entry. ff_h_ftsf_fsat_functional_secondfactorsfactorization_primes_entry + S (ftsf_factor_fsat_functional_secondfactorsfactorization_primes) = S ((S (ftsf_index_fsat_functional_secondfactorsfactorization_primes)) * mv_factor_scale_functional_secondfactors)) /\ exists ff_q_ftsf_fsat_functional_secondfactorsfactorization_primes_entry. mv_factor_code_functional_secondfactors = ff_q_ftsf_fsat_functional_secondfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_functional_secondfactorsfactorization_primes)) * mv_factor_scale_functional_secondfactors) + (ftsf_factor_fsat_functional_secondfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_functional_secondfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_functional_secondfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_functional_secondfactorsfactorization_primes_prime. ftsf_factor_fsat_functional_secondfactorsfactorization_primes = frm_prime_left_ftsf_fsat_functional_secondfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_functional_secondfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_functional_secondfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_functional_secondfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_functional_secondfactorsparityeven. (mv_factor_count_functional_secondfactors) = 2 * mv_even_half_functional_secondfactorsparityeven) /\ ((b) = 2))) \/ (((exists mv_odd_half_functional_secondfactorsparityodd. (mv_factor_count_functional_secondfactors) = 2 * mv_odd_half_functional_secondfactorsparityodd + 1) /\ ((b) = 1))))))))))) -> a = b

multiple_decidable_nonzero

inherited alpha v30 · read exact theorem evidence

Bundle node 78; exact statement SHA-256 08cd13450e5d21cb8318d95c115340c0ad6bfe7b90d4bba6ef8905d3d90c4684

Exact first-order statement

forall d n. ~(d = 0) -> (exists q. n = d * q) \/ ~(exists q. n = d * q)

one_mul

inherited alpha v30 · read exact theorem evidence

Bundle node 9; exact statement SHA-256 a3fba3e972fc2ec6f5a274a8d21550e1081cf5f1581eda98922616aa20cda490

Exact first-order statement

forall n. 1 * n = n

signed_add_zero_left

Inherited Alpha proof; no standalone historical explorer page · read exact theorem evidence

Bundle node 204; exact statement SHA-256 afb5ba61d840581893d6d198841aca38eff57cfe962462807b08de3b40139ec6

Exact first-order statement

forall input. (exists sa_lp_zero_left sa_ln_zero_left sa_rp_zero_left sa_rn_zero_left sa_op_zero_left sa_on_zero_left. (((0 = 2 * sa_lp_zero_left /\ sa_ln_zero_left = 0) \/ exists sd_half_zero_left_left. ((0 = 2 * sd_half_zero_left_left + 1 /\ sa_lp_zero_left = 0) /\ sa_ln_zero_left = S sd_half_zero_left_left)) /\ (((input = 2 * sa_rp_zero_left /\ sa_rn_zero_left = 0) \/ exists sd_half_zero_left_right. ((input = 2 * sd_half_zero_left_right + 1 /\ sa_rp_zero_left = 0) /\ sa_rn_zero_left = S sd_half_zero_left_right)) /\ (((input = 2 * sa_op_zero_left /\ sa_on_zero_left = 0) \/ exists sd_half_zero_left_output. ((input = 2 * sd_half_zero_left_output + 1 /\ sa_op_zero_left = 0) /\ sa_on_zero_left = S sd_half_zero_left_output)) /\ (sa_lp_zero_left + sa_rp_zero_left) + sa_on_zero_left = (sa_ln_zero_left + sa_rn_zero_left) + sa_op_zero_left))))

signed_decode_total

Inherited Alpha proof; no standalone historical explorer page · read exact theorem evidence

Bundle node 193; exact statement SHA-256 c057ebd0f11884b8c25ade6f499a867c82213a4257ae911d3362737171491bb9

Exact first-order statement

forall code. exists pos neg. ((code = 2 * pos /\ neg = 0) \/ exists sd_half_total. ((code = 2 * sd_half_total + 1 /\ pos = 0) /\ neg = S sd_half_total))

succ_le_succ

inherited alpha v30 · read exact theorem evidence

Bundle node 33; exact statement SHA-256 97c872aaa1b7fe31e8728e6f814edf1e967b5a4009d1e7716d52d4c136ac0a06

Exact first-order statement

forall a b. (exists k. k + a = b) -> exists r. r + S a = S b

zero_add

inherited alpha v30 · read exact theorem evidence

Bundle node 0; exact statement SHA-256 b759e0dfbf2a583a91d2b5db09cc55d201ef09cc1690d6ab1a32fcca5af5cdb9

Exact first-order statement

forall n. 0 + n = n

zero_le

inherited alpha v30 · read exact theorem evidence

Bundle node 25; exact statement SHA-256 d3cad8d0d0ea07e339bdb8eb3b864e3511e648763977ff6882e77d60c984aa01

Exact first-order statement

forall n. 0 <= n