One and delta convolution tables — exact evidence

Current Alpha v34 checked use; first admitted v31; not Stable. Original HA and the independently compiled Lean checker have freshly verified the complete bundle before this page was generated.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.

282 checked bundle nodes · 760 proof edges · 18734 body proof nodes.

Literal self-contained proof bundle · SHA-256 232ddd461eb83d97c1a6255a872be7e970b635ce1d4e958c8bed7706419687b7

dirichlet_units_candidate.py

Unchanged historical local checkpoint record · Historical snapshot manifest. Those records retain their original non-admitting flags; current authority comes from the separate freshly verified v31 release.

Exact theorem nodes and inherited prerequisites

DU0001 dirichlet_constant_one_table_value · actual bundle node 256
DU0002 dirichlet_kronecker_delta_table_one_value · actual bundle node 257
DU0003 dirichlet_kronecker_delta_table_other_value · actual bundle node 258
DU0004 dirichlet_kronecker_delta_value_exists · actual bundle node 259
DU0005 dirichlet_constant_one_table_append · actual bundle node 260
DU0006 dirichlet_kronecker_delta_table_append · actual bundle node 261
DU0007 dirichlet_constant_one_table_exists · actual bundle node 262
DU0008 dirichlet_kronecker_delta_table_exists · actual bundle node 263
DU0009 dirichlet_constant_one_table_reencoding · actual bundle node 264
DU000A dirichlet_constant_one_table_positive_unique · actual bundle node 265
DU000B dirichlet_kronecker_delta_table_reencoding · actual bundle node 266
DU000C dirichlet_kronecker_delta_table_positive_unique · actual bundle node 267
DU000D dirichlet_delta_right_entry_before_input · actual bundle node 268
DU000E dirichlet_delta_right_last_entry · actual bundle node 269
DU000F dirichlet_delta_right_sum_value · actual bundle node 270
DU0010 dirichlet_delta_right_sum · actual bundle node 271
DU0011 dirichlet_delta_right_table · actual bundle node 272
DU0012 dirichlet_delta_left_table · actual bundle node 273
DU0013 dirichlet_delta_unit_exists · actual bundle node 274
DU0014 dirichlet_constant_one_entry_to_divisor_mask · actual bundle node 275
DU0015 dirichlet_constant_one_entry_from_divisor_mask · actual bundle node 276
DU0016 dirichlet_constant_one_prefix_to_divisor_mask · actual bundle node 277
DU0017 dirichlet_constant_one_prefix_from_divisor_mask · actual bundle node 278
DU0018 dirichlet_constant_one_sum_iff · actual bundle node 279
DU0019 dirichlet_constant_one_realizes_divisor_sum · actual bundle node 280

arithmetic_signed_table_append · checked inherited prerequisite

Exact statement in the checked dependency cone

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_equal_entry_transport · checked inherited prerequisite

Exact statement in the checked dependency cone

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_singleton · checked inherited prerequisite

Exact statement in the checked dependency cone

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)))))))))

dirichlet_convolution_entry_from_quotient · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n d q a b z. ~(d=0) -> n=d*q -> (exists dst_positive_code_keep_left dst_positive_scale_keep_left dst_negative_code_keep_left dst_negative_scale_keep_left dst_positive_keep_left dst_negative_keep_left. (((F) = (((((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) * S ((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) + ((dst_positive_scale_keep_left) + (dst_positive_scale_keep_left))) + (((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left)))) * S ((((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) * S ((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) + ((dst_positive_scale_keep_left) + (dst_positive_scale_keep_left))) + (((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left)))) + ((((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left))) + (((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left)))))) /\ (((((exists ff_h_pvs_keep_leftpositive. ff_h_pvs_keep_leftpositive + S (dst_positive_keep_left) = S ((S (d)) * dst_positive_scale_keep_left)) /\ exists ff_q_pvs_keep_leftpositive. dst_positive_code_keep_left = ff_q_pvs_keep_leftpositive * S ((S (d)) * dst_positive_scale_keep_left) + (dst_positive_keep_left))) /\ (((((exists ff_h_pvs_keep_leftnegative. ff_h_pvs_keep_leftnegative + S (dst_negative_keep_left) = S ((S (d)) * dst_negative_scale_keep_left)) /\ exists ff_q_pvs_keep_leftnegative. dst_negative_code_keep_left = ff_q_pvs_keep_leftnegative * S ((S (d)) * dst_negative_scale_keep_left) + (dst_negative_keep_left))) /\ (exists ge_balance_positive_keep_leftvalue ge_balance_negative_keep_leftvalue. (((((a) = 2 * (ge_balance_positive_keep_leftvalue) /\ (ge_balance_negative_keep_leftvalue) = 0) \/ exists ge_signed_half_keep_leftvaluedecode. (((a) = 2 * ge_signed_half_keep_leftvaluedecode + 1 /\ (ge_balance_positive_keep_leftvalue) = 0) /\ (ge_balance_negative_keep_leftvalue) = S ge_signed_half_keep_leftvaluedecode))) /\ ((dst_positive_keep_left) + ge_balance_negative_keep_leftvalue = (dst_negative_keep_left) + ge_balance_positive_keep_leftvalue))))))))) -> (exists dst_positive_code_keep_right dst_positive_scale_keep_right dst_negative_code_keep_right dst_negative_scale_keep_right dst_positive_keep_right dst_negative_keep_right. (((G) = (((((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) * S ((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) + ((dst_positive_scale_keep_right) + (dst_positive_scale_keep_right))) + (((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right)))) * S ((((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) * S ((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) + ((dst_positive_scale_keep_right) + (dst_positive_scale_keep_right))) + (((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right)))) + ((((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right))) + (((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right)))))) /\ (((((exists ff_h_pvs_keep_rightpositive. ff_h_pvs_keep_rightpositive + S (dst_positive_keep_right) = S ((S (q)) * dst_positive_scale_keep_right)) /\ exists ff_q_pvs_keep_rightpositive. dst_positive_code_keep_right = ff_q_pvs_keep_rightpositive * S ((S (q)) * dst_positive_scale_keep_right) + (dst_positive_keep_right))) /\ (((((exists ff_h_pvs_keep_rightnegative. ff_h_pvs_keep_rightnegative + S (dst_negative_keep_right) = S ((S (q)) * dst_negative_scale_keep_right)) /\ exists ff_q_pvs_keep_rightnegative. dst_negative_code_keep_right = ff_q_pvs_keep_rightnegative * S ((S (q)) * dst_negative_scale_keep_right) + (dst_negative_keep_right))) /\ (exists ge_balance_positive_keep_rightvalue ge_balance_negative_keep_rightvalue. (((((b) = 2 * (ge_balance_positive_keep_rightvalue) /\ (ge_balance_negative_keep_rightvalue) = 0) \/ exists ge_signed_half_keep_rightvaluedecode. (((b) = 2 * ge_signed_half_keep_rightvaluedecode + 1 /\ (ge_balance_positive_keep_rightvalue) = 0) /\ (ge_balance_negative_keep_rightvalue) = S ge_signed_half_keep_rightvaluedecode))) /\ ((dst_positive_keep_right) + ge_balance_negative_keep_rightvalue = (dst_negative_keep_right) + ge_balance_positive_keep_rightvalue))))))))) -> (exists sto_ap_keep_product sto_an_keep_product sto_bp_keep_product sto_bn_keep_product sto_cp_keep_product sto_cn_keep_product. (((((a) = 2 * (sto_ap_keep_product) /\ (sto_an_keep_product) = 0) \/ exists ge_signed_half_keep_productleft. (((a) = 2 * ge_signed_half_keep_productleft + 1 /\ (sto_ap_keep_product) = 0) /\ (sto_an_keep_product) = S ge_signed_half_keep_productleft))) /\ ((((((b) = 2 * (sto_bp_keep_product) /\ (sto_bn_keep_product) = 0) \/ exists ge_signed_half_keep_productright. (((b) = 2 * ge_signed_half_keep_productright + 1 /\ (sto_bp_keep_product) = 0) /\ (sto_bn_keep_product) = S ge_signed_half_keep_productright))) /\ ((((((z) = 2 * (sto_cp_keep_product) /\ (sto_cn_keep_product) = 0) \/ exists ge_signed_half_keep_productoutput. (((z) = 2 * ge_signed_half_keep_productoutput + 1 /\ (sto_cp_keep_product) = 0) /\ (sto_cn_keep_product) = S ge_signed_half_keep_productoutput))) /\ ((sto_ap_keep_product * sto_bp_keep_product + sto_an_keep_product * sto_bn_keep_product) + sto_cn_keep_product = (sto_ap_keep_product * sto_bn_keep_product + sto_an_keep_product * sto_bp_keep_product) + sto_cp_keep_product))))))) -> ((((~((d)=0)) /\ (exists dc_quotient_keep_result dc_left_keep_result dc_right_keep_result. (((n)=(d)*dc_quotient_keep_result) /\ (((exists dst_positive_code_keep_resultleft dst_positive_scale_keep_resultleft dst_negative_code_keep_resultleft dst_negative_scale_keep_resultleft dst_positive_keep_resultleft dst_negative_keep_resultleft. (((F) = (((((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) * S ((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) + ((dst_positive_scale_keep_resultleft) + (dst_positive_scale_keep_resultleft))) + (((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft)))) * S ((((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) * S ((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) + ((dst_positive_scale_keep_resultleft) + (dst_positive_scale_keep_resultleft))) + (((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft)))) + ((((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft))) + (((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft)))))) /\ (((((exists ff_h_pvs_keep_resultleftpositive. ff_h_pvs_keep_resultleftpositive + S (dst_positive_keep_resultleft) = S ((S (d)) * dst_positive_scale_keep_resultleft)) /\ exists ff_q_pvs_keep_resultleftpositive. dst_positive_code_keep_resultleft = ff_q_pvs_keep_resultleftpositive * S ((S (d)) * dst_positive_scale_keep_resultleft) + (dst_positive_keep_resultleft))) /\ (((((exists ff_h_pvs_keep_resultleftnegative. ff_h_pvs_keep_resultleftnegative + S (dst_negative_keep_resultleft) = S ((S (d)) * dst_negative_scale_keep_resultleft)) /\ exists ff_q_pvs_keep_resultleftnegative. dst_negative_code_keep_resultleft = ff_q_pvs_keep_resultleftnegative * S ((S (d)) * dst_negative_scale_keep_resultleft) + (dst_negative_keep_resultleft))) /\ (exists ge_balance_positive_keep_resultleftvalue ge_balance_negative_keep_resultleftvalue. (((((dc_left_keep_result) = 2 * (ge_balance_positive_keep_resultleftvalue) /\ (ge_balance_negative_keep_resultleftvalue) = 0) \/ exists ge_signed_half_keep_resultleftvaluedecode. (((dc_left_keep_result) = 2 * ge_signed_half_keep_resultleftvaluedecode + 1 /\ (ge_balance_positive_keep_resultleftvalue) = 0) /\ (ge_balance_negative_keep_resultleftvalue) = S ge_signed_half_keep_resultleftvaluedecode))) /\ ((dst_positive_keep_resultleft) + ge_balance_negative_keep_resultleftvalue = (dst_negative_keep_resultleft) + ge_balance_positive_keep_resultleftvalue))))))))) /\ (((exists dst_positive_code_keep_resultright dst_positive_scale_keep_resultright dst_negative_code_keep_resultright dst_negative_scale_keep_resultright dst_positive_keep_resultright dst_negative_keep_resultright. (((G) = (((((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) * S ((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) + ((dst_positive_scale_keep_resultright) + (dst_positive_scale_keep_resultright))) + (((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright)))) * S ((((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) * S ((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) + ((dst_positive_scale_keep_resultright) + (dst_positive_scale_keep_resultright))) + (((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright)))) + ((((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright))) + (((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright)))))) /\ (((((exists ff_h_pvs_keep_resultrightpositive. ff_h_pvs_keep_resultrightpositive + S (dst_positive_keep_resultright) = S ((S (dc_quotient_keep_result)) * dst_positive_scale_keep_resultright)) /\ exists ff_q_pvs_keep_resultrightpositive. dst_positive_code_keep_resultright = ff_q_pvs_keep_resultrightpositive * S ((S (dc_quotient_keep_result)) * dst_positive_scale_keep_resultright) + (dst_positive_keep_resultright))) /\ (((((exists ff_h_pvs_keep_resultrightnegative. ff_h_pvs_keep_resultrightnegative + S (dst_negative_keep_resultright) = S ((S (dc_quotient_keep_result)) * dst_negative_scale_keep_resultright)) /\ exists ff_q_pvs_keep_resultrightnegative. dst_negative_code_keep_resultright = ff_q_pvs_keep_resultrightnegative * S ((S (dc_quotient_keep_result)) * dst_negative_scale_keep_resultright) + (dst_negative_keep_resultright))) /\ (exists ge_balance_positive_keep_resultrightvalue ge_balance_negative_keep_resultrightvalue. (((((dc_right_keep_result) = 2 * (ge_balance_positive_keep_resultrightvalue) /\ (ge_balance_negative_keep_resultrightvalue) = 0) \/ exists ge_signed_half_keep_resultrightvaluedecode. (((dc_right_keep_result) = 2 * ge_signed_half_keep_resultrightvaluedecode + 1 /\ (ge_balance_positive_keep_resultrightvalue) = 0) /\ (ge_balance_negative_keep_resultrightvalue) = S ge_signed_half_keep_resultrightvaluedecode))) /\ ((dst_positive_keep_resultright) + ge_balance_negative_keep_resultrightvalue = (dst_negative_keep_resultright) + ge_balance_positive_keep_resultrightvalue))))))))) /\ (exists sto_ap_keep_resultproduct sto_an_keep_resultproduct sto_bp_keep_resultproduct sto_bn_keep_resultproduct sto_cp_keep_resultproduct sto_cn_keep_resultproduct. (((((dc_left_keep_result) = 2 * (sto_ap_keep_resultproduct) /\ (sto_an_keep_resultproduct) = 0) \/ exists ge_signed_half_keep_resultproductleft. (((dc_left_keep_result) = 2 * ge_signed_half_keep_resultproductleft + 1 /\ (sto_ap_keep_resultproduct) = 0) /\ (sto_an_keep_resultproduct) = S ge_signed_half_keep_resultproductleft))) /\ ((((((dc_right_keep_result) = 2 * (sto_bp_keep_resultproduct) /\ (sto_bn_keep_resultproduct) = 0) \/ exists ge_signed_half_keep_resultproductright. (((dc_right_keep_result) = 2 * ge_signed_half_keep_resultproductright + 1 /\ (sto_bp_keep_resultproduct) = 0) /\ (sto_bn_keep_resultproduct) = S ge_signed_half_keep_resultproductright))) /\ ((((((z) = 2 * (sto_cp_keep_resultproduct) /\ (sto_cn_keep_resultproduct) = 0) \/ exists ge_signed_half_keep_resultproductoutput. (((z) = 2 * ge_signed_half_keep_resultproductoutput + 1 /\ (sto_cp_keep_resultproduct) = 0) /\ (sto_cn_keep_resultproduct) = S ge_signed_half_keep_resultproductoutput))) /\ ((sto_ap_keep_resultproduct * sto_bp_keep_resultproduct + sto_an_keep_resultproduct * sto_bn_keep_resultproduct) + sto_cn_keep_resultproduct = (sto_ap_keep_resultproduct * sto_bn_keep_resultproduct + sto_an_keep_resultproduct * sto_bp_keep_resultproduct) + sto_cp_keep_resultproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_keep_resultnondivisor. (n) = (d) * pvs_factor_keep_resultnondivisor)) /\ ((z)=0))))

dirichlet_convolution_prefix_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n l M d z. (((exists dst_positive_code_lookup_prefixtable dst_positive_scale_lookup_prefixtable dst_negative_code_lookup_prefixtable dst_negative_scale_lookup_prefixtable. (((M) = (((((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) * S ((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) + ((dst_positive_scale_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable))) + (((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)))) * S ((((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) * S ((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) + ((dst_positive_scale_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable))) + (((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)))) + ((((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable))) + (((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)))))) /\ (forall dst_index_lookup_prefixtable. (exists pvs_le_gap_lookup_prefixtabledomain. pvs_le_gap_lookup_prefixtabledomain + (dst_index_lookup_prefixtable) = (l)) -> exists dst_positive_lookup_prefixtable dst_negative_lookup_prefixtable dst_value_lookup_prefixtable. ((((exists ff_h_pvs_lookup_prefixtableentrypositive. ff_h_pvs_lookup_prefixtableentrypositive + S (dst_positive_lookup_prefixtable) = S ((S (dst_index_lookup_prefixtable)) * dst_positive_scale_lookup_prefixtable)) /\ exists ff_q_pvs_lookup_prefixtableentrypositive. dst_positive_code_lookup_prefixtable = ff_q_pvs_lookup_prefixtableentrypositive * S ((S (dst_index_lookup_prefixtable)) * dst_positive_scale_lookup_prefixtable) + (dst_positive_lookup_prefixtable))) /\ (((((exists ff_h_pvs_lookup_prefixtableentrynegative. ff_h_pvs_lookup_prefixtableentrynegative + S (dst_negative_lookup_prefixtable) = S ((S (dst_index_lookup_prefixtable)) * dst_negative_scale_lookup_prefixtable)) /\ exists ff_q_pvs_lookup_prefixtableentrynegative. dst_negative_code_lookup_prefixtable = ff_q_pvs_lookup_prefixtableentrynegative * S ((S (dst_index_lookup_prefixtable)) * dst_negative_scale_lookup_prefixtable) + (dst_negative_lookup_prefixtable))) /\ (exists ge_balance_positive_lookup_prefixtableentryvalue ge_balance_negative_lookup_prefixtableentryvalue. (((((dst_value_lookup_prefixtable) = 2 * (ge_balance_positive_lookup_prefixtableentryvalue) /\ (ge_balance_negative_lookup_prefixtableentryvalue) = 0) \/ exists ge_signed_half_lookup_prefixtableentryvaluedecode. (((dst_value_lookup_prefixtable) = 2 * ge_signed_half_lookup_prefixtableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixtableentryvalue) = 0) /\ (ge_balance_negative_lookup_prefixtableentryvalue) = S ge_signed_half_lookup_prefixtableentryvaluedecode))) /\ ((dst_positive_lookup_prefixtable) + ge_balance_negative_lookup_prefixtableentryvalue = (dst_negative_lookup_prefixtable) + ge_balance_positive_lookup_prefixtableentryvalue))))))))) /\ (forall dc_index_lookup_prefix dc_value_lookup_prefix. (exists pvs_le_gap_lookup_prefixdomain. pvs_le_gap_lookup_prefixdomain + (dc_index_lookup_prefix) = (l)) -> (exists dst_positive_code_lookup_prefixlookup dst_positive_scale_lookup_prefixlookup dst_negative_code_lookup_prefixlookup dst_negative_scale_lookup_prefixlookup dst_positive_lookup_prefixlookup dst_negative_lookup_prefixlookup. (((M) = (((((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) * S ((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) + ((dst_positive_scale_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup))) + (((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)))) * S ((((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) * S ((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) + ((dst_positive_scale_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup))) + (((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)))) + ((((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup))) + (((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)))))) /\ (((((exists ff_h_pvs_lookup_prefixlookuppositive. ff_h_pvs_lookup_prefixlookuppositive + S (dst_positive_lookup_prefixlookup) = S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixlookup)) /\ exists ff_q_pvs_lookup_prefixlookuppositive. dst_positive_code_lookup_prefixlookup = ff_q_pvs_lookup_prefixlookuppositive * S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixlookup) + (dst_positive_lookup_prefixlookup))) /\ (((((exists ff_h_pvs_lookup_prefixlookupnegative. ff_h_pvs_lookup_prefixlookupnegative + S (dst_negative_lookup_prefixlookup) = S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixlookup)) /\ exists ff_q_pvs_lookup_prefixlookupnegative. dst_negative_code_lookup_prefixlookup = ff_q_pvs_lookup_prefixlookupnegative * S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixlookup) + (dst_negative_lookup_prefixlookup))) /\ (exists ge_balance_positive_lookup_prefixlookupvalue ge_balance_negative_lookup_prefixlookupvalue. (((((dc_value_lookup_prefix) = 2 * (ge_balance_positive_lookup_prefixlookupvalue) /\ (ge_balance_negative_lookup_prefixlookupvalue) = 0) \/ exists ge_signed_half_lookup_prefixlookupvaluedecode. (((dc_value_lookup_prefix) = 2 * ge_signed_half_lookup_prefixlookupvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixlookupvalue) = 0) /\ (ge_balance_negative_lookup_prefixlookupvalue) = S ge_signed_half_lookup_prefixlookupvaluedecode))) /\ ((dst_positive_lookup_prefixlookup) + ge_balance_negative_lookup_prefixlookupvalue = (dst_negative_lookup_prefixlookup) + ge_balance_positive_lookup_prefixlookupvalue))))))))) -> ((((~((dc_index_lookup_prefix)=0)) /\ (exists dc_quotient_lookup_prefixentry dc_left_lookup_prefixentry dc_right_lookup_prefixentry. (((n)=(dc_index_lookup_prefix)*dc_quotient_lookup_prefixentry) /\ (((exists dst_positive_code_lookup_prefixentryleft dst_positive_scale_lookup_prefixentryleft dst_negative_code_lookup_prefixentryleft dst_negative_scale_lookup_prefixentryleft dst_positive_lookup_prefixentryleft dst_negative_lookup_prefixentryleft. (((F) = (((((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) * S ((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) + ((dst_positive_scale_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft))) + (((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)))) * S ((((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) * S ((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) + ((dst_positive_scale_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft))) + (((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)))) + ((((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft))) + (((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)))))) /\ (((((exists ff_h_pvs_lookup_prefixentryleftpositive. ff_h_pvs_lookup_prefixentryleftpositive + S (dst_positive_lookup_prefixentryleft) = S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixentryleft)) /\ exists ff_q_pvs_lookup_prefixentryleftpositive. dst_positive_code_lookup_prefixentryleft = ff_q_pvs_lookup_prefixentryleftpositive * S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixentryleft) + (dst_positive_lookup_prefixentryleft))) /\ (((((exists ff_h_pvs_lookup_prefixentryleftnegative. ff_h_pvs_lookup_prefixentryleftnegative + S (dst_negative_lookup_prefixentryleft) = S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixentryleft)) /\ exists ff_q_pvs_lookup_prefixentryleftnegative. dst_negative_code_lookup_prefixentryleft = ff_q_pvs_lookup_prefixentryleftnegative * S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixentryleft) + (dst_negative_lookup_prefixentryleft))) /\ (exists ge_balance_positive_lookup_prefixentryleftvalue ge_balance_negative_lookup_prefixentryleftvalue. (((((dc_left_lookup_prefixentry) = 2 * (ge_balance_positive_lookup_prefixentryleftvalue) /\ (ge_balance_negative_lookup_prefixentryleftvalue) = 0) \/ exists ge_signed_half_lookup_prefixentryleftvaluedecode. (((dc_left_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryleftvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixentryleftvalue) = 0) /\ (ge_balance_negative_lookup_prefixentryleftvalue) = S ge_signed_half_lookup_prefixentryleftvaluedecode))) /\ ((dst_positive_lookup_prefixentryleft) + ge_balance_negative_lookup_prefixentryleftvalue = (dst_negative_lookup_prefixentryleft) + ge_balance_positive_lookup_prefixentryleftvalue))))))))) /\ (((exists dst_positive_code_lookup_prefixentryright dst_positive_scale_lookup_prefixentryright dst_negative_code_lookup_prefixentryright dst_negative_scale_lookup_prefixentryright dst_positive_lookup_prefixentryright dst_negative_lookup_prefixentryright. (((G) = (((((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) * S ((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) + ((dst_positive_scale_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright))) + (((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)))) * S ((((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) * S ((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) + ((dst_positive_scale_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright))) + (((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)))) + ((((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright))) + (((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)))))) /\ (((((exists ff_h_pvs_lookup_prefixentryrightpositive. ff_h_pvs_lookup_prefixentryrightpositive + S (dst_positive_lookup_prefixentryright) = S ((S (dc_quotient_lookup_prefixentry)) * dst_positive_scale_lookup_prefixentryright)) /\ exists ff_q_pvs_lookup_prefixentryrightpositive. dst_positive_code_lookup_prefixentryright = ff_q_pvs_lookup_prefixentryrightpositive * S ((S (dc_quotient_lookup_prefixentry)) * dst_positive_scale_lookup_prefixentryright) + (dst_positive_lookup_prefixentryright))) /\ (((((exists ff_h_pvs_lookup_prefixentryrightnegative. ff_h_pvs_lookup_prefixentryrightnegative + S (dst_negative_lookup_prefixentryright) = S ((S (dc_quotient_lookup_prefixentry)) * dst_negative_scale_lookup_prefixentryright)) /\ exists ff_q_pvs_lookup_prefixentryrightnegative. dst_negative_code_lookup_prefixentryright = ff_q_pvs_lookup_prefixentryrightnegative * S ((S (dc_quotient_lookup_prefixentry)) * dst_negative_scale_lookup_prefixentryright) + (dst_negative_lookup_prefixentryright))) /\ (exists ge_balance_positive_lookup_prefixentryrightvalue ge_balance_negative_lookup_prefixentryrightvalue. (((((dc_right_lookup_prefixentry) = 2 * (ge_balance_positive_lookup_prefixentryrightvalue) /\ (ge_balance_negative_lookup_prefixentryrightvalue) = 0) \/ exists ge_signed_half_lookup_prefixentryrightvaluedecode. (((dc_right_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryrightvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixentryrightvalue) = 0) /\ (ge_balance_negative_lookup_prefixentryrightvalue) = S ge_signed_half_lookup_prefixentryrightvaluedecode))) /\ ((dst_positive_lookup_prefixentryright) + ge_balance_negative_lookup_prefixentryrightvalue = (dst_negative_lookup_prefixentryright) + ge_balance_positive_lookup_prefixentryrightvalue))))))))) /\ (exists sto_ap_lookup_prefixentryproduct sto_an_lookup_prefixentryproduct sto_bp_lookup_prefixentryproduct sto_bn_lookup_prefixentryproduct sto_cp_lookup_prefixentryproduct sto_cn_lookup_prefixentryproduct. (((((dc_left_lookup_prefixentry) = 2 * (sto_ap_lookup_prefixentryproduct) /\ (sto_an_lookup_prefixentryproduct) = 0) \/ exists ge_signed_half_lookup_prefixentryproductleft. (((dc_left_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryproductleft + 1 /\ (sto_ap_lookup_prefixentryproduct) = 0) /\ (sto_an_lookup_prefixentryproduct) = S ge_signed_half_lookup_prefixentryproductleft))) /\ ((((((dc_right_lookup_prefixentry) = 2 * (sto_bp_lookup_prefixentryproduct) /\ (sto_bn_lookup_prefixentryproduct) = 0) \/ exists ge_signed_half_lookup_prefixentryproductright. (((dc_right_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryproductright + 1 /\ (sto_bp_lookup_prefixentryproduct) = 0) /\ (sto_bn_lookup_prefixentryproduct) = S ge_signed_half_lookup_prefixentryproductright))) /\ ((((((dc_value_lookup_prefix) = 2 * (sto_cp_lookup_prefixentryproduct) /\ (sto_cn_lookup_prefixentryproduct) = 0) \/ exists ge_signed_half_lookup_prefixentryproductoutput. (((dc_value_lookup_prefix) = 2 * ge_signed_half_lookup_prefixentryproductoutput + 1 /\ (sto_cp_lookup_prefixentryproduct) = 0) /\ (sto_cn_lookup_prefixentryproduct) = S ge_signed_half_lookup_prefixentryproductoutput))) /\ ((sto_ap_lookup_prefixentryproduct * sto_bp_lookup_prefixentryproduct + sto_an_lookup_prefixentryproduct * sto_bn_lookup_prefixentryproduct) + sto_cn_lookup_prefixentryproduct = (sto_ap_lookup_prefixentryproduct * sto_bn_lookup_prefixentryproduct + sto_an_lookup_prefixentryproduct * sto_bp_lookup_prefixentryproduct) + sto_cp_lookup_prefixentryproduct))))))))))))))) \/ ((((dc_index_lookup_prefix)=0 \/ ~(exists pvs_factor_lookup_prefixentrynondivisor. (n) = (dc_index_lookup_prefix) * pvs_factor_lookup_prefixentrynondivisor)) /\ ((dc_value_lookup_prefix)=0))))))) -> (exists pvs_le_gap_lookup_bound. pvs_le_gap_lookup_bound + (d) = (l)) -> (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 (d)) * dst_positive_scale_lookup_entry)) /\ exists ff_q_pvs_lookup_entrypositive. dst_positive_code_lookup_entry = ff_q_pvs_lookup_entrypositive * S ((S (d)) * 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 (d)) * dst_negative_scale_lookup_entry)) /\ exists ff_q_pvs_lookup_entrynegative. dst_negative_code_lookup_entry = ff_q_pvs_lookup_entrynegative * S ((S (d)) * 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))))))))) -> ((((~((d)=0)) /\ (exists dc_quotient_lookup_result dc_left_lookup_result dc_right_lookup_result. (((n)=(d)*dc_quotient_lookup_result) /\ (((exists dst_positive_code_lookup_resultleft dst_positive_scale_lookup_resultleft dst_negative_code_lookup_resultleft dst_negative_scale_lookup_resultleft dst_positive_lookup_resultleft dst_negative_lookup_resultleft. (((F) = (((((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) * S ((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) + ((dst_positive_scale_lookup_resultleft) + (dst_positive_scale_lookup_resultleft))) + (((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)))) * S ((((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) * S ((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) + ((dst_positive_scale_lookup_resultleft) + (dst_positive_scale_lookup_resultleft))) + (((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)))) + ((((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft))) + (((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)))))) /\ (((((exists ff_h_pvs_lookup_resultleftpositive. ff_h_pvs_lookup_resultleftpositive + S (dst_positive_lookup_resultleft) = S ((S (d)) * dst_positive_scale_lookup_resultleft)) /\ exists ff_q_pvs_lookup_resultleftpositive. dst_positive_code_lookup_resultleft = ff_q_pvs_lookup_resultleftpositive * S ((S (d)) * dst_positive_scale_lookup_resultleft) + (dst_positive_lookup_resultleft))) /\ (((((exists ff_h_pvs_lookup_resultleftnegative. ff_h_pvs_lookup_resultleftnegative + S (dst_negative_lookup_resultleft) = S ((S (d)) * dst_negative_scale_lookup_resultleft)) /\ exists ff_q_pvs_lookup_resultleftnegative. dst_negative_code_lookup_resultleft = ff_q_pvs_lookup_resultleftnegative * S ((S (d)) * dst_negative_scale_lookup_resultleft) + (dst_negative_lookup_resultleft))) /\ (exists ge_balance_positive_lookup_resultleftvalue ge_balance_negative_lookup_resultleftvalue. (((((dc_left_lookup_result) = 2 * (ge_balance_positive_lookup_resultleftvalue) /\ (ge_balance_negative_lookup_resultleftvalue) = 0) \/ exists ge_signed_half_lookup_resultleftvaluedecode. (((dc_left_lookup_result) = 2 * ge_signed_half_lookup_resultleftvaluedecode + 1 /\ (ge_balance_positive_lookup_resultleftvalue) = 0) /\ (ge_balance_negative_lookup_resultleftvalue) = S ge_signed_half_lookup_resultleftvaluedecode))) /\ ((dst_positive_lookup_resultleft) + ge_balance_negative_lookup_resultleftvalue = (dst_negative_lookup_resultleft) + ge_balance_positive_lookup_resultleftvalue))))))))) /\ (((exists dst_positive_code_lookup_resultright dst_positive_scale_lookup_resultright dst_negative_code_lookup_resultright dst_negative_scale_lookup_resultright dst_positive_lookup_resultright dst_negative_lookup_resultright. (((G) = (((((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) * S ((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) + ((dst_positive_scale_lookup_resultright) + (dst_positive_scale_lookup_resultright))) + (((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright)))) * S ((((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) * S ((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) + ((dst_positive_scale_lookup_resultright) + (dst_positive_scale_lookup_resultright))) + (((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright)))) + ((((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright))) + (((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright)))))) /\ (((((exists ff_h_pvs_lookup_resultrightpositive. ff_h_pvs_lookup_resultrightpositive + S (dst_positive_lookup_resultright) = S ((S (dc_quotient_lookup_result)) * dst_positive_scale_lookup_resultright)) /\ exists ff_q_pvs_lookup_resultrightpositive. dst_positive_code_lookup_resultright = ff_q_pvs_lookup_resultrightpositive * S ((S (dc_quotient_lookup_result)) * dst_positive_scale_lookup_resultright) + (dst_positive_lookup_resultright))) /\ (((((exists ff_h_pvs_lookup_resultrightnegative. ff_h_pvs_lookup_resultrightnegative + S (dst_negative_lookup_resultright) = S ((S (dc_quotient_lookup_result)) * dst_negative_scale_lookup_resultright)) /\ exists ff_q_pvs_lookup_resultrightnegative. dst_negative_code_lookup_resultright = ff_q_pvs_lookup_resultrightnegative * S ((S (dc_quotient_lookup_result)) * dst_negative_scale_lookup_resultright) + (dst_negative_lookup_resultright))) /\ (exists ge_balance_positive_lookup_resultrightvalue ge_balance_negative_lookup_resultrightvalue. (((((dc_right_lookup_result) = 2 * (ge_balance_positive_lookup_resultrightvalue) /\ (ge_balance_negative_lookup_resultrightvalue) = 0) \/ exists ge_signed_half_lookup_resultrightvaluedecode. (((dc_right_lookup_result) = 2 * ge_signed_half_lookup_resultrightvaluedecode + 1 /\ (ge_balance_positive_lookup_resultrightvalue) = 0) /\ (ge_balance_negative_lookup_resultrightvalue) = S ge_signed_half_lookup_resultrightvaluedecode))) /\ ((dst_positive_lookup_resultright) + ge_balance_negative_lookup_resultrightvalue = (dst_negative_lookup_resultright) + ge_balance_positive_lookup_resultrightvalue))))))))) /\ (exists sto_ap_lookup_resultproduct sto_an_lookup_resultproduct sto_bp_lookup_resultproduct sto_bn_lookup_resultproduct sto_cp_lookup_resultproduct sto_cn_lookup_resultproduct. (((((dc_left_lookup_result) = 2 * (sto_ap_lookup_resultproduct) /\ (sto_an_lookup_resultproduct) = 0) \/ exists ge_signed_half_lookup_resultproductleft. (((dc_left_lookup_result) = 2 * ge_signed_half_lookup_resultproductleft + 1 /\ (sto_ap_lookup_resultproduct) = 0) /\ (sto_an_lookup_resultproduct) = S ge_signed_half_lookup_resultproductleft))) /\ ((((((dc_right_lookup_result) = 2 * (sto_bp_lookup_resultproduct) /\ (sto_bn_lookup_resultproduct) = 0) \/ exists ge_signed_half_lookup_resultproductright. (((dc_right_lookup_result) = 2 * ge_signed_half_lookup_resultproductright + 1 /\ (sto_bp_lookup_resultproduct) = 0) /\ (sto_bn_lookup_resultproduct) = S ge_signed_half_lookup_resultproductright))) /\ ((((((z) = 2 * (sto_cp_lookup_resultproduct) /\ (sto_cn_lookup_resultproduct) = 0) \/ exists ge_signed_half_lookup_resultproductoutput. (((z) = 2 * ge_signed_half_lookup_resultproductoutput + 1 /\ (sto_cp_lookup_resultproduct) = 0) /\ (sto_cn_lookup_resultproduct) = S ge_signed_half_lookup_resultproductoutput))) /\ ((sto_ap_lookup_resultproduct * sto_bp_lookup_resultproduct + sto_an_lookup_resultproduct * sto_bn_lookup_resultproduct) + sto_cn_lookup_resultproduct = (sto_ap_lookup_resultproduct * sto_bn_lookup_resultproduct + sto_an_lookup_resultproduct * sto_bp_lookup_resultproduct) + sto_cp_lookup_resultproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_lookup_resultnondivisor. (n) = (d) * pvs_factor_lookup_resultnondivisor)) /\ ((z)=0))))

dirichlet_convolution_prefix_value_from_entry · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n l M d z. (((exists dst_positive_code_value_prefixtable dst_positive_scale_value_prefixtable dst_negative_code_value_prefixtable dst_negative_scale_value_prefixtable. (((M) = (((((dst_positive_code_value_prefixtable) + (dst_positive_scale_value_prefixtable)) * S ((dst_positive_code_value_prefixtable) + (dst_positive_scale_value_prefixtable)) + ((dst_positive_scale_value_prefixtable) + (dst_positive_scale_value_prefixtable))) + (((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) * S ((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) + ((dst_negative_scale_value_prefixtable) + (dst_negative_scale_value_prefixtable)))) * S ((((dst_positive_code_value_prefixtable) + (dst_positive_scale_value_prefixtable)) * S ((dst_positive_code_value_prefixtable) + (dst_positive_scale_value_prefixtable)) + ((dst_positive_scale_value_prefixtable) + (dst_positive_scale_value_prefixtable))) + (((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) * S ((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) + ((dst_negative_scale_value_prefixtable) + (dst_negative_scale_value_prefixtable)))) + ((((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) * S ((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) + ((dst_negative_scale_value_prefixtable) + (dst_negative_scale_value_prefixtable))) + (((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) * S ((dst_negative_code_value_prefixtable) + (dst_negative_scale_value_prefixtable)) + ((dst_negative_scale_value_prefixtable) + (dst_negative_scale_value_prefixtable)))))) /\ (forall dst_index_value_prefixtable. (exists pvs_le_gap_value_prefixtabledomain. pvs_le_gap_value_prefixtabledomain + (dst_index_value_prefixtable) = (l)) -> exists dst_positive_value_prefixtable dst_negative_value_prefixtable dst_value_value_prefixtable. ((((exists ff_h_pvs_value_prefixtableentrypositive. ff_h_pvs_value_prefixtableentrypositive + S (dst_positive_value_prefixtable) = S ((S (dst_index_value_prefixtable)) * dst_positive_scale_value_prefixtable)) /\ exists ff_q_pvs_value_prefixtableentrypositive. dst_positive_code_value_prefixtable = ff_q_pvs_value_prefixtableentrypositive * S ((S (dst_index_value_prefixtable)) * dst_positive_scale_value_prefixtable) + (dst_positive_value_prefixtable))) /\ (((((exists ff_h_pvs_value_prefixtableentrynegative. ff_h_pvs_value_prefixtableentrynegative + S (dst_negative_value_prefixtable) = S ((S (dst_index_value_prefixtable)) * dst_negative_scale_value_prefixtable)) /\ exists ff_q_pvs_value_prefixtableentrynegative. dst_negative_code_value_prefixtable = ff_q_pvs_value_prefixtableentrynegative * S ((S (dst_index_value_prefixtable)) * dst_negative_scale_value_prefixtable) + (dst_negative_value_prefixtable))) /\ (exists ge_balance_positive_value_prefixtableentryvalue ge_balance_negative_value_prefixtableentryvalue. (((((dst_value_value_prefixtable) = 2 * (ge_balance_positive_value_prefixtableentryvalue) /\ (ge_balance_negative_value_prefixtableentryvalue) = 0) \/ exists ge_signed_half_value_prefixtableentryvaluedecode. (((dst_value_value_prefixtable) = 2 * ge_signed_half_value_prefixtableentryvaluedecode + 1 /\ (ge_balance_positive_value_prefixtableentryvalue) = 0) /\ (ge_balance_negative_value_prefixtableentryvalue) = S ge_signed_half_value_prefixtableentryvaluedecode))) /\ ((dst_positive_value_prefixtable) + ge_balance_negative_value_prefixtableentryvalue = (dst_negative_value_prefixtable) + ge_balance_positive_value_prefixtableentryvalue))))))))) /\ (forall dc_index_value_prefix dc_value_value_prefix. (exists pvs_le_gap_value_prefixdomain. pvs_le_gap_value_prefixdomain + (dc_index_value_prefix) = (l)) -> (exists dst_positive_code_value_prefixlookup dst_positive_scale_value_prefixlookup dst_negative_code_value_prefixlookup dst_negative_scale_value_prefixlookup dst_positive_value_prefixlookup dst_negative_value_prefixlookup. (((M) = (((((dst_positive_code_value_prefixlookup) + (dst_positive_scale_value_prefixlookup)) * S ((dst_positive_code_value_prefixlookup) + (dst_positive_scale_value_prefixlookup)) + ((dst_positive_scale_value_prefixlookup) + (dst_positive_scale_value_prefixlookup))) + (((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) * S ((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) + ((dst_negative_scale_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)))) * S ((((dst_positive_code_value_prefixlookup) + (dst_positive_scale_value_prefixlookup)) * S ((dst_positive_code_value_prefixlookup) + (dst_positive_scale_value_prefixlookup)) + ((dst_positive_scale_value_prefixlookup) + (dst_positive_scale_value_prefixlookup))) + (((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) * S ((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) + ((dst_negative_scale_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)))) + ((((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) * S ((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) + ((dst_negative_scale_value_prefixlookup) + (dst_negative_scale_value_prefixlookup))) + (((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) * S ((dst_negative_code_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)) + ((dst_negative_scale_value_prefixlookup) + (dst_negative_scale_value_prefixlookup)))))) /\ (((((exists ff_h_pvs_value_prefixlookuppositive. ff_h_pvs_value_prefixlookuppositive + S (dst_positive_value_prefixlookup) = S ((S (dc_index_value_prefix)) * dst_positive_scale_value_prefixlookup)) /\ exists ff_q_pvs_value_prefixlookuppositive. dst_positive_code_value_prefixlookup = ff_q_pvs_value_prefixlookuppositive * S ((S (dc_index_value_prefix)) * dst_positive_scale_value_prefixlookup) + (dst_positive_value_prefixlookup))) /\ (((((exists ff_h_pvs_value_prefixlookupnegative. ff_h_pvs_value_prefixlookupnegative + S (dst_negative_value_prefixlookup) = S ((S (dc_index_value_prefix)) * dst_negative_scale_value_prefixlookup)) /\ exists ff_q_pvs_value_prefixlookupnegative. dst_negative_code_value_prefixlookup = ff_q_pvs_value_prefixlookupnegative * S ((S (dc_index_value_prefix)) * dst_negative_scale_value_prefixlookup) + (dst_negative_value_prefixlookup))) /\ (exists ge_balance_positive_value_prefixlookupvalue ge_balance_negative_value_prefixlookupvalue. (((((dc_value_value_prefix) = 2 * (ge_balance_positive_value_prefixlookupvalue) /\ (ge_balance_negative_value_prefixlookupvalue) = 0) \/ exists ge_signed_half_value_prefixlookupvaluedecode. (((dc_value_value_prefix) = 2 * ge_signed_half_value_prefixlookupvaluedecode + 1 /\ (ge_balance_positive_value_prefixlookupvalue) = 0) /\ (ge_balance_negative_value_prefixlookupvalue) = S ge_signed_half_value_prefixlookupvaluedecode))) /\ ((dst_positive_value_prefixlookup) + ge_balance_negative_value_prefixlookupvalue = (dst_negative_value_prefixlookup) + ge_balance_positive_value_prefixlookupvalue))))))))) -> ((((~((dc_index_value_prefix)=0)) /\ (exists dc_quotient_value_prefixentry dc_left_value_prefixentry dc_right_value_prefixentry. (((n)=(dc_index_value_prefix)*dc_quotient_value_prefixentry) /\ (((exists dst_positive_code_value_prefixentryleft dst_positive_scale_value_prefixentryleft dst_negative_code_value_prefixentryleft dst_negative_scale_value_prefixentryleft dst_positive_value_prefixentryleft dst_negative_value_prefixentryleft. (((F) = (((((dst_positive_code_value_prefixentryleft) + (dst_positive_scale_value_prefixentryleft)) * S ((dst_positive_code_value_prefixentryleft) + (dst_positive_scale_value_prefixentryleft)) + ((dst_positive_scale_value_prefixentryleft) + (dst_positive_scale_value_prefixentryleft))) + (((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) * S ((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) + ((dst_negative_scale_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)))) * S ((((dst_positive_code_value_prefixentryleft) + (dst_positive_scale_value_prefixentryleft)) * S ((dst_positive_code_value_prefixentryleft) + (dst_positive_scale_value_prefixentryleft)) + ((dst_positive_scale_value_prefixentryleft) + (dst_positive_scale_value_prefixentryleft))) + (((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) * S ((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) + ((dst_negative_scale_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)))) + ((((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) * S ((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) + ((dst_negative_scale_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft))) + (((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) * S ((dst_negative_code_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)) + ((dst_negative_scale_value_prefixentryleft) + (dst_negative_scale_value_prefixentryleft)))))) /\ (((((exists ff_h_pvs_value_prefixentryleftpositive. ff_h_pvs_value_prefixentryleftpositive + S (dst_positive_value_prefixentryleft) = S ((S (dc_index_value_prefix)) * dst_positive_scale_value_prefixentryleft)) /\ exists ff_q_pvs_value_prefixentryleftpositive. dst_positive_code_value_prefixentryleft = ff_q_pvs_value_prefixentryleftpositive * S ((S (dc_index_value_prefix)) * dst_positive_scale_value_prefixentryleft) + (dst_positive_value_prefixentryleft))) /\ (((((exists ff_h_pvs_value_prefixentryleftnegative. ff_h_pvs_value_prefixentryleftnegative + S (dst_negative_value_prefixentryleft) = S ((S (dc_index_value_prefix)) * dst_negative_scale_value_prefixentryleft)) /\ exists ff_q_pvs_value_prefixentryleftnegative. dst_negative_code_value_prefixentryleft = ff_q_pvs_value_prefixentryleftnegative * S ((S (dc_index_value_prefix)) * dst_negative_scale_value_prefixentryleft) + (dst_negative_value_prefixentryleft))) /\ (exists ge_balance_positive_value_prefixentryleftvalue ge_balance_negative_value_prefixentryleftvalue. (((((dc_left_value_prefixentry) = 2 * (ge_balance_positive_value_prefixentryleftvalue) /\ (ge_balance_negative_value_prefixentryleftvalue) = 0) \/ exists ge_signed_half_value_prefixentryleftvaluedecode. (((dc_left_value_prefixentry) = 2 * ge_signed_half_value_prefixentryleftvaluedecode + 1 /\ (ge_balance_positive_value_prefixentryleftvalue) = 0) /\ (ge_balance_negative_value_prefixentryleftvalue) = S ge_signed_half_value_prefixentryleftvaluedecode))) /\ ((dst_positive_value_prefixentryleft) + ge_balance_negative_value_prefixentryleftvalue = (dst_negative_value_prefixentryleft) + ge_balance_positive_value_prefixentryleftvalue))))))))) /\ (((exists dst_positive_code_value_prefixentryright dst_positive_scale_value_prefixentryright dst_negative_code_value_prefixentryright dst_negative_scale_value_prefixentryright dst_positive_value_prefixentryright dst_negative_value_prefixentryright. (((G) = (((((dst_positive_code_value_prefixentryright) + (dst_positive_scale_value_prefixentryright)) * S ((dst_positive_code_value_prefixentryright) + (dst_positive_scale_value_prefixentryright)) + ((dst_positive_scale_value_prefixentryright) + (dst_positive_scale_value_prefixentryright))) + (((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) * S ((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) + ((dst_negative_scale_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)))) * S ((((dst_positive_code_value_prefixentryright) + (dst_positive_scale_value_prefixentryright)) * S ((dst_positive_code_value_prefixentryright) + (dst_positive_scale_value_prefixentryright)) + ((dst_positive_scale_value_prefixentryright) + (dst_positive_scale_value_prefixentryright))) + (((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) * S ((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) + ((dst_negative_scale_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)))) + ((((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) * S ((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) + ((dst_negative_scale_value_prefixentryright) + (dst_negative_scale_value_prefixentryright))) + (((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) * S ((dst_negative_code_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)) + ((dst_negative_scale_value_prefixentryright) + (dst_negative_scale_value_prefixentryright)))))) /\ (((((exists ff_h_pvs_value_prefixentryrightpositive. ff_h_pvs_value_prefixentryrightpositive + S (dst_positive_value_prefixentryright) = S ((S (dc_quotient_value_prefixentry)) * dst_positive_scale_value_prefixentryright)) /\ exists ff_q_pvs_value_prefixentryrightpositive. dst_positive_code_value_prefixentryright = ff_q_pvs_value_prefixentryrightpositive * S ((S (dc_quotient_value_prefixentry)) * dst_positive_scale_value_prefixentryright) + (dst_positive_value_prefixentryright))) /\ (((((exists ff_h_pvs_value_prefixentryrightnegative. ff_h_pvs_value_prefixentryrightnegative + S (dst_negative_value_prefixentryright) = S ((S (dc_quotient_value_prefixentry)) * dst_negative_scale_value_prefixentryright)) /\ exists ff_q_pvs_value_prefixentryrightnegative. dst_negative_code_value_prefixentryright = ff_q_pvs_value_prefixentryrightnegative * S ((S (dc_quotient_value_prefixentry)) * dst_negative_scale_value_prefixentryright) + (dst_negative_value_prefixentryright))) /\ (exists ge_balance_positive_value_prefixentryrightvalue ge_balance_negative_value_prefixentryrightvalue. (((((dc_right_value_prefixentry) = 2 * (ge_balance_positive_value_prefixentryrightvalue) /\ (ge_balance_negative_value_prefixentryrightvalue) = 0) \/ exists ge_signed_half_value_prefixentryrightvaluedecode. (((dc_right_value_prefixentry) = 2 * ge_signed_half_value_prefixentryrightvaluedecode + 1 /\ (ge_balance_positive_value_prefixentryrightvalue) = 0) /\ (ge_balance_negative_value_prefixentryrightvalue) = S ge_signed_half_value_prefixentryrightvaluedecode))) /\ ((dst_positive_value_prefixentryright) + ge_balance_negative_value_prefixentryrightvalue = (dst_negative_value_prefixentryright) + ge_balance_positive_value_prefixentryrightvalue))))))))) /\ (exists sto_ap_value_prefixentryproduct sto_an_value_prefixentryproduct sto_bp_value_prefixentryproduct sto_bn_value_prefixentryproduct sto_cp_value_prefixentryproduct sto_cn_value_prefixentryproduct. (((((dc_left_value_prefixentry) = 2 * (sto_ap_value_prefixentryproduct) /\ (sto_an_value_prefixentryproduct) = 0) \/ exists ge_signed_half_value_prefixentryproductleft. (((dc_left_value_prefixentry) = 2 * ge_signed_half_value_prefixentryproductleft + 1 /\ (sto_ap_value_prefixentryproduct) = 0) /\ (sto_an_value_prefixentryproduct) = S ge_signed_half_value_prefixentryproductleft))) /\ ((((((dc_right_value_prefixentry) = 2 * (sto_bp_value_prefixentryproduct) /\ (sto_bn_value_prefixentryproduct) = 0) \/ exists ge_signed_half_value_prefixentryproductright. (((dc_right_value_prefixentry) = 2 * ge_signed_half_value_prefixentryproductright + 1 /\ (sto_bp_value_prefixentryproduct) = 0) /\ (sto_bn_value_prefixentryproduct) = S ge_signed_half_value_prefixentryproductright))) /\ ((((((dc_value_value_prefix) = 2 * (sto_cp_value_prefixentryproduct) /\ (sto_cn_value_prefixentryproduct) = 0) \/ exists ge_signed_half_value_prefixentryproductoutput. (((dc_value_value_prefix) = 2 * ge_signed_half_value_prefixentryproductoutput + 1 /\ (sto_cp_value_prefixentryproduct) = 0) /\ (sto_cn_value_prefixentryproduct) = S ge_signed_half_value_prefixentryproductoutput))) /\ ((sto_ap_value_prefixentryproduct * sto_bp_value_prefixentryproduct + sto_an_value_prefixentryproduct * sto_bn_value_prefixentryproduct) + sto_cn_value_prefixentryproduct = (sto_ap_value_prefixentryproduct * sto_bn_value_prefixentryproduct + sto_an_value_prefixentryproduct * sto_bp_value_prefixentryproduct) + sto_cp_value_prefixentryproduct))))))))))))))) \/ ((((dc_index_value_prefix)=0 \/ ~(exists pvs_factor_value_prefixentrynondivisor. (n) = (dc_index_value_prefix) * pvs_factor_value_prefixentrynondivisor)) /\ ((dc_value_value_prefix)=0))))))) -> (exists pvs_le_gap_value_bound. pvs_le_gap_value_bound + (d) = (l)) -> ((((~((d)=0)) /\ (exists dc_quotient_value_graph dc_left_value_graph dc_right_value_graph. (((n)=(d)*dc_quotient_value_graph) /\ (((exists dst_positive_code_value_graphleft dst_positive_scale_value_graphleft dst_negative_code_value_graphleft dst_negative_scale_value_graphleft dst_positive_value_graphleft dst_negative_value_graphleft. (((F) = (((((dst_positive_code_value_graphleft) + (dst_positive_scale_value_graphleft)) * S ((dst_positive_code_value_graphleft) + (dst_positive_scale_value_graphleft)) + ((dst_positive_scale_value_graphleft) + (dst_positive_scale_value_graphleft))) + (((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) * S ((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) + ((dst_negative_scale_value_graphleft) + (dst_negative_scale_value_graphleft)))) * S ((((dst_positive_code_value_graphleft) + (dst_positive_scale_value_graphleft)) * S ((dst_positive_code_value_graphleft) + (dst_positive_scale_value_graphleft)) + ((dst_positive_scale_value_graphleft) + (dst_positive_scale_value_graphleft))) + (((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) * S ((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) + ((dst_negative_scale_value_graphleft) + (dst_negative_scale_value_graphleft)))) + ((((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) * S ((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) + ((dst_negative_scale_value_graphleft) + (dst_negative_scale_value_graphleft))) + (((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) * S ((dst_negative_code_value_graphleft) + (dst_negative_scale_value_graphleft)) + ((dst_negative_scale_value_graphleft) + (dst_negative_scale_value_graphleft)))))) /\ (((((exists ff_h_pvs_value_graphleftpositive. ff_h_pvs_value_graphleftpositive + S (dst_positive_value_graphleft) = S ((S (d)) * dst_positive_scale_value_graphleft)) /\ exists ff_q_pvs_value_graphleftpositive. dst_positive_code_value_graphleft = ff_q_pvs_value_graphleftpositive * S ((S (d)) * dst_positive_scale_value_graphleft) + (dst_positive_value_graphleft))) /\ (((((exists ff_h_pvs_value_graphleftnegative. ff_h_pvs_value_graphleftnegative + S (dst_negative_value_graphleft) = S ((S (d)) * dst_negative_scale_value_graphleft)) /\ exists ff_q_pvs_value_graphleftnegative. dst_negative_code_value_graphleft = ff_q_pvs_value_graphleftnegative * S ((S (d)) * dst_negative_scale_value_graphleft) + (dst_negative_value_graphleft))) /\ (exists ge_balance_positive_value_graphleftvalue ge_balance_negative_value_graphleftvalue. (((((dc_left_value_graph) = 2 * (ge_balance_positive_value_graphleftvalue) /\ (ge_balance_negative_value_graphleftvalue) = 0) \/ exists ge_signed_half_value_graphleftvaluedecode. (((dc_left_value_graph) = 2 * ge_signed_half_value_graphleftvaluedecode + 1 /\ (ge_balance_positive_value_graphleftvalue) = 0) /\ (ge_balance_negative_value_graphleftvalue) = S ge_signed_half_value_graphleftvaluedecode))) /\ ((dst_positive_value_graphleft) + ge_balance_negative_value_graphleftvalue = (dst_negative_value_graphleft) + ge_balance_positive_value_graphleftvalue))))))))) /\ (((exists dst_positive_code_value_graphright dst_positive_scale_value_graphright dst_negative_code_value_graphright dst_negative_scale_value_graphright dst_positive_value_graphright dst_negative_value_graphright. (((G) = (((((dst_positive_code_value_graphright) + (dst_positive_scale_value_graphright)) * S ((dst_positive_code_value_graphright) + (dst_positive_scale_value_graphright)) + ((dst_positive_scale_value_graphright) + (dst_positive_scale_value_graphright))) + (((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) * S ((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) + ((dst_negative_scale_value_graphright) + (dst_negative_scale_value_graphright)))) * S ((((dst_positive_code_value_graphright) + (dst_positive_scale_value_graphright)) * S ((dst_positive_code_value_graphright) + (dst_positive_scale_value_graphright)) + ((dst_positive_scale_value_graphright) + (dst_positive_scale_value_graphright))) + (((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) * S ((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) + ((dst_negative_scale_value_graphright) + (dst_negative_scale_value_graphright)))) + ((((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) * S ((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) + ((dst_negative_scale_value_graphright) + (dst_negative_scale_value_graphright))) + (((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) * S ((dst_negative_code_value_graphright) + (dst_negative_scale_value_graphright)) + ((dst_negative_scale_value_graphright) + (dst_negative_scale_value_graphright)))))) /\ (((((exists ff_h_pvs_value_graphrightpositive. ff_h_pvs_value_graphrightpositive + S (dst_positive_value_graphright) = S ((S (dc_quotient_value_graph)) * dst_positive_scale_value_graphright)) /\ exists ff_q_pvs_value_graphrightpositive. dst_positive_code_value_graphright = ff_q_pvs_value_graphrightpositive * S ((S (dc_quotient_value_graph)) * dst_positive_scale_value_graphright) + (dst_positive_value_graphright))) /\ (((((exists ff_h_pvs_value_graphrightnegative. ff_h_pvs_value_graphrightnegative + S (dst_negative_value_graphright) = S ((S (dc_quotient_value_graph)) * dst_negative_scale_value_graphright)) /\ exists ff_q_pvs_value_graphrightnegative. dst_negative_code_value_graphright = ff_q_pvs_value_graphrightnegative * S ((S (dc_quotient_value_graph)) * dst_negative_scale_value_graphright) + (dst_negative_value_graphright))) /\ (exists ge_balance_positive_value_graphrightvalue ge_balance_negative_value_graphrightvalue. (((((dc_right_value_graph) = 2 * (ge_balance_positive_value_graphrightvalue) /\ (ge_balance_negative_value_graphrightvalue) = 0) \/ exists ge_signed_half_value_graphrightvaluedecode. (((dc_right_value_graph) = 2 * ge_signed_half_value_graphrightvaluedecode + 1 /\ (ge_balance_positive_value_graphrightvalue) = 0) /\ (ge_balance_negative_value_graphrightvalue) = S ge_signed_half_value_graphrightvaluedecode))) /\ ((dst_positive_value_graphright) + ge_balance_negative_value_graphrightvalue = (dst_negative_value_graphright) + ge_balance_positive_value_graphrightvalue))))))))) /\ (exists sto_ap_value_graphproduct sto_an_value_graphproduct sto_bp_value_graphproduct sto_bn_value_graphproduct sto_cp_value_graphproduct sto_cn_value_graphproduct. (((((dc_left_value_graph) = 2 * (sto_ap_value_graphproduct) /\ (sto_an_value_graphproduct) = 0) \/ exists ge_signed_half_value_graphproductleft. (((dc_left_value_graph) = 2 * ge_signed_half_value_graphproductleft + 1 /\ (sto_ap_value_graphproduct) = 0) /\ (sto_an_value_graphproduct) = S ge_signed_half_value_graphproductleft))) /\ ((((((dc_right_value_graph) = 2 * (sto_bp_value_graphproduct) /\ (sto_bn_value_graphproduct) = 0) \/ exists ge_signed_half_value_graphproductright. (((dc_right_value_graph) = 2 * ge_signed_half_value_graphproductright + 1 /\ (sto_bp_value_graphproduct) = 0) /\ (sto_bn_value_graphproduct) = S ge_signed_half_value_graphproductright))) /\ ((((((z) = 2 * (sto_cp_value_graphproduct) /\ (sto_cn_value_graphproduct) = 0) \/ exists ge_signed_half_value_graphproductoutput. (((z) = 2 * ge_signed_half_value_graphproductoutput + 1 /\ (sto_cp_value_graphproduct) = 0) /\ (sto_cn_value_graphproduct) = S ge_signed_half_value_graphproductoutput))) /\ ((sto_ap_value_graphproduct * sto_bp_value_graphproduct + sto_an_value_graphproduct * sto_bn_value_graphproduct) + sto_cn_value_graphproduct = (sto_ap_value_graphproduct * sto_bn_value_graphproduct + sto_an_value_graphproduct * sto_bp_value_graphproduct) + sto_cp_value_graphproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_value_graphnondivisor. (n) = (d) * pvs_factor_value_graphnondivisor)) /\ ((z)=0)))) -> (exists dst_positive_code_value_result dst_positive_scale_value_result dst_negative_code_value_result dst_negative_scale_value_result dst_positive_value_result dst_negative_value_result. (((M) = (((((dst_positive_code_value_result) + (dst_positive_scale_value_result)) * S ((dst_positive_code_value_result) + (dst_positive_scale_value_result)) + ((dst_positive_scale_value_result) + (dst_positive_scale_value_result))) + (((dst_negative_code_value_result) + (dst_negative_scale_value_result)) * S ((dst_negative_code_value_result) + (dst_negative_scale_value_result)) + ((dst_negative_scale_value_result) + (dst_negative_scale_value_result)))) * S ((((dst_positive_code_value_result) + (dst_positive_scale_value_result)) * S ((dst_positive_code_value_result) + (dst_positive_scale_value_result)) + ((dst_positive_scale_value_result) + (dst_positive_scale_value_result))) + (((dst_negative_code_value_result) + (dst_negative_scale_value_result)) * S ((dst_negative_code_value_result) + (dst_negative_scale_value_result)) + ((dst_negative_scale_value_result) + (dst_negative_scale_value_result)))) + ((((dst_negative_code_value_result) + (dst_negative_scale_value_result)) * S ((dst_negative_code_value_result) + (dst_negative_scale_value_result)) + ((dst_negative_scale_value_result) + (dst_negative_scale_value_result))) + (((dst_negative_code_value_result) + (dst_negative_scale_value_result)) * S ((dst_negative_code_value_result) + (dst_negative_scale_value_result)) + ((dst_negative_scale_value_result) + (dst_negative_scale_value_result)))))) /\ (((((exists ff_h_pvs_value_resultpositive. ff_h_pvs_value_resultpositive + S (dst_positive_value_result) = S ((S (d)) * dst_positive_scale_value_result)) /\ exists ff_q_pvs_value_resultpositive. dst_positive_code_value_result = ff_q_pvs_value_resultpositive * S ((S (d)) * dst_positive_scale_value_result) + (dst_positive_value_result))) /\ (((((exists ff_h_pvs_value_resultnegative. ff_h_pvs_value_resultnegative + S (dst_negative_value_result) = S ((S (d)) * dst_negative_scale_value_result)) /\ exists ff_q_pvs_value_resultnegative. dst_negative_code_value_result = ff_q_pvs_value_resultnegative * S ((S (d)) * dst_negative_scale_value_result) + (dst_negative_value_result))) /\ (exists ge_balance_positive_value_resultvalue ge_balance_negative_value_resultvalue. (((((z) = 2 * (ge_balance_positive_value_resultvalue) /\ (ge_balance_negative_value_resultvalue) = 0) \/ exists ge_signed_half_value_resultvaluedecode. (((z) = 2 * ge_signed_half_value_resultvaluedecode + 1 /\ (ge_balance_positive_value_resultvalue) = 0) /\ (ge_balance_negative_value_resultvalue) = S ge_signed_half_value_resultvaluedecode))) /\ ((dst_positive_value_result) + ge_balance_negative_value_resultvalue = (dst_negative_value_result) + ge_balance_positive_value_resultvalue)))))))))

dirichlet_convolution_sum_exists · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F G n. (exists dst_positive_code_sum_total_left dst_positive_scale_sum_total_left dst_negative_code_sum_total_left dst_negative_scale_sum_total_left. (((F) = (((((dst_positive_code_sum_total_left) + (dst_positive_scale_sum_total_left)) * S ((dst_positive_code_sum_total_left) + (dst_positive_scale_sum_total_left)) + ((dst_positive_scale_sum_total_left) + (dst_positive_scale_sum_total_left))) + (((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) * S ((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) + ((dst_negative_scale_sum_total_left) + (dst_negative_scale_sum_total_left)))) * S ((((dst_positive_code_sum_total_left) + (dst_positive_scale_sum_total_left)) * S ((dst_positive_code_sum_total_left) + (dst_positive_scale_sum_total_left)) + ((dst_positive_scale_sum_total_left) + (dst_positive_scale_sum_total_left))) + (((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) * S ((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) + ((dst_negative_scale_sum_total_left) + (dst_negative_scale_sum_total_left)))) + ((((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) * S ((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) + ((dst_negative_scale_sum_total_left) + (dst_negative_scale_sum_total_left))) + (((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) * S ((dst_negative_code_sum_total_left) + (dst_negative_scale_sum_total_left)) + ((dst_negative_scale_sum_total_left) + (dst_negative_scale_sum_total_left)))))) /\ (forall dst_index_sum_total_left. (exists pvs_le_gap_sum_total_leftdomain. pvs_le_gap_sum_total_leftdomain + (dst_index_sum_total_left) = (N)) -> exists dst_positive_sum_total_left dst_negative_sum_total_left dst_value_sum_total_left. ((((exists ff_h_pvs_sum_total_leftentrypositive. ff_h_pvs_sum_total_leftentrypositive + S (dst_positive_sum_total_left) = S ((S (dst_index_sum_total_left)) * dst_positive_scale_sum_total_left)) /\ exists ff_q_pvs_sum_total_leftentrypositive. dst_positive_code_sum_total_left = ff_q_pvs_sum_total_leftentrypositive * S ((S (dst_index_sum_total_left)) * dst_positive_scale_sum_total_left) + (dst_positive_sum_total_left))) /\ (((((exists ff_h_pvs_sum_total_leftentrynegative. ff_h_pvs_sum_total_leftentrynegative + S (dst_negative_sum_total_left) = S ((S (dst_index_sum_total_left)) * dst_negative_scale_sum_total_left)) /\ exists ff_q_pvs_sum_total_leftentrynegative. dst_negative_code_sum_total_left = ff_q_pvs_sum_total_leftentrynegative * S ((S (dst_index_sum_total_left)) * dst_negative_scale_sum_total_left) + (dst_negative_sum_total_left))) /\ (exists ge_balance_positive_sum_total_leftentryvalue ge_balance_negative_sum_total_leftentryvalue. (((((dst_value_sum_total_left) = 2 * (ge_balance_positive_sum_total_leftentryvalue) /\ (ge_balance_negative_sum_total_leftentryvalue) = 0) \/ exists ge_signed_half_sum_total_leftentryvaluedecode. (((dst_value_sum_total_left) = 2 * ge_signed_half_sum_total_leftentryvaluedecode + 1 /\ (ge_balance_positive_sum_total_leftentryvalue) = 0) /\ (ge_balance_negative_sum_total_leftentryvalue) = S ge_signed_half_sum_total_leftentryvaluedecode))) /\ ((dst_positive_sum_total_left) + ge_balance_negative_sum_total_leftentryvalue = (dst_negative_sum_total_left) + ge_balance_positive_sum_total_leftentryvalue))))))))) -> (exists dst_positive_code_sum_total_right dst_positive_scale_sum_total_right dst_negative_code_sum_total_right dst_negative_scale_sum_total_right. (((G) = (((((dst_positive_code_sum_total_right) + (dst_positive_scale_sum_total_right)) * S ((dst_positive_code_sum_total_right) + (dst_positive_scale_sum_total_right)) + ((dst_positive_scale_sum_total_right) + (dst_positive_scale_sum_total_right))) + (((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) * S ((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) + ((dst_negative_scale_sum_total_right) + (dst_negative_scale_sum_total_right)))) * S ((((dst_positive_code_sum_total_right) + (dst_positive_scale_sum_total_right)) * S ((dst_positive_code_sum_total_right) + (dst_positive_scale_sum_total_right)) + ((dst_positive_scale_sum_total_right) + (dst_positive_scale_sum_total_right))) + (((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) * S ((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) + ((dst_negative_scale_sum_total_right) + (dst_negative_scale_sum_total_right)))) + ((((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) * S ((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) + ((dst_negative_scale_sum_total_right) + (dst_negative_scale_sum_total_right))) + (((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) * S ((dst_negative_code_sum_total_right) + (dst_negative_scale_sum_total_right)) + ((dst_negative_scale_sum_total_right) + (dst_negative_scale_sum_total_right)))))) /\ (forall dst_index_sum_total_right. (exists pvs_le_gap_sum_total_rightdomain. pvs_le_gap_sum_total_rightdomain + (dst_index_sum_total_right) = (N)) -> exists dst_positive_sum_total_right dst_negative_sum_total_right dst_value_sum_total_right. ((((exists ff_h_pvs_sum_total_rightentrypositive. ff_h_pvs_sum_total_rightentrypositive + S (dst_positive_sum_total_right) = S ((S (dst_index_sum_total_right)) * dst_positive_scale_sum_total_right)) /\ exists ff_q_pvs_sum_total_rightentrypositive. dst_positive_code_sum_total_right = ff_q_pvs_sum_total_rightentrypositive * S ((S (dst_index_sum_total_right)) * dst_positive_scale_sum_total_right) + (dst_positive_sum_total_right))) /\ (((((exists ff_h_pvs_sum_total_rightentrynegative. ff_h_pvs_sum_total_rightentrynegative + S (dst_negative_sum_total_right) = S ((S (dst_index_sum_total_right)) * dst_negative_scale_sum_total_right)) /\ exists ff_q_pvs_sum_total_rightentrynegative. dst_negative_code_sum_total_right = ff_q_pvs_sum_total_rightentrynegative * S ((S (dst_index_sum_total_right)) * dst_negative_scale_sum_total_right) + (dst_negative_sum_total_right))) /\ (exists ge_balance_positive_sum_total_rightentryvalue ge_balance_negative_sum_total_rightentryvalue. (((((dst_value_sum_total_right) = 2 * (ge_balance_positive_sum_total_rightentryvalue) /\ (ge_balance_negative_sum_total_rightentryvalue) = 0) \/ exists ge_signed_half_sum_total_rightentryvaluedecode. (((dst_value_sum_total_right) = 2 * ge_signed_half_sum_total_rightentryvaluedecode + 1 /\ (ge_balance_positive_sum_total_rightentryvalue) = 0) /\ (ge_balance_negative_sum_total_rightentryvalue) = S ge_signed_half_sum_total_rightentryvaluedecode))) /\ ((dst_positive_sum_total_right) + ge_balance_negative_sum_total_rightentryvalue = (dst_negative_sum_total_right) + ge_balance_positive_sum_total_rightentryvalue))))))))) -> ~(n=0) -> (exists pvs_le_gap_sum_total_bound. pvs_le_gap_sum_total_bound + (n) = (N)) -> exists z. (((~((n)=0)) /\ (exists dc_mask_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. (((dc_mask_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 dc_index_sum_total_resultmask dc_value_sum_total_resultmask. (exists pvs_le_gap_sum_total_resultmaskdomain. pvs_le_gap_sum_total_resultmaskdomain + (dc_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. (((dc_mask_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 (dc_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 (dc_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 (dc_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 (dc_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. (((((dc_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. (((dc_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))))))))) -> ((((~((dc_index_sum_total_resultmask)=0)) /\ (exists dc_quotient_sum_total_resultmaskentry dc_left_sum_total_resultmaskentry dc_right_sum_total_resultmaskentry. (((n)=(dc_index_sum_total_resultmask)*dc_quotient_sum_total_resultmaskentry) /\ (((exists dst_positive_code_sum_total_resultmaskentryleft dst_positive_scale_sum_total_resultmaskentryleft dst_negative_code_sum_total_resultmaskentryleft dst_negative_scale_sum_total_resultmaskentryleft dst_positive_sum_total_resultmaskentryleft dst_negative_sum_total_resultmaskentryleft. (((F) = (((((dst_positive_code_sum_total_resultmaskentryleft) + (dst_positive_scale_sum_total_resultmaskentryleft)) * S ((dst_positive_code_sum_total_resultmaskentryleft) + (dst_positive_scale_sum_total_resultmaskentryleft)) + ((dst_positive_scale_sum_total_resultmaskentryleft) + (dst_positive_scale_sum_total_resultmaskentryleft))) + (((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) * S ((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) + ((dst_negative_scale_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)))) * S ((((dst_positive_code_sum_total_resultmaskentryleft) + (dst_positive_scale_sum_total_resultmaskentryleft)) * S ((dst_positive_code_sum_total_resultmaskentryleft) + (dst_positive_scale_sum_total_resultmaskentryleft)) + ((dst_positive_scale_sum_total_resultmaskentryleft) + (dst_positive_scale_sum_total_resultmaskentryleft))) + (((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) * S ((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) + ((dst_negative_scale_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)))) + ((((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) * S ((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) + ((dst_negative_scale_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft))) + (((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) * S ((dst_negative_code_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)) + ((dst_negative_scale_sum_total_resultmaskentryleft) + (dst_negative_scale_sum_total_resultmaskentryleft)))))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryleftpositive. ff_h_pvs_sum_total_resultmaskentryleftpositive + S (dst_positive_sum_total_resultmaskentryleft) = S ((S (dc_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmaskentryleft)) /\ exists ff_q_pvs_sum_total_resultmaskentryleftpositive. dst_positive_code_sum_total_resultmaskentryleft = ff_q_pvs_sum_total_resultmaskentryleftpositive * S ((S (dc_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmaskentryleft) + (dst_positive_sum_total_resultmaskentryleft))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryleftnegative. ff_h_pvs_sum_total_resultmaskentryleftnegative + S (dst_negative_sum_total_resultmaskentryleft) = S ((S (dc_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmaskentryleft)) /\ exists ff_q_pvs_sum_total_resultmaskentryleftnegative. dst_negative_code_sum_total_resultmaskentryleft = ff_q_pvs_sum_total_resultmaskentryleftnegative * S ((S (dc_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmaskentryleft) + (dst_negative_sum_total_resultmaskentryleft))) /\ (exists ge_balance_positive_sum_total_resultmaskentryleftvalue ge_balance_negative_sum_total_resultmaskentryleftvalue. (((((dc_left_sum_total_resultmaskentry) = 2 * (ge_balance_positive_sum_total_resultmaskentryleftvalue) /\ (ge_balance_negative_sum_total_resultmaskentryleftvalue) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryleftvaluedecode. (((dc_left_sum_total_resultmaskentry) = 2 * ge_signed_half_sum_total_resultmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmaskentryleftvalue) = 0) /\ (ge_balance_negative_sum_total_resultmaskentryleftvalue) = S ge_signed_half_sum_total_resultmaskentryleftvaluedecode))) /\ ((dst_positive_sum_total_resultmaskentryleft) + ge_balance_negative_sum_total_resultmaskentryleftvalue = (dst_negative_sum_total_resultmaskentryleft) + ge_balance_positive_sum_total_resultmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_sum_total_resultmaskentryright dst_positive_scale_sum_total_resultmaskentryright dst_negative_code_sum_total_resultmaskentryright dst_negative_scale_sum_total_resultmaskentryright dst_positive_sum_total_resultmaskentryright dst_negative_sum_total_resultmaskentryright. (((G) = (((((dst_positive_code_sum_total_resultmaskentryright) + (dst_positive_scale_sum_total_resultmaskentryright)) * S ((dst_positive_code_sum_total_resultmaskentryright) + (dst_positive_scale_sum_total_resultmaskentryright)) + ((dst_positive_scale_sum_total_resultmaskentryright) + (dst_positive_scale_sum_total_resultmaskentryright))) + (((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) * S ((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) + ((dst_negative_scale_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)))) * S ((((dst_positive_code_sum_total_resultmaskentryright) + (dst_positive_scale_sum_total_resultmaskentryright)) * S ((dst_positive_code_sum_total_resultmaskentryright) + (dst_positive_scale_sum_total_resultmaskentryright)) + ((dst_positive_scale_sum_total_resultmaskentryright) + (dst_positive_scale_sum_total_resultmaskentryright))) + (((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) * S ((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) + ((dst_negative_scale_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)))) + ((((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) * S ((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) + ((dst_negative_scale_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright))) + (((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) * S ((dst_negative_code_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)) + ((dst_negative_scale_sum_total_resultmaskentryright) + (dst_negative_scale_sum_total_resultmaskentryright)))))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryrightpositive. ff_h_pvs_sum_total_resultmaskentryrightpositive + S (dst_positive_sum_total_resultmaskentryright) = S ((S (dc_quotient_sum_total_resultmaskentry)) * dst_positive_scale_sum_total_resultmaskentryright)) /\ exists ff_q_pvs_sum_total_resultmaskentryrightpositive. dst_positive_code_sum_total_resultmaskentryright = ff_q_pvs_sum_total_resultmaskentryrightpositive * S ((S (dc_quotient_sum_total_resultmaskentry)) * dst_positive_scale_sum_total_resultmaskentryright) + (dst_positive_sum_total_resultmaskentryright))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryrightnegative. ff_h_pvs_sum_total_resultmaskentryrightnegative + S (dst_negative_sum_total_resultmaskentryright) = S ((S (dc_quotient_sum_total_resultmaskentry)) * dst_negative_scale_sum_total_resultmaskentryright)) /\ exists ff_q_pvs_sum_total_resultmaskentryrightnegative. dst_negative_code_sum_total_resultmaskentryright = ff_q_pvs_sum_total_resultmaskentryrightnegative * S ((S (dc_quotient_sum_total_resultmaskentry)) * dst_negative_scale_sum_total_resultmaskentryright) + (dst_negative_sum_total_resultmaskentryright))) /\ (exists ge_balance_positive_sum_total_resultmaskentryrightvalue ge_balance_negative_sum_total_resultmaskentryrightvalue. (((((dc_right_sum_total_resultmaskentry) = 2 * (ge_balance_positive_sum_total_resultmaskentryrightvalue) /\ (ge_balance_negative_sum_total_resultmaskentryrightvalue) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryrightvaluedecode. (((dc_right_sum_total_resultmaskentry) = 2 * ge_signed_half_sum_total_resultmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmaskentryrightvalue) = 0) /\ (ge_balance_negative_sum_total_resultmaskentryrightvalue) = S ge_signed_half_sum_total_resultmaskentryrightvaluedecode))) /\ ((dst_positive_sum_total_resultmaskentryright) + ge_balance_negative_sum_total_resultmaskentryrightvalue = (dst_negative_sum_total_resultmaskentryright) + ge_balance_positive_sum_total_resultmaskentryrightvalue))))))))) /\ (exists sto_ap_sum_total_resultmaskentryproduct sto_an_sum_total_resultmaskentryproduct sto_bp_sum_total_resultmaskentryproduct sto_bn_sum_total_resultmaskentryproduct sto_cp_sum_total_resultmaskentryproduct sto_cn_sum_total_resultmaskentryproduct. (((((dc_left_sum_total_resultmaskentry) = 2 * (sto_ap_sum_total_resultmaskentryproduct) /\ (sto_an_sum_total_resultmaskentryproduct) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryproductleft. (((dc_left_sum_total_resultmaskentry) = 2 * ge_signed_half_sum_total_resultmaskentryproductleft + 1 /\ (sto_ap_sum_total_resultmaskentryproduct) = 0) /\ (sto_an_sum_total_resultmaskentryproduct) = S ge_signed_half_sum_total_resultmaskentryproductleft))) /\ ((((((dc_right_sum_total_resultmaskentry) = 2 * (sto_bp_sum_total_resultmaskentryproduct) /\ (sto_bn_sum_total_resultmaskentryproduct) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryproductright. (((dc_right_sum_total_resultmaskentry) = 2 * ge_signed_half_sum_total_resultmaskentryproductright + 1 /\ (sto_bp_sum_total_resultmaskentryproduct) = 0) /\ (sto_bn_sum_total_resultmaskentryproduct) = S ge_signed_half_sum_total_resultmaskentryproductright))) /\ ((((((dc_value_sum_total_resultmask) = 2 * (sto_cp_sum_total_resultmaskentryproduct) /\ (sto_cn_sum_total_resultmaskentryproduct) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryproductoutput. (((dc_value_sum_total_resultmask) = 2 * ge_signed_half_sum_total_resultmaskentryproductoutput + 1 /\ (sto_cp_sum_total_resultmaskentryproduct) = 0) /\ (sto_cn_sum_total_resultmaskentryproduct) = S ge_signed_half_sum_total_resultmaskentryproductoutput))) /\ ((sto_ap_sum_total_resultmaskentryproduct * sto_bp_sum_total_resultmaskentryproduct + sto_an_sum_total_resultmaskentryproduct * sto_bn_sum_total_resultmaskentryproduct) + sto_cn_sum_total_resultmaskentryproduct = (sto_ap_sum_total_resultmaskentryproduct * sto_bn_sum_total_resultmaskentryproduct + sto_an_sum_total_resultmaskentryproduct * sto_bp_sum_total_resultmaskentryproduct) + sto_cp_sum_total_resultmaskentryproduct))))))))))))))) \/ ((((dc_index_sum_total_resultmask)=0 \/ ~(exists pvs_factor_sum_total_resultmaskentrynondivisor. (n) = (dc_index_sum_total_resultmask) * pvs_factor_sum_total_resultmaskentrynondivisor)) /\ ((dc_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. (((dc_mask_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)))))))))))))

dirichlet_convolution_table_commutative · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F G H. (((exists dst_positive_code_table_commutative_sourceleft dst_positive_scale_table_commutative_sourceleft dst_negative_code_table_commutative_sourceleft dst_negative_scale_table_commutative_sourceleft. (((F) = (((((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) * S ((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) + ((dst_positive_scale_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft))) + (((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)))) * S ((((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) * S ((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) + ((dst_positive_scale_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft))) + (((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)))) + ((((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft))) + (((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)))))) /\ (forall dst_index_table_commutative_sourceleft. (exists pvs_le_gap_table_commutative_sourceleftdomain. pvs_le_gap_table_commutative_sourceleftdomain + (dst_index_table_commutative_sourceleft) = (N)) -> exists dst_positive_table_commutative_sourceleft dst_negative_table_commutative_sourceleft dst_value_table_commutative_sourceleft. ((((exists ff_h_pvs_table_commutative_sourceleftentrypositive. ff_h_pvs_table_commutative_sourceleftentrypositive + S (dst_positive_table_commutative_sourceleft) = S ((S (dst_index_table_commutative_sourceleft)) * dst_positive_scale_table_commutative_sourceleft)) /\ exists ff_q_pvs_table_commutative_sourceleftentrypositive. dst_positive_code_table_commutative_sourceleft = ff_q_pvs_table_commutative_sourceleftentrypositive * S ((S (dst_index_table_commutative_sourceleft)) * dst_positive_scale_table_commutative_sourceleft) + (dst_positive_table_commutative_sourceleft))) /\ (((((exists ff_h_pvs_table_commutative_sourceleftentrynegative. ff_h_pvs_table_commutative_sourceleftentrynegative + S (dst_negative_table_commutative_sourceleft) = S ((S (dst_index_table_commutative_sourceleft)) * dst_negative_scale_table_commutative_sourceleft)) /\ exists ff_q_pvs_table_commutative_sourceleftentrynegative. dst_negative_code_table_commutative_sourceleft = ff_q_pvs_table_commutative_sourceleftentrynegative * S ((S (dst_index_table_commutative_sourceleft)) * dst_negative_scale_table_commutative_sourceleft) + (dst_negative_table_commutative_sourceleft))) /\ (exists ge_balance_positive_table_commutative_sourceleftentryvalue ge_balance_negative_table_commutative_sourceleftentryvalue. (((((dst_value_table_commutative_sourceleft) = 2 * (ge_balance_positive_table_commutative_sourceleftentryvalue) /\ (ge_balance_negative_table_commutative_sourceleftentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourceleftentryvaluedecode. (((dst_value_table_commutative_sourceleft) = 2 * ge_signed_half_table_commutative_sourceleftentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourceleftentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourceleftentryvalue) = S ge_signed_half_table_commutative_sourceleftentryvaluedecode))) /\ ((dst_positive_table_commutative_sourceleft) + ge_balance_negative_table_commutative_sourceleftentryvalue = (dst_negative_table_commutative_sourceleft) + ge_balance_positive_table_commutative_sourceleftentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_sourceright dst_positive_scale_table_commutative_sourceright dst_negative_code_table_commutative_sourceright dst_negative_scale_table_commutative_sourceright. (((G) = (((((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) * S ((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) + ((dst_positive_scale_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright))) + (((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)))) * S ((((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) * S ((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) + ((dst_positive_scale_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright))) + (((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)))) + ((((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright))) + (((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)))))) /\ (forall dst_index_table_commutative_sourceright. (exists pvs_le_gap_table_commutative_sourcerightdomain. pvs_le_gap_table_commutative_sourcerightdomain + (dst_index_table_commutative_sourceright) = (N)) -> exists dst_positive_table_commutative_sourceright dst_negative_table_commutative_sourceright dst_value_table_commutative_sourceright. ((((exists ff_h_pvs_table_commutative_sourcerightentrypositive. ff_h_pvs_table_commutative_sourcerightentrypositive + S (dst_positive_table_commutative_sourceright) = S ((S (dst_index_table_commutative_sourceright)) * dst_positive_scale_table_commutative_sourceright)) /\ exists ff_q_pvs_table_commutative_sourcerightentrypositive. dst_positive_code_table_commutative_sourceright = ff_q_pvs_table_commutative_sourcerightentrypositive * S ((S (dst_index_table_commutative_sourceright)) * dst_positive_scale_table_commutative_sourceright) + (dst_positive_table_commutative_sourceright))) /\ (((((exists ff_h_pvs_table_commutative_sourcerightentrynegative. ff_h_pvs_table_commutative_sourcerightentrynegative + S (dst_negative_table_commutative_sourceright) = S ((S (dst_index_table_commutative_sourceright)) * dst_negative_scale_table_commutative_sourceright)) /\ exists ff_q_pvs_table_commutative_sourcerightentrynegative. dst_negative_code_table_commutative_sourceright = ff_q_pvs_table_commutative_sourcerightentrynegative * S ((S (dst_index_table_commutative_sourceright)) * dst_negative_scale_table_commutative_sourceright) + (dst_negative_table_commutative_sourceright))) /\ (exists ge_balance_positive_table_commutative_sourcerightentryvalue ge_balance_negative_table_commutative_sourcerightentryvalue. (((((dst_value_table_commutative_sourceright) = 2 * (ge_balance_positive_table_commutative_sourcerightentryvalue) /\ (ge_balance_negative_table_commutative_sourcerightentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcerightentryvaluedecode. (((dst_value_table_commutative_sourceright) = 2 * ge_signed_half_table_commutative_sourcerightentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcerightentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcerightentryvalue) = S ge_signed_half_table_commutative_sourcerightentryvaluedecode))) /\ ((dst_positive_table_commutative_sourceright) + ge_balance_negative_table_commutative_sourcerightentryvalue = (dst_negative_table_commutative_sourceright) + ge_balance_positive_table_commutative_sourcerightentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_sourcetable dst_positive_scale_table_commutative_sourcetable dst_negative_code_table_commutative_sourcetable dst_negative_scale_table_commutative_sourcetable. (((H) = (((((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) * S ((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) + ((dst_positive_scale_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable))) + (((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)))) * S ((((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) * S ((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) + ((dst_positive_scale_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable))) + (((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)))) + ((((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable))) + (((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)))))) /\ (forall dst_index_table_commutative_sourcetable. (exists pvs_le_gap_table_commutative_sourcetabledomain. pvs_le_gap_table_commutative_sourcetabledomain + (dst_index_table_commutative_sourcetable) = (N)) -> exists dst_positive_table_commutative_sourcetable dst_negative_table_commutative_sourcetable dst_value_table_commutative_sourcetable. ((((exists ff_h_pvs_table_commutative_sourcetableentrypositive. ff_h_pvs_table_commutative_sourcetableentrypositive + S (dst_positive_table_commutative_sourcetable) = S ((S (dst_index_table_commutative_sourcetable)) * dst_positive_scale_table_commutative_sourcetable)) /\ exists ff_q_pvs_table_commutative_sourcetableentrypositive. dst_positive_code_table_commutative_sourcetable = ff_q_pvs_table_commutative_sourcetableentrypositive * S ((S (dst_index_table_commutative_sourcetable)) * dst_positive_scale_table_commutative_sourcetable) + (dst_positive_table_commutative_sourcetable))) /\ (((((exists ff_h_pvs_table_commutative_sourcetableentrynegative. ff_h_pvs_table_commutative_sourcetableentrynegative + S (dst_negative_table_commutative_sourcetable) = S ((S (dst_index_table_commutative_sourcetable)) * dst_negative_scale_table_commutative_sourcetable)) /\ exists ff_q_pvs_table_commutative_sourcetableentrynegative. dst_negative_code_table_commutative_sourcetable = ff_q_pvs_table_commutative_sourcetableentrynegative * S ((S (dst_index_table_commutative_sourcetable)) * dst_negative_scale_table_commutative_sourcetable) + (dst_negative_table_commutative_sourcetable))) /\ (exists ge_balance_positive_table_commutative_sourcetableentryvalue ge_balance_negative_table_commutative_sourcetableentryvalue. (((((dst_value_table_commutative_sourcetable) = 2 * (ge_balance_positive_table_commutative_sourcetableentryvalue) /\ (ge_balance_negative_table_commutative_sourcetableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcetableentryvaluedecode. (((dst_value_table_commutative_sourcetable) = 2 * ge_signed_half_table_commutative_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcetableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcetableentryvalue) = S ge_signed_half_table_commutative_sourcetableentryvaluedecode))) /\ ((dst_positive_table_commutative_sourcetable) + ge_balance_negative_table_commutative_sourcetableentryvalue = (dst_negative_table_commutative_sourcetable) + ge_balance_positive_table_commutative_sourcetableentryvalue))))))))) /\ (forall dc_input_table_commutative_source dc_output_table_commutative_source. ~(dc_input_table_commutative_source=0) -> (exists pvs_le_gap_table_commutative_sourcedomain. pvs_le_gap_table_commutative_sourcedomain + (dc_input_table_commutative_source) = (N)) -> (exists dst_positive_code_table_commutative_sourcelookup dst_positive_scale_table_commutative_sourcelookup dst_negative_code_table_commutative_sourcelookup dst_negative_scale_table_commutative_sourcelookup dst_positive_table_commutative_sourcelookup dst_negative_table_commutative_sourcelookup. (((H) = (((((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) * S ((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) + ((dst_positive_scale_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup))) + (((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)))) * S ((((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) * S ((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) + ((dst_positive_scale_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup))) + (((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)))) + ((((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup))) + (((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcelookuppositive. ff_h_pvs_table_commutative_sourcelookuppositive + S (dst_positive_table_commutative_sourcelookup) = S ((S (dc_input_table_commutative_source)) * dst_positive_scale_table_commutative_sourcelookup)) /\ exists ff_q_pvs_table_commutative_sourcelookuppositive. dst_positive_code_table_commutative_sourcelookup = ff_q_pvs_table_commutative_sourcelookuppositive * S ((S (dc_input_table_commutative_source)) * dst_positive_scale_table_commutative_sourcelookup) + (dst_positive_table_commutative_sourcelookup))) /\ (((((exists ff_h_pvs_table_commutative_sourcelookupnegative. ff_h_pvs_table_commutative_sourcelookupnegative + S (dst_negative_table_commutative_sourcelookup) = S ((S (dc_input_table_commutative_source)) * dst_negative_scale_table_commutative_sourcelookup)) /\ exists ff_q_pvs_table_commutative_sourcelookupnegative. dst_negative_code_table_commutative_sourcelookup = ff_q_pvs_table_commutative_sourcelookupnegative * S ((S (dc_input_table_commutative_source)) * dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_table_commutative_sourcelookup))) /\ (exists ge_balance_positive_table_commutative_sourcelookupvalue ge_balance_negative_table_commutative_sourcelookupvalue. (((((dc_output_table_commutative_source) = 2 * (ge_balance_positive_table_commutative_sourcelookupvalue) /\ (ge_balance_negative_table_commutative_sourcelookupvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcelookupvaluedecode. (((dc_output_table_commutative_source) = 2 * ge_signed_half_table_commutative_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcelookupvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcelookupvalue) = S ge_signed_half_table_commutative_sourcelookupvaluedecode))) /\ ((dst_positive_table_commutative_sourcelookup) + ge_balance_negative_table_commutative_sourcelookupvalue = (dst_negative_table_commutative_sourcelookup) + ge_balance_positive_table_commutative_sourcelookupvalue))))))))) -> (((~((dc_input_table_commutative_source)=0)) /\ (exists dc_mask_table_commutative_sourcevalue. ((((exists dst_positive_code_table_commutative_sourcevaluemasktable dst_positive_scale_table_commutative_sourcevaluemasktable dst_negative_code_table_commutative_sourcevaluemasktable dst_negative_scale_table_commutative_sourcevaluemasktable. (((dc_mask_table_commutative_sourcevalue) = (((((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) * S ((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) + ((dst_positive_scale_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable))) + (((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)))) * S ((((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) * S ((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) + ((dst_positive_scale_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable))) + (((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)))) + ((((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable))) + (((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)))))) /\ (forall dst_index_table_commutative_sourcevaluemasktable. (exists pvs_le_gap_table_commutative_sourcevaluemasktabledomain. pvs_le_gap_table_commutative_sourcevaluemasktabledomain + (dst_index_table_commutative_sourcevaluemasktable) = (dc_input_table_commutative_source)) -> exists dst_positive_table_commutative_sourcevaluemasktable dst_negative_table_commutative_sourcevaluemasktable dst_value_table_commutative_sourcevaluemasktable. ((((exists ff_h_pvs_table_commutative_sourcevaluemasktableentrypositive. ff_h_pvs_table_commutative_sourcevaluemasktableentrypositive + S (dst_positive_table_commutative_sourcevaluemasktable) = S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_positive_scale_table_commutative_sourcevaluemasktable)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasktableentrypositive. dst_positive_code_table_commutative_sourcevaluemasktable = ff_q_pvs_table_commutative_sourcevaluemasktableentrypositive * S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_positive_scale_table_commutative_sourcevaluemasktable) + (dst_positive_table_commutative_sourcevaluemasktable))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemasktableentrynegative. ff_h_pvs_table_commutative_sourcevaluemasktableentrynegative + S (dst_negative_table_commutative_sourcevaluemasktable) = S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_negative_scale_table_commutative_sourcevaluemasktable)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasktableentrynegative. dst_negative_code_table_commutative_sourcevaluemasktable = ff_q_pvs_table_commutative_sourcevaluemasktableentrynegative * S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_table_commutative_sourcevaluemasktable))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue. (((((dst_value_table_commutative_sourcevaluemasktable) = 2 * (ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemasktableentryvaluedecode. (((dst_value_table_commutative_sourcevaluemasktable) = 2 * ge_signed_half_table_commutative_sourcevaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue) = S ge_signed_half_table_commutative_sourcevaluemasktableentryvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemasktable) + ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue = (dst_negative_table_commutative_sourcevaluemasktable) + ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue))))))))) /\ (forall dc_index_table_commutative_sourcevaluemask dc_value_table_commutative_sourcevaluemask. (exists pvs_le_gap_table_commutative_sourcevaluemaskdomain. pvs_le_gap_table_commutative_sourcevaluemaskdomain + (dc_index_table_commutative_sourcevaluemask) = (dc_input_table_commutative_source)) -> (exists dst_positive_code_table_commutative_sourcevaluemasklookup dst_positive_scale_table_commutative_sourcevaluemasklookup dst_negative_code_table_commutative_sourcevaluemasklookup dst_negative_scale_table_commutative_sourcevaluemasklookup dst_positive_table_commutative_sourcevaluemasklookup dst_negative_table_commutative_sourcevaluemasklookup. (((dc_mask_table_commutative_sourcevalue) = (((((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) + ((dst_positive_scale_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup))) + (((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)))) * S ((((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) + ((dst_positive_scale_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup))) + (((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)))) + ((((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup))) + (((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemasklookuppositive. ff_h_pvs_table_commutative_sourcevaluemasklookuppositive + S (dst_positive_table_commutative_sourcevaluemasklookup) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasklookuppositive. dst_positive_code_table_commutative_sourcevaluemasklookup = ff_q_pvs_table_commutative_sourcevaluemasklookuppositive * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemasklookup) + (dst_positive_table_commutative_sourcevaluemasklookup))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemasklookupnegative. ff_h_pvs_table_commutative_sourcevaluemasklookupnegative + S (dst_negative_table_commutative_sourcevaluemasklookup) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasklookupnegative. dst_negative_code_table_commutative_sourcevaluemasklookup = ff_q_pvs_table_commutative_sourcevaluemasklookupnegative * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_table_commutative_sourcevaluemasklookup))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemasklookupvalue ge_balance_negative_table_commutative_sourcevaluemasklookupvalue. (((((dc_value_table_commutative_sourcevaluemask) = 2 * (ge_balance_positive_table_commutative_sourcevaluemasklookupvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemasklookupvaluedecode. (((dc_value_table_commutative_sourcevaluemask) = 2 * ge_signed_half_table_commutative_sourcevaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemasklookupvalue) = S ge_signed_half_table_commutative_sourcevaluemasklookupvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemasklookup) + ge_balance_negative_table_commutative_sourcevaluemasklookupvalue = (dst_negative_table_commutative_sourcevaluemasklookup) + ge_balance_positive_table_commutative_sourcevaluemasklookupvalue))))))))) -> ((((~((dc_index_table_commutative_sourcevaluemask)=0)) /\ (exists dc_quotient_table_commutative_sourcevaluemaskentry dc_left_table_commutative_sourcevaluemaskentry dc_right_table_commutative_sourcevaluemaskentry. (((dc_input_table_commutative_source)=(dc_index_table_commutative_sourcevaluemask)*dc_quotient_table_commutative_sourcevaluemaskentry) /\ (((exists dst_positive_code_table_commutative_sourcevaluemaskentryleft dst_positive_scale_table_commutative_sourcevaluemaskentryleft dst_negative_code_table_commutative_sourcevaluemaskentryleft dst_negative_scale_table_commutative_sourcevaluemaskentryleft dst_positive_table_commutative_sourcevaluemaskentryleft dst_negative_table_commutative_sourcevaluemaskentryleft. (((F) = (((((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)))) * S ((((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)))) + ((((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryleftpositive. ff_h_pvs_table_commutative_sourcevaluemaskentryleftpositive + S (dst_positive_table_commutative_sourcevaluemaskentryleft) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryleftpositive. dst_positive_code_table_commutative_sourcevaluemaskentryleft = ff_q_pvs_table_commutative_sourcevaluemaskentryleftpositive * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemaskentryleft) + (dst_positive_table_commutative_sourcevaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryleftnegative. ff_h_pvs_table_commutative_sourcevaluemaskentryleftnegative + S (dst_negative_table_commutative_sourcevaluemaskentryleft) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryleftnegative. dst_negative_code_table_commutative_sourcevaluemaskentryleft = ff_q_pvs_table_commutative_sourcevaluemaskentryleftnegative * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_table_commutative_sourcevaluemaskentryleft))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue. (((((dc_left_table_commutative_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryleftvaluedecode. (((dc_left_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue) = S ge_signed_half_table_commutative_sourcevaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemaskentryleft) + ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue = (dst_negative_table_commutative_sourcevaluemaskentryleft) + ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_commutative_sourcevaluemaskentryright dst_positive_scale_table_commutative_sourcevaluemaskentryright dst_negative_code_table_commutative_sourcevaluemaskentryright dst_negative_scale_table_commutative_sourcevaluemaskentryright dst_positive_table_commutative_sourcevaluemaskentryright dst_negative_table_commutative_sourcevaluemaskentryright. (((G) = (((((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)))) * S ((((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)))) + ((((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryrightpositive. ff_h_pvs_table_commutative_sourcevaluemaskentryrightpositive + S (dst_positive_table_commutative_sourcevaluemaskentryright) = S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_positive_scale_table_commutative_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryrightpositive. dst_positive_code_table_commutative_sourcevaluemaskentryright = ff_q_pvs_table_commutative_sourcevaluemaskentryrightpositive * S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_positive_scale_table_commutative_sourcevaluemaskentryright) + (dst_positive_table_commutative_sourcevaluemaskentryright))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryrightnegative. ff_h_pvs_table_commutative_sourcevaluemaskentryrightnegative + S (dst_negative_table_commutative_sourcevaluemaskentryright) = S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_negative_scale_table_commutative_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryrightnegative. dst_negative_code_table_commutative_sourcevaluemaskentryright = ff_q_pvs_table_commutative_sourcevaluemaskentryrightnegative * S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_table_commutative_sourcevaluemaskentryright))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue. (((((dc_right_table_commutative_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryrightvaluedecode. (((dc_right_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue) = S ge_signed_half_table_commutative_sourcevaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemaskentryright) + ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue = (dst_negative_table_commutative_sourcevaluemaskentryright) + ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_commutative_sourcevaluemaskentryproduct sto_an_table_commutative_sourcevaluemaskentryproduct sto_bp_table_commutative_sourcevaluemaskentryproduct sto_bn_table_commutative_sourcevaluemaskentryproduct sto_cp_table_commutative_sourcevaluemaskentryproduct sto_cn_table_commutative_sourcevaluemaskentryproduct. (((((dc_left_table_commutative_sourcevaluemaskentry) = 2 * (sto_ap_table_commutative_sourcevaluemaskentryproduct) /\ (sto_an_table_commutative_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryproductleft. (((dc_left_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryproductleft + 1 /\ (sto_ap_table_commutative_sourcevaluemaskentryproduct) = 0) /\ (sto_an_table_commutative_sourcevaluemaskentryproduct) = S ge_signed_half_table_commutative_sourcevaluemaskentryproductleft))) /\ ((((((dc_right_table_commutative_sourcevaluemaskentry) = 2 * (sto_bp_table_commutative_sourcevaluemaskentryproduct) /\ (sto_bn_table_commutative_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryproductright. (((dc_right_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryproductright + 1 /\ (sto_bp_table_commutative_sourcevaluemaskentryproduct) = 0) /\ (sto_bn_table_commutative_sourcevaluemaskentryproduct) = S ge_signed_half_table_commutative_sourcevaluemaskentryproductright))) /\ ((((((dc_value_table_commutative_sourcevaluemask) = 2 * (sto_cp_table_commutative_sourcevaluemaskentryproduct) /\ (sto_cn_table_commutative_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryproductoutput. (((dc_value_table_commutative_sourcevaluemask) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryproductoutput + 1 /\ (sto_cp_table_commutative_sourcevaluemaskentryproduct) = 0) /\ (sto_cn_table_commutative_sourcevaluemaskentryproduct) = S ge_signed_half_table_commutative_sourcevaluemaskentryproductoutput))) /\ ((sto_ap_table_commutative_sourcevaluemaskentryproduct * sto_bp_table_commutative_sourcevaluemaskentryproduct + sto_an_table_commutative_sourcevaluemaskentryproduct * sto_bn_table_commutative_sourcevaluemaskentryproduct) + sto_cn_table_commutative_sourcevaluemaskentryproduct = (sto_ap_table_commutative_sourcevaluemaskentryproduct * sto_bn_table_commutative_sourcevaluemaskentryproduct + sto_an_table_commutative_sourcevaluemaskentryproduct * sto_bp_table_commutative_sourcevaluemaskentryproduct) + sto_cp_table_commutative_sourcevaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_commutative_sourcevaluemask)=0 \/ ~(exists pvs_factor_table_commutative_sourcevaluemaskentrynondivisor. (dc_input_table_commutative_source) = (dc_index_table_commutative_sourcevaluemask) * pvs_factor_table_commutative_sourcevaluemaskentrynondivisor)) /\ ((dc_value_table_commutative_sourcevaluemask)=0))))))) /\ (exists dst_positive_code_table_commutative_sourcevaluefold dst_positive_scale_table_commutative_sourcevaluefold dst_negative_code_table_commutative_sourcevaluefold dst_negative_scale_table_commutative_sourcevaluefold dst_positive_sum_table_commutative_sourcevaluefold dst_negative_sum_table_commutative_sourcevaluefold. (((dc_mask_table_commutative_sourcevalue) = (((((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) * S ((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) + ((dst_positive_scale_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold))) + (((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)))) * S ((((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) * S ((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) + ((dst_positive_scale_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold))) + (((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)))) + ((((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold))) + (((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)))))) /\ (((exists fs_u_dst_table_commutative_sourcevaluefoldpositive fs_v_dst_table_commutative_sourcevaluefoldpositive. ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_start. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_start. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_terminal. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_terminal + S (dst_positive_sum_table_commutative_sourcevaluefold) = S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_terminal. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_terminal * S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (dst_positive_sum_table_commutative_sourcevaluefold))) /\ forall fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps. (exists fs_lt_dst_table_commutative_sourcevaluefoldpositive_body_steps_bound. fs_lt_dst_table_commutative_sourcevaluefoldpositive_body_steps_bound + S fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps = S (dc_input_table_commutative_source)) -> exists fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps. ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand + S (fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_sourcevaluefold)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand. dst_positive_code_table_commutative_sourcevaluefold = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_sourcevaluefold) + (fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial + S (fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor + S (fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps))) /\ fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps = fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps + fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_commutative_sourcevaluefoldnegative fs_v_dst_table_commutative_sourcevaluefoldnegative. ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_start. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_start. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_terminal. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_terminal + S (dst_negative_sum_table_commutative_sourcevaluefold) = S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_terminal. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_terminal * S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (dst_negative_sum_table_commutative_sourcevaluefold))) /\ forall fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps. (exists fs_lt_dst_table_commutative_sourcevaluefoldnegative_body_steps_bound. fs_lt_dst_table_commutative_sourcevaluefoldnegative_body_steps_bound + S fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps = S (dc_input_table_commutative_source)) -> exists fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps. ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand + S (fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_sourcevaluefold)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand. dst_negative_code_table_commutative_sourcevaluefold = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_sourcevaluefold) + (fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial + S (fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor + S (fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps))) /\ fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps = fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps + fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_commutative_sourcevaluefoldresult ge_balance_negative_table_commutative_sourcevaluefoldresult. (((((dc_output_table_commutative_source) = 2 * (ge_balance_positive_table_commutative_sourcevaluefoldresult) /\ (ge_balance_negative_table_commutative_sourcevaluefoldresult) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluefoldresultdecode. (((dc_output_table_commutative_source) = 2 * ge_signed_half_table_commutative_sourcevaluefoldresultdecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluefoldresult) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluefoldresult) = S ge_signed_half_table_commutative_sourcevaluefoldresultdecode))) /\ ((dst_positive_sum_table_commutative_sourcevaluefold) + ge_balance_negative_table_commutative_sourcevaluefoldresult = (dst_negative_sum_table_commutative_sourcevaluefold) + ge_balance_positive_table_commutative_sourcevaluefoldresult)))))))))))))))))))) -> (((exists dst_positive_code_table_commutative_resultleft dst_positive_scale_table_commutative_resultleft dst_negative_code_table_commutative_resultleft dst_negative_scale_table_commutative_resultleft. (((G) = (((((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) * S ((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) + ((dst_positive_scale_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft))) + (((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)))) * S ((((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) * S ((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) + ((dst_positive_scale_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft))) + (((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)))) + ((((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft))) + (((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)))))) /\ (forall dst_index_table_commutative_resultleft. (exists pvs_le_gap_table_commutative_resultleftdomain. pvs_le_gap_table_commutative_resultleftdomain + (dst_index_table_commutative_resultleft) = (N)) -> exists dst_positive_table_commutative_resultleft dst_negative_table_commutative_resultleft dst_value_table_commutative_resultleft. ((((exists ff_h_pvs_table_commutative_resultleftentrypositive. ff_h_pvs_table_commutative_resultleftentrypositive + S (dst_positive_table_commutative_resultleft) = S ((S (dst_index_table_commutative_resultleft)) * dst_positive_scale_table_commutative_resultleft)) /\ exists ff_q_pvs_table_commutative_resultleftentrypositive. dst_positive_code_table_commutative_resultleft = ff_q_pvs_table_commutative_resultleftentrypositive * S ((S (dst_index_table_commutative_resultleft)) * dst_positive_scale_table_commutative_resultleft) + (dst_positive_table_commutative_resultleft))) /\ (((((exists ff_h_pvs_table_commutative_resultleftentrynegative. ff_h_pvs_table_commutative_resultleftentrynegative + S (dst_negative_table_commutative_resultleft) = S ((S (dst_index_table_commutative_resultleft)) * dst_negative_scale_table_commutative_resultleft)) /\ exists ff_q_pvs_table_commutative_resultleftentrynegative. dst_negative_code_table_commutative_resultleft = ff_q_pvs_table_commutative_resultleftentrynegative * S ((S (dst_index_table_commutative_resultleft)) * dst_negative_scale_table_commutative_resultleft) + (dst_negative_table_commutative_resultleft))) /\ (exists ge_balance_positive_table_commutative_resultleftentryvalue ge_balance_negative_table_commutative_resultleftentryvalue. (((((dst_value_table_commutative_resultleft) = 2 * (ge_balance_positive_table_commutative_resultleftentryvalue) /\ (ge_balance_negative_table_commutative_resultleftentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resultleftentryvaluedecode. (((dst_value_table_commutative_resultleft) = 2 * ge_signed_half_table_commutative_resultleftentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultleftentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resultleftentryvalue) = S ge_signed_half_table_commutative_resultleftentryvaluedecode))) /\ ((dst_positive_table_commutative_resultleft) + ge_balance_negative_table_commutative_resultleftentryvalue = (dst_negative_table_commutative_resultleft) + ge_balance_positive_table_commutative_resultleftentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_resultright dst_positive_scale_table_commutative_resultright dst_negative_code_table_commutative_resultright dst_negative_scale_table_commutative_resultright. (((F) = (((((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) * S ((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) + ((dst_positive_scale_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright))) + (((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)))) * S ((((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) * S ((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) + ((dst_positive_scale_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright))) + (((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)))) + ((((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright))) + (((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)))))) /\ (forall dst_index_table_commutative_resultright. (exists pvs_le_gap_table_commutative_resultrightdomain. pvs_le_gap_table_commutative_resultrightdomain + (dst_index_table_commutative_resultright) = (N)) -> exists dst_positive_table_commutative_resultright dst_negative_table_commutative_resultright dst_value_table_commutative_resultright. ((((exists ff_h_pvs_table_commutative_resultrightentrypositive. ff_h_pvs_table_commutative_resultrightentrypositive + S (dst_positive_table_commutative_resultright) = S ((S (dst_index_table_commutative_resultright)) * dst_positive_scale_table_commutative_resultright)) /\ exists ff_q_pvs_table_commutative_resultrightentrypositive. dst_positive_code_table_commutative_resultright = ff_q_pvs_table_commutative_resultrightentrypositive * S ((S (dst_index_table_commutative_resultright)) * dst_positive_scale_table_commutative_resultright) + (dst_positive_table_commutative_resultright))) /\ (((((exists ff_h_pvs_table_commutative_resultrightentrynegative. ff_h_pvs_table_commutative_resultrightentrynegative + S (dst_negative_table_commutative_resultright) = S ((S (dst_index_table_commutative_resultright)) * dst_negative_scale_table_commutative_resultright)) /\ exists ff_q_pvs_table_commutative_resultrightentrynegative. dst_negative_code_table_commutative_resultright = ff_q_pvs_table_commutative_resultrightentrynegative * S ((S (dst_index_table_commutative_resultright)) * dst_negative_scale_table_commutative_resultright) + (dst_negative_table_commutative_resultright))) /\ (exists ge_balance_positive_table_commutative_resultrightentryvalue ge_balance_negative_table_commutative_resultrightentryvalue. (((((dst_value_table_commutative_resultright) = 2 * (ge_balance_positive_table_commutative_resultrightentryvalue) /\ (ge_balance_negative_table_commutative_resultrightentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resultrightentryvaluedecode. (((dst_value_table_commutative_resultright) = 2 * ge_signed_half_table_commutative_resultrightentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultrightentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resultrightentryvalue) = S ge_signed_half_table_commutative_resultrightentryvaluedecode))) /\ ((dst_positive_table_commutative_resultright) + ge_balance_negative_table_commutative_resultrightentryvalue = (dst_negative_table_commutative_resultright) + ge_balance_positive_table_commutative_resultrightentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_resulttable dst_positive_scale_table_commutative_resulttable dst_negative_code_table_commutative_resulttable dst_negative_scale_table_commutative_resulttable. (((H) = (((((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) * S ((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) + ((dst_positive_scale_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable))) + (((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)))) * S ((((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) * S ((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) + ((dst_positive_scale_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable))) + (((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)))) + ((((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable))) + (((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)))))) /\ (forall dst_index_table_commutative_resulttable. (exists pvs_le_gap_table_commutative_resulttabledomain. pvs_le_gap_table_commutative_resulttabledomain + (dst_index_table_commutative_resulttable) = (N)) -> exists dst_positive_table_commutative_resulttable dst_negative_table_commutative_resulttable dst_value_table_commutative_resulttable. ((((exists ff_h_pvs_table_commutative_resulttableentrypositive. ff_h_pvs_table_commutative_resulttableentrypositive + S (dst_positive_table_commutative_resulttable) = S ((S (dst_index_table_commutative_resulttable)) * dst_positive_scale_table_commutative_resulttable)) /\ exists ff_q_pvs_table_commutative_resulttableentrypositive. dst_positive_code_table_commutative_resulttable = ff_q_pvs_table_commutative_resulttableentrypositive * S ((S (dst_index_table_commutative_resulttable)) * dst_positive_scale_table_commutative_resulttable) + (dst_positive_table_commutative_resulttable))) /\ (((((exists ff_h_pvs_table_commutative_resulttableentrynegative. ff_h_pvs_table_commutative_resulttableentrynegative + S (dst_negative_table_commutative_resulttable) = S ((S (dst_index_table_commutative_resulttable)) * dst_negative_scale_table_commutative_resulttable)) /\ exists ff_q_pvs_table_commutative_resulttableentrynegative. dst_negative_code_table_commutative_resulttable = ff_q_pvs_table_commutative_resulttableentrynegative * S ((S (dst_index_table_commutative_resulttable)) * dst_negative_scale_table_commutative_resulttable) + (dst_negative_table_commutative_resulttable))) /\ (exists ge_balance_positive_table_commutative_resulttableentryvalue ge_balance_negative_table_commutative_resulttableentryvalue. (((((dst_value_table_commutative_resulttable) = 2 * (ge_balance_positive_table_commutative_resulttableentryvalue) /\ (ge_balance_negative_table_commutative_resulttableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resulttableentryvaluedecode. (((dst_value_table_commutative_resulttable) = 2 * ge_signed_half_table_commutative_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resulttableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resulttableentryvalue) = S ge_signed_half_table_commutative_resulttableentryvaluedecode))) /\ ((dst_positive_table_commutative_resulttable) + ge_balance_negative_table_commutative_resulttableentryvalue = (dst_negative_table_commutative_resulttable) + ge_balance_positive_table_commutative_resulttableentryvalue))))))))) /\ (forall dc_input_table_commutative_result dc_output_table_commutative_result. ~(dc_input_table_commutative_result=0) -> (exists pvs_le_gap_table_commutative_resultdomain. pvs_le_gap_table_commutative_resultdomain + (dc_input_table_commutative_result) = (N)) -> (exists dst_positive_code_table_commutative_resultlookup dst_positive_scale_table_commutative_resultlookup dst_negative_code_table_commutative_resultlookup dst_negative_scale_table_commutative_resultlookup dst_positive_table_commutative_resultlookup dst_negative_table_commutative_resultlookup. (((H) = (((((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) * S ((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) + ((dst_positive_scale_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup))) + (((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)))) * S ((((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) * S ((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) + ((dst_positive_scale_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup))) + (((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)))) + ((((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup))) + (((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)))))) /\ (((((exists ff_h_pvs_table_commutative_resultlookuppositive. ff_h_pvs_table_commutative_resultlookuppositive + S (dst_positive_table_commutative_resultlookup) = S ((S (dc_input_table_commutative_result)) * dst_positive_scale_table_commutative_resultlookup)) /\ exists ff_q_pvs_table_commutative_resultlookuppositive. dst_positive_code_table_commutative_resultlookup = ff_q_pvs_table_commutative_resultlookuppositive * S ((S (dc_input_table_commutative_result)) * dst_positive_scale_table_commutative_resultlookup) + (dst_positive_table_commutative_resultlookup))) /\ (((((exists ff_h_pvs_table_commutative_resultlookupnegative. ff_h_pvs_table_commutative_resultlookupnegative + S (dst_negative_table_commutative_resultlookup) = S ((S (dc_input_table_commutative_result)) * dst_negative_scale_table_commutative_resultlookup)) /\ exists ff_q_pvs_table_commutative_resultlookupnegative. dst_negative_code_table_commutative_resultlookup = ff_q_pvs_table_commutative_resultlookupnegative * S ((S (dc_input_table_commutative_result)) * dst_negative_scale_table_commutative_resultlookup) + (dst_negative_table_commutative_resultlookup))) /\ (exists ge_balance_positive_table_commutative_resultlookupvalue ge_balance_negative_table_commutative_resultlookupvalue. (((((dc_output_table_commutative_result) = 2 * (ge_balance_positive_table_commutative_resultlookupvalue) /\ (ge_balance_negative_table_commutative_resultlookupvalue) = 0) \/ exists ge_signed_half_table_commutative_resultlookupvaluedecode. (((dc_output_table_commutative_result) = 2 * ge_signed_half_table_commutative_resultlookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultlookupvalue) = 0) /\ (ge_balance_negative_table_commutative_resultlookupvalue) = S ge_signed_half_table_commutative_resultlookupvaluedecode))) /\ ((dst_positive_table_commutative_resultlookup) + ge_balance_negative_table_commutative_resultlookupvalue = (dst_negative_table_commutative_resultlookup) + ge_balance_positive_table_commutative_resultlookupvalue))))))))) -> (((~((dc_input_table_commutative_result)=0)) /\ (exists dc_mask_table_commutative_resultvalue. ((((exists dst_positive_code_table_commutative_resultvaluemasktable dst_positive_scale_table_commutative_resultvaluemasktable dst_negative_code_table_commutative_resultvaluemasktable dst_negative_scale_table_commutative_resultvaluemasktable. (((dc_mask_table_commutative_resultvalue) = (((((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) * S ((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) + ((dst_positive_scale_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable))) + (((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)))) * S ((((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) * S ((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) + ((dst_positive_scale_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable))) + (((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)))) + ((((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable))) + (((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)))))) /\ (forall dst_index_table_commutative_resultvaluemasktable. (exists pvs_le_gap_table_commutative_resultvaluemasktabledomain. pvs_le_gap_table_commutative_resultvaluemasktabledomain + (dst_index_table_commutative_resultvaluemasktable) = (dc_input_table_commutative_result)) -> exists dst_positive_table_commutative_resultvaluemasktable dst_negative_table_commutative_resultvaluemasktable dst_value_table_commutative_resultvaluemasktable. ((((exists ff_h_pvs_table_commutative_resultvaluemasktableentrypositive. ff_h_pvs_table_commutative_resultvaluemasktableentrypositive + S (dst_positive_table_commutative_resultvaluemasktable) = S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_positive_scale_table_commutative_resultvaluemasktable)) /\ exists ff_q_pvs_table_commutative_resultvaluemasktableentrypositive. dst_positive_code_table_commutative_resultvaluemasktable = ff_q_pvs_table_commutative_resultvaluemasktableentrypositive * S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_positive_scale_table_commutative_resultvaluemasktable) + (dst_positive_table_commutative_resultvaluemasktable))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemasktableentrynegative. ff_h_pvs_table_commutative_resultvaluemasktableentrynegative + S (dst_negative_table_commutative_resultvaluemasktable) = S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_negative_scale_table_commutative_resultvaluemasktable)) /\ exists ff_q_pvs_table_commutative_resultvaluemasktableentrynegative. dst_negative_code_table_commutative_resultvaluemasktable = ff_q_pvs_table_commutative_resultvaluemasktableentrynegative * S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_table_commutative_resultvaluemasktable))) /\ (exists ge_balance_positive_table_commutative_resultvaluemasktableentryvalue ge_balance_negative_table_commutative_resultvaluemasktableentryvalue. (((((dst_value_table_commutative_resultvaluemasktable) = 2 * (ge_balance_positive_table_commutative_resultvaluemasktableentryvalue) /\ (ge_balance_negative_table_commutative_resultvaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemasktableentryvaluedecode. (((dst_value_table_commutative_resultvaluemasktable) = 2 * ge_signed_half_table_commutative_resultvaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemasktableentryvalue) = S ge_signed_half_table_commutative_resultvaluemasktableentryvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemasktable) + ge_balance_negative_table_commutative_resultvaluemasktableentryvalue = (dst_negative_table_commutative_resultvaluemasktable) + ge_balance_positive_table_commutative_resultvaluemasktableentryvalue))))))))) /\ (forall dc_index_table_commutative_resultvaluemask dc_value_table_commutative_resultvaluemask. (exists pvs_le_gap_table_commutative_resultvaluemaskdomain. pvs_le_gap_table_commutative_resultvaluemaskdomain + (dc_index_table_commutative_resultvaluemask) = (dc_input_table_commutative_result)) -> (exists dst_positive_code_table_commutative_resultvaluemasklookup dst_positive_scale_table_commutative_resultvaluemasklookup dst_negative_code_table_commutative_resultvaluemasklookup dst_negative_scale_table_commutative_resultvaluemasklookup dst_positive_table_commutative_resultvaluemasklookup dst_negative_table_commutative_resultvaluemasklookup. (((dc_mask_table_commutative_resultvalue) = (((((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) * S ((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) + ((dst_positive_scale_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup))) + (((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)))) * S ((((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) * S ((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) + ((dst_positive_scale_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup))) + (((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)))) + ((((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup))) + (((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemasklookuppositive. ff_h_pvs_table_commutative_resultvaluemasklookuppositive + S (dst_positive_table_commutative_resultvaluemasklookup) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemasklookup)) /\ exists ff_q_pvs_table_commutative_resultvaluemasklookuppositive. dst_positive_code_table_commutative_resultvaluemasklookup = ff_q_pvs_table_commutative_resultvaluemasklookuppositive * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemasklookup) + (dst_positive_table_commutative_resultvaluemasklookup))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemasklookupnegative. ff_h_pvs_table_commutative_resultvaluemasklookupnegative + S (dst_negative_table_commutative_resultvaluemasklookup) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemasklookup)) /\ exists ff_q_pvs_table_commutative_resultvaluemasklookupnegative. dst_negative_code_table_commutative_resultvaluemasklookup = ff_q_pvs_table_commutative_resultvaluemasklookupnegative * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_table_commutative_resultvaluemasklookup))) /\ (exists ge_balance_positive_table_commutative_resultvaluemasklookupvalue ge_balance_negative_table_commutative_resultvaluemasklookupvalue. (((((dc_value_table_commutative_resultvaluemask) = 2 * (ge_balance_positive_table_commutative_resultvaluemasklookupvalue) /\ (ge_balance_negative_table_commutative_resultvaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemasklookupvaluedecode. (((dc_value_table_commutative_resultvaluemask) = 2 * ge_signed_half_table_commutative_resultvaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemasklookupvalue) = S ge_signed_half_table_commutative_resultvaluemasklookupvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemasklookup) + ge_balance_negative_table_commutative_resultvaluemasklookupvalue = (dst_negative_table_commutative_resultvaluemasklookup) + ge_balance_positive_table_commutative_resultvaluemasklookupvalue))))))))) -> ((((~((dc_index_table_commutative_resultvaluemask)=0)) /\ (exists dc_quotient_table_commutative_resultvaluemaskentry dc_left_table_commutative_resultvaluemaskentry dc_right_table_commutative_resultvaluemaskentry. (((dc_input_table_commutative_result)=(dc_index_table_commutative_resultvaluemask)*dc_quotient_table_commutative_resultvaluemaskentry) /\ (((exists dst_positive_code_table_commutative_resultvaluemaskentryleft dst_positive_scale_table_commutative_resultvaluemaskentryleft dst_negative_code_table_commutative_resultvaluemaskentryleft dst_negative_scale_table_commutative_resultvaluemaskentryleft dst_positive_table_commutative_resultvaluemaskentryleft dst_negative_table_commutative_resultvaluemaskentryleft. (((G) = (((((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft))) + (((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)))) * S ((((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft))) + (((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)))) + ((((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft))) + (((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryleftpositive. ff_h_pvs_table_commutative_resultvaluemaskentryleftpositive + S (dst_positive_table_commutative_resultvaluemaskentryleft) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryleftpositive. dst_positive_code_table_commutative_resultvaluemaskentryleft = ff_q_pvs_table_commutative_resultvaluemaskentryleftpositive * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemaskentryleft) + (dst_positive_table_commutative_resultvaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryleftnegative. ff_h_pvs_table_commutative_resultvaluemaskentryleftnegative + S (dst_negative_table_commutative_resultvaluemaskentryleft) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryleftnegative. dst_negative_code_table_commutative_resultvaluemaskentryleft = ff_q_pvs_table_commutative_resultvaluemaskentryleftnegative * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_table_commutative_resultvaluemaskentryleft))) /\ (exists ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue. (((((dc_left_table_commutative_resultvaluemaskentry) = 2 * (ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryleftvaluedecode. (((dc_left_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue) = S ge_signed_half_table_commutative_resultvaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemaskentryleft) + ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue = (dst_negative_table_commutative_resultvaluemaskentryleft) + ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_commutative_resultvaluemaskentryright dst_positive_scale_table_commutative_resultvaluemaskentryright dst_negative_code_table_commutative_resultvaluemaskentryright dst_negative_scale_table_commutative_resultvaluemaskentryright dst_positive_table_commutative_resultvaluemaskentryright dst_negative_table_commutative_resultvaluemaskentryright. (((F) = (((((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright))) + (((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)))) * S ((((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright))) + (((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)))) + ((((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright))) + (((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryrightpositive. ff_h_pvs_table_commutative_resultvaluemaskentryrightpositive + S (dst_positive_table_commutative_resultvaluemaskentryright) = S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_positive_scale_table_commutative_resultvaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryrightpositive. dst_positive_code_table_commutative_resultvaluemaskentryright = ff_q_pvs_table_commutative_resultvaluemaskentryrightpositive * S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_positive_scale_table_commutative_resultvaluemaskentryright) + (dst_positive_table_commutative_resultvaluemaskentryright))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryrightnegative. ff_h_pvs_table_commutative_resultvaluemaskentryrightnegative + S (dst_negative_table_commutative_resultvaluemaskentryright) = S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_negative_scale_table_commutative_resultvaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryrightnegative. dst_negative_code_table_commutative_resultvaluemaskentryright = ff_q_pvs_table_commutative_resultvaluemaskentryrightnegative * S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_table_commutative_resultvaluemaskentryright))) /\ (exists ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue. (((((dc_right_table_commutative_resultvaluemaskentry) = 2 * (ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryrightvaluedecode. (((dc_right_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue) = S ge_signed_half_table_commutative_resultvaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemaskentryright) + ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue = (dst_negative_table_commutative_resultvaluemaskentryright) + ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_commutative_resultvaluemaskentryproduct sto_an_table_commutative_resultvaluemaskentryproduct sto_bp_table_commutative_resultvaluemaskentryproduct sto_bn_table_commutative_resultvaluemaskentryproduct sto_cp_table_commutative_resultvaluemaskentryproduct sto_cn_table_commutative_resultvaluemaskentryproduct. (((((dc_left_table_commutative_resultvaluemaskentry) = 2 * (sto_ap_table_commutative_resultvaluemaskentryproduct) /\ (sto_an_table_commutative_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryproductleft. (((dc_left_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryproductleft + 1 /\ (sto_ap_table_commutative_resultvaluemaskentryproduct) = 0) /\ (sto_an_table_commutative_resultvaluemaskentryproduct) = S ge_signed_half_table_commutative_resultvaluemaskentryproductleft))) /\ ((((((dc_right_table_commutative_resultvaluemaskentry) = 2 * (sto_bp_table_commutative_resultvaluemaskentryproduct) /\ (sto_bn_table_commutative_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryproductright. (((dc_right_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryproductright + 1 /\ (sto_bp_table_commutative_resultvaluemaskentryproduct) = 0) /\ (sto_bn_table_commutative_resultvaluemaskentryproduct) = S ge_signed_half_table_commutative_resultvaluemaskentryproductright))) /\ ((((((dc_value_table_commutative_resultvaluemask) = 2 * (sto_cp_table_commutative_resultvaluemaskentryproduct) /\ (sto_cn_table_commutative_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryproductoutput. (((dc_value_table_commutative_resultvaluemask) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryproductoutput + 1 /\ (sto_cp_table_commutative_resultvaluemaskentryproduct) = 0) /\ (sto_cn_table_commutative_resultvaluemaskentryproduct) = S ge_signed_half_table_commutative_resultvaluemaskentryproductoutput))) /\ ((sto_ap_table_commutative_resultvaluemaskentryproduct * sto_bp_table_commutative_resultvaluemaskentryproduct + sto_an_table_commutative_resultvaluemaskentryproduct * sto_bn_table_commutative_resultvaluemaskentryproduct) + sto_cn_table_commutative_resultvaluemaskentryproduct = (sto_ap_table_commutative_resultvaluemaskentryproduct * sto_bn_table_commutative_resultvaluemaskentryproduct + sto_an_table_commutative_resultvaluemaskentryproduct * sto_bp_table_commutative_resultvaluemaskentryproduct) + sto_cp_table_commutative_resultvaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_commutative_resultvaluemask)=0 \/ ~(exists pvs_factor_table_commutative_resultvaluemaskentrynondivisor. (dc_input_table_commutative_result) = (dc_index_table_commutative_resultvaluemask) * pvs_factor_table_commutative_resultvaluemaskentrynondivisor)) /\ ((dc_value_table_commutative_resultvaluemask)=0))))))) /\ (exists dst_positive_code_table_commutative_resultvaluefold dst_positive_scale_table_commutative_resultvaluefold dst_negative_code_table_commutative_resultvaluefold dst_negative_scale_table_commutative_resultvaluefold dst_positive_sum_table_commutative_resultvaluefold dst_negative_sum_table_commutative_resultvaluefold. (((dc_mask_table_commutative_resultvalue) = (((((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) * S ((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) + ((dst_positive_scale_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold))) + (((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)))) * S ((((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) * S ((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) + ((dst_positive_scale_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold))) + (((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)))) + ((((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold))) + (((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)))))) /\ (((exists fs_u_dst_table_commutative_resultvaluefoldpositive fs_v_dst_table_commutative_resultvaluefoldpositive. ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_start. fs_h_dst_table_commutative_resultvaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_start. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_terminal. fs_h_dst_table_commutative_resultvaluefoldpositive_body_terminal + S (dst_positive_sum_table_commutative_resultvaluefold) = S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_terminal. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_terminal * S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (dst_positive_sum_table_commutative_resultvaluefold))) /\ forall fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps. (exists fs_lt_dst_table_commutative_resultvaluefoldpositive_body_steps_bound. fs_lt_dst_table_commutative_resultvaluefoldpositive_body_steps_bound + S fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps = S (dc_input_table_commutative_result)) -> exists fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps. ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_summand. fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_summand + S (fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_resultvaluefold)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_summand. dst_positive_code_table_commutative_resultvaluefold = fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_resultvaluefold) + (fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_partial. fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_partial + S (fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_partial. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_successor. fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_successor + S (fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_successor. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps))) /\ fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps = fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps + fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_commutative_resultvaluefoldnegative fs_v_dst_table_commutative_resultvaluefoldnegative. ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_start. fs_h_dst_table_commutative_resultvaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_start. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_terminal. fs_h_dst_table_commutative_resultvaluefoldnegative_body_terminal + S (dst_negative_sum_table_commutative_resultvaluefold) = S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_terminal. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_terminal * S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (dst_negative_sum_table_commutative_resultvaluefold))) /\ forall fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps. (exists fs_lt_dst_table_commutative_resultvaluefoldnegative_body_steps_bound. fs_lt_dst_table_commutative_resultvaluefoldnegative_body_steps_bound + S fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps = S (dc_input_table_commutative_result)) -> exists fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps. ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_summand. fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_summand + S (fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_resultvaluefold)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_summand. dst_negative_code_table_commutative_resultvaluefold = fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_resultvaluefold) + (fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_partial. fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_partial + S (fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_partial. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_successor. fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_successor + S (fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_successor. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps))) /\ fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps = fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps + fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_commutative_resultvaluefoldresult ge_balance_negative_table_commutative_resultvaluefoldresult. (((((dc_output_table_commutative_result) = 2 * (ge_balance_positive_table_commutative_resultvaluefoldresult) /\ (ge_balance_negative_table_commutative_resultvaluefoldresult) = 0) \/ exists ge_signed_half_table_commutative_resultvaluefoldresultdecode. (((dc_output_table_commutative_result) = 2 * ge_signed_half_table_commutative_resultvaluefoldresultdecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluefoldresult) = 0) /\ (ge_balance_negative_table_commutative_resultvaluefoldresult) = S ge_signed_half_table_commutative_resultvaluefoldresultdecode))) /\ ((dst_positive_sum_table_commutative_resultvaluefold) + ge_balance_negative_table_commutative_resultvaluefoldresult = (dst_negative_sum_table_commutative_resultvaluefold) + ge_balance_positive_table_commutative_resultvaluefoldresult))))))))))))))))))))

divisor_le_nonzero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall d n. ~(n = 0) -> (exists q. n = d * q) -> exists k. k + d = n
```

divisor_signed_table_at_functional · checked inherited prerequisite

Exact statement in the checked dependency cone

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_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

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)))))))))

eq_decidable · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. a = b \/ ~(a = b)
```
factor_nonzero_right · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n c d. ~(n = 0) -> n = c * d -> ~(d = 0)
```
le_eq_or_lt · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + a = b) -> a = b \/ exists k. k + S a = b
```
le_of_succ_le_succ · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + S a = S b) -> exists r. r + a = b
```
le_refl · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. n <= n
```
le_succ_self · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. n <= S n
```
le_trans · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n m k. n <= m -> m <= k -> n <= k
```
le_zero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. n <= 0 -> n = 0
```
lt_not_le · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + S a = b) -> ~ (exists k. k + b = a)
```
mul_comm · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n m. n * m = m * n
```
mul_one · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. n * 1 = n
```
one_le_of_ne_zero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. ~(n = 0) -> 1 <= n
```

signed_mul_functional · checked inherited prerequisite

Exact statement in the checked dependency cone

forall left right output1 output2. (exists sm_lp_functional_left sm_ln_functional_left sm_rp_functional_left sm_rn_functional_left sm_op_functional_left sm_on_functional_left. (((left = 2 * sm_lp_functional_left /\ sm_ln_functional_left = 0) \/ exists sd_half_functional_left_left. ((left = 2 * sd_half_functional_left_left + 1 /\ sm_lp_functional_left = 0) /\ sm_ln_functional_left = S sd_half_functional_left_left)) /\ (((right = 2 * sm_rp_functional_left /\ sm_rn_functional_left = 0) \/ exists sd_half_functional_left_right. ((right = 2 * sd_half_functional_left_right + 1 /\ sm_rp_functional_left = 0) /\ sm_rn_functional_left = S sd_half_functional_left_right)) /\ (((output1 = 2 * sm_op_functional_left /\ sm_on_functional_left = 0) \/ exists sd_half_functional_left_output. ((output1 = 2 * sd_half_functional_left_output + 1 /\ sm_op_functional_left = 0) /\ sm_on_functional_left = S sd_half_functional_left_output)) /\ (sm_lp_functional_left * sm_rp_functional_left + sm_ln_functional_left * sm_rn_functional_left) + sm_on_functional_left = (sm_lp_functional_left * sm_rn_functional_left + sm_ln_functional_left * sm_rp_functional_left) + sm_op_functional_left)))) -> (exists sm_lp_functional_right sm_ln_functional_right sm_rp_functional_right sm_rn_functional_right sm_op_functional_right sm_on_functional_right. (((left = 2 * sm_lp_functional_right /\ sm_ln_functional_right = 0) \/ exists sd_half_functional_right_left. ((left = 2 * sd_half_functional_right_left + 1 /\ sm_lp_functional_right = 0) /\ sm_ln_functional_right = S sd_half_functional_right_left)) /\ (((right = 2 * sm_rp_functional_right /\ sm_rn_functional_right = 0) \/ exists sd_half_functional_right_right. ((right = 2 * sd_half_functional_right_right + 1 /\ sm_rp_functional_right = 0) /\ sm_rn_functional_right = S sd_half_functional_right_right)) /\ (((output2 = 2 * sm_op_functional_right /\ sm_on_functional_right = 0) \/ exists sd_half_functional_right_output. ((output2 = 2 * sd_half_functional_right_output + 1 /\ sm_op_functional_right = 0) /\ sm_on_functional_right = S sd_half_functional_right_output)) /\ (sm_lp_functional_right * sm_rp_functional_right + sm_ln_functional_right * sm_rn_functional_right) + sm_on_functional_right = (sm_lp_functional_right * sm_rn_functional_right + sm_ln_functional_right * sm_rp_functional_right) + sm_op_functional_right)))) -> output1 = output2

signed_mul_one_right · checked inherited prerequisite

Exact statement in the checked dependency cone

forall input. (exists sm_lp_one_right sm_ln_one_right sm_rp_one_right sm_rn_one_right sm_op_one_right sm_on_one_right. (((input = 2 * sm_lp_one_right /\ sm_ln_one_right = 0) \/ exists sd_half_one_right_left. ((input = 2 * sd_half_one_right_left + 1 /\ sm_lp_one_right = 0) /\ sm_ln_one_right = S sd_half_one_right_left)) /\ (((2 = 2 * sm_rp_one_right /\ sm_rn_one_right = 0) \/ exists sd_half_one_right_right. ((2 = 2 * sd_half_one_right_right + 1 /\ sm_rp_one_right = 0) /\ sm_rn_one_right = S sd_half_one_right_right)) /\ (((input = 2 * sm_op_one_right /\ sm_on_one_right = 0) \/ exists sd_half_one_right_output. ((input = 2 * sd_half_one_right_output + 1 /\ sm_op_one_right = 0) /\ sm_on_one_right = S sd_half_one_right_output)) /\ (sm_lp_one_right * sm_rp_one_right + sm_ln_one_right * sm_rn_one_right) + sm_on_one_right = (sm_lp_one_right * sm_rn_one_right + sm_ln_one_right * sm_rp_one_right) + sm_op_one_right))))

signed_mul_zero_right · checked inherited prerequisite

Exact statement in the checked dependency cone

forall input. (exists sm_lp_zero_right sm_ln_zero_right sm_rp_zero_right sm_rn_zero_right sm_op_zero_right sm_on_zero_right. (((input = 2 * sm_lp_zero_right /\ sm_ln_zero_right = 0) \/ exists sd_half_zero_right_left. ((input = 2 * sd_half_zero_right_left + 1 /\ sm_lp_zero_right = 0) /\ sm_ln_zero_right = S sd_half_zero_right_left)) /\ (((0 = 2 * sm_rp_zero_right /\ sm_rn_zero_right = 0) \/ exists sd_half_zero_right_right. ((0 = 2 * sd_half_zero_right_right + 1 /\ sm_rp_zero_right = 0) /\ sm_rn_zero_right = S sd_half_zero_right_right)) /\ (((0 = 2 * sm_op_zero_right /\ sm_on_zero_right = 0) \/ exists sd_half_zero_right_output. ((0 = 2 * sd_half_zero_right_output + 1 /\ sm_op_zero_right = 0) /\ sm_on_zero_right = S sd_half_zero_right_output)) /\ (sm_lp_zero_right * sm_rp_zero_right + sm_ln_zero_right * sm_rn_zero_right) + sm_on_zero_right = (sm_lp_zero_right * sm_rn_zero_right + sm_ln_zero_right * sm_rp_zero_right) + sm_op_zero_right))))

signed_prefix_sum_last_value · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F l a z. (forall sfs_index_last_zeros sfs_value_last_zeros. (exists pvs_le_gap_last_zeroslower. pvs_le_gap_last_zeroslower + (0) = (sfs_index_last_zeros)) -> (exists pvs_gap_last_zerosupper. pvs_gap_last_zerosupper + S (sfs_index_last_zeros) = (l)) -> (exists dst_positive_code_last_zerosentry dst_positive_scale_last_zerosentry dst_negative_code_last_zerosentry dst_negative_scale_last_zerosentry dst_positive_last_zerosentry dst_negative_last_zerosentry. (((F) = (((((dst_positive_code_last_zerosentry) + (dst_positive_scale_last_zerosentry)) * S ((dst_positive_code_last_zerosentry) + (dst_positive_scale_last_zerosentry)) + ((dst_positive_scale_last_zerosentry) + (dst_positive_scale_last_zerosentry))) + (((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) * S ((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) + ((dst_negative_scale_last_zerosentry) + (dst_negative_scale_last_zerosentry)))) * S ((((dst_positive_code_last_zerosentry) + (dst_positive_scale_last_zerosentry)) * S ((dst_positive_code_last_zerosentry) + (dst_positive_scale_last_zerosentry)) + ((dst_positive_scale_last_zerosentry) + (dst_positive_scale_last_zerosentry))) + (((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) * S ((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) + ((dst_negative_scale_last_zerosentry) + (dst_negative_scale_last_zerosentry)))) + ((((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) * S ((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) + ((dst_negative_scale_last_zerosentry) + (dst_negative_scale_last_zerosentry))) + (((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) * S ((dst_negative_code_last_zerosentry) + (dst_negative_scale_last_zerosentry)) + ((dst_negative_scale_last_zerosentry) + (dst_negative_scale_last_zerosentry)))))) /\ (((((exists ff_h_pvs_last_zerosentrypositive. ff_h_pvs_last_zerosentrypositive + S (dst_positive_last_zerosentry) = S ((S (sfs_index_last_zeros)) * dst_positive_scale_last_zerosentry)) /\ exists ff_q_pvs_last_zerosentrypositive. dst_positive_code_last_zerosentry = ff_q_pvs_last_zerosentrypositive * S ((S (sfs_index_last_zeros)) * dst_positive_scale_last_zerosentry) + (dst_positive_last_zerosentry))) /\ (((((exists ff_h_pvs_last_zerosentrynegative. ff_h_pvs_last_zerosentrynegative + S (dst_negative_last_zerosentry) = S ((S (sfs_index_last_zeros)) * dst_negative_scale_last_zerosentry)) /\ exists ff_q_pvs_last_zerosentrynegative. dst_negative_code_last_zerosentry = ff_q_pvs_last_zerosentrynegative * S ((S (sfs_index_last_zeros)) * dst_negative_scale_last_zerosentry) + (dst_negative_last_zerosentry))) /\ (exists ge_balance_positive_last_zerosentryvalue ge_balance_negative_last_zerosentryvalue. (((((sfs_value_last_zeros) = 2 * (ge_balance_positive_last_zerosentryvalue) /\ (ge_balance_negative_last_zerosentryvalue) = 0) \/ exists ge_signed_half_last_zerosentryvaluedecode. (((sfs_value_last_zeros) = 2 * ge_signed_half_last_zerosentryvaluedecode + 1 /\ (ge_balance_positive_last_zerosentryvalue) = 0) /\ (ge_balance_negative_last_zerosentryvalue) = S ge_signed_half_last_zerosentryvaluedecode))) /\ ((dst_positive_last_zerosentry) + ge_balance_negative_last_zerosentryvalue = (dst_negative_last_zerosentry) + ge_balance_positive_last_zerosentryvalue))))))))) -> sfs_value_last_zeros=0) -> (exists dst_positive_code_last_value dst_positive_scale_last_value dst_negative_code_last_value dst_negative_scale_last_value dst_positive_last_value dst_negative_last_value. (((F) = (((((dst_positive_code_last_value) + (dst_positive_scale_last_value)) * S ((dst_positive_code_last_value) + (dst_positive_scale_last_value)) + ((dst_positive_scale_last_value) + (dst_positive_scale_last_value))) + (((dst_negative_code_last_value) + (dst_negative_scale_last_value)) * S ((dst_negative_code_last_value) + (dst_negative_scale_last_value)) + ((dst_negative_scale_last_value) + (dst_negative_scale_last_value)))) * S ((((dst_positive_code_last_value) + (dst_positive_scale_last_value)) * S ((dst_positive_code_last_value) + (dst_positive_scale_last_value)) + ((dst_positive_scale_last_value) + (dst_positive_scale_last_value))) + (((dst_negative_code_last_value) + (dst_negative_scale_last_value)) * S ((dst_negative_code_last_value) + (dst_negative_scale_last_value)) + ((dst_negative_scale_last_value) + (dst_negative_scale_last_value)))) + ((((dst_negative_code_last_value) + (dst_negative_scale_last_value)) * S ((dst_negative_code_last_value) + (dst_negative_scale_last_value)) + ((dst_negative_scale_last_value) + (dst_negative_scale_last_value))) + (((dst_negative_code_last_value) + (dst_negative_scale_last_value)) * S ((dst_negative_code_last_value) + (dst_negative_scale_last_value)) + ((dst_negative_scale_last_value) + (dst_negative_scale_last_value)))))) /\ (((((exists ff_h_pvs_last_valuepositive. ff_h_pvs_last_valuepositive + S (dst_positive_last_value) = S ((S (l)) * dst_positive_scale_last_value)) /\ exists ff_q_pvs_last_valuepositive. dst_positive_code_last_value = ff_q_pvs_last_valuepositive * S ((S (l)) * dst_positive_scale_last_value) + (dst_positive_last_value))) /\ (((((exists ff_h_pvs_last_valuenegative. ff_h_pvs_last_valuenegative + S (dst_negative_last_value) = S ((S (l)) * dst_negative_scale_last_value)) /\ exists ff_q_pvs_last_valuenegative. dst_negative_code_last_value = ff_q_pvs_last_valuenegative * S ((S (l)) * dst_negative_scale_last_value) + (dst_negative_last_value))) /\ (exists ge_balance_positive_last_valuevalue ge_balance_negative_last_valuevalue. (((((a) = 2 * (ge_balance_positive_last_valuevalue) /\ (ge_balance_negative_last_valuevalue) = 0) \/ exists ge_signed_half_last_valuevaluedecode. (((a) = 2 * ge_signed_half_last_valuevaluedecode + 1 /\ (ge_balance_positive_last_valuevalue) = 0) /\ (ge_balance_negative_last_valuevalue) = S ge_signed_half_last_valuevaluedecode))) /\ ((dst_positive_last_value) + ge_balance_negative_last_valuevalue = (dst_negative_last_value) + ge_balance_positive_last_valuevalue))))))))) -> (exists dst_positive_code_last_sum dst_positive_scale_last_sum dst_negative_code_last_sum dst_negative_scale_last_sum dst_positive_sum_last_sum dst_negative_sum_last_sum. (((F) = (((((dst_positive_code_last_sum) + (dst_positive_scale_last_sum)) * S ((dst_positive_code_last_sum) + (dst_positive_scale_last_sum)) + ((dst_positive_scale_last_sum) + (dst_positive_scale_last_sum))) + (((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) * S ((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) + ((dst_negative_scale_last_sum) + (dst_negative_scale_last_sum)))) * S ((((dst_positive_code_last_sum) + (dst_positive_scale_last_sum)) * S ((dst_positive_code_last_sum) + (dst_positive_scale_last_sum)) + ((dst_positive_scale_last_sum) + (dst_positive_scale_last_sum))) + (((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) * S ((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) + ((dst_negative_scale_last_sum) + (dst_negative_scale_last_sum)))) + ((((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) * S ((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) + ((dst_negative_scale_last_sum) + (dst_negative_scale_last_sum))) + (((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) * S ((dst_negative_code_last_sum) + (dst_negative_scale_last_sum)) + ((dst_negative_scale_last_sum) + (dst_negative_scale_last_sum)))))) /\ (((exists fs_u_dst_last_sumpositive fs_v_dst_last_sumpositive. ((((exists fs_h_dst_last_sumpositive_body_start. fs_h_dst_last_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_last_sumpositive)) /\ exists fs_q_dst_last_sumpositive_body_start. fs_u_dst_last_sumpositive = fs_q_dst_last_sumpositive_body_start * S ((S (0)) * fs_v_dst_last_sumpositive) + (0))) /\ ((((exists fs_h_dst_last_sumpositive_body_terminal. fs_h_dst_last_sumpositive_body_terminal + S (dst_positive_sum_last_sum) = S ((S (S l)) * fs_v_dst_last_sumpositive)) /\ exists fs_q_dst_last_sumpositive_body_terminal. fs_u_dst_last_sumpositive = fs_q_dst_last_sumpositive_body_terminal * S ((S (S l)) * fs_v_dst_last_sumpositive) + (dst_positive_sum_last_sum))) /\ forall fs_i_dst_last_sumpositive_body_steps. (exists fs_lt_dst_last_sumpositive_body_steps_bound. fs_lt_dst_last_sumpositive_body_steps_bound + S fs_i_dst_last_sumpositive_body_steps = S l) -> exists fs_a_dst_last_sumpositive_body_steps fs_r_dst_last_sumpositive_body_steps fs_s_dst_last_sumpositive_body_steps. ((((exists fs_h_dst_last_sumpositive_body_steps_summand. fs_h_dst_last_sumpositive_body_steps_summand + S (fs_a_dst_last_sumpositive_body_steps) = S ((S (fs_i_dst_last_sumpositive_body_steps)) * dst_positive_scale_last_sum)) /\ exists fs_q_dst_last_sumpositive_body_steps_summand. dst_positive_code_last_sum = fs_q_dst_last_sumpositive_body_steps_summand * S ((S (fs_i_dst_last_sumpositive_body_steps)) * dst_positive_scale_last_sum) + (fs_a_dst_last_sumpositive_body_steps))) /\ ((((exists fs_h_dst_last_sumpositive_body_steps_partial. fs_h_dst_last_sumpositive_body_steps_partial + S (fs_r_dst_last_sumpositive_body_steps) = S ((S (fs_i_dst_last_sumpositive_body_steps)) * fs_v_dst_last_sumpositive)) /\ exists fs_q_dst_last_sumpositive_body_steps_partial. fs_u_dst_last_sumpositive = fs_q_dst_last_sumpositive_body_steps_partial * S ((S (fs_i_dst_last_sumpositive_body_steps)) * fs_v_dst_last_sumpositive) + (fs_r_dst_last_sumpositive_body_steps))) /\ ((((exists fs_h_dst_last_sumpositive_body_steps_successor. fs_h_dst_last_sumpositive_body_steps_successor + S (fs_s_dst_last_sumpositive_body_steps) = S ((S (S fs_i_dst_last_sumpositive_body_steps)) * fs_v_dst_last_sumpositive)) /\ exists fs_q_dst_last_sumpositive_body_steps_successor. fs_u_dst_last_sumpositive = fs_q_dst_last_sumpositive_body_steps_successor * S ((S (S fs_i_dst_last_sumpositive_body_steps)) * fs_v_dst_last_sumpositive) + (fs_s_dst_last_sumpositive_body_steps))) /\ fs_s_dst_last_sumpositive_body_steps = fs_r_dst_last_sumpositive_body_steps + fs_a_dst_last_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_last_sumnegative fs_v_dst_last_sumnegative. ((((exists fs_h_dst_last_sumnegative_body_start. fs_h_dst_last_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_last_sumnegative)) /\ exists fs_q_dst_last_sumnegative_body_start. fs_u_dst_last_sumnegative = fs_q_dst_last_sumnegative_body_start * S ((S (0)) * fs_v_dst_last_sumnegative) + (0))) /\ ((((exists fs_h_dst_last_sumnegative_body_terminal. fs_h_dst_last_sumnegative_body_terminal + S (dst_negative_sum_last_sum) = S ((S (S l)) * fs_v_dst_last_sumnegative)) /\ exists fs_q_dst_last_sumnegative_body_terminal. fs_u_dst_last_sumnegative = fs_q_dst_last_sumnegative_body_terminal * S ((S (S l)) * fs_v_dst_last_sumnegative) + (dst_negative_sum_last_sum))) /\ forall fs_i_dst_last_sumnegative_body_steps. (exists fs_lt_dst_last_sumnegative_body_steps_bound. fs_lt_dst_last_sumnegative_body_steps_bound + S fs_i_dst_last_sumnegative_body_steps = S l) -> exists fs_a_dst_last_sumnegative_body_steps fs_r_dst_last_sumnegative_body_steps fs_s_dst_last_sumnegative_body_steps. ((((exists fs_h_dst_last_sumnegative_body_steps_summand. fs_h_dst_last_sumnegative_body_steps_summand + S (fs_a_dst_last_sumnegative_body_steps) = S ((S (fs_i_dst_last_sumnegative_body_steps)) * dst_negative_scale_last_sum)) /\ exists fs_q_dst_last_sumnegative_body_steps_summand. dst_negative_code_last_sum = fs_q_dst_last_sumnegative_body_steps_summand * S ((S (fs_i_dst_last_sumnegative_body_steps)) * dst_negative_scale_last_sum) + (fs_a_dst_last_sumnegative_body_steps))) /\ ((((exists fs_h_dst_last_sumnegative_body_steps_partial. fs_h_dst_last_sumnegative_body_steps_partial + S (fs_r_dst_last_sumnegative_body_steps) = S ((S (fs_i_dst_last_sumnegative_body_steps)) * fs_v_dst_last_sumnegative)) /\ exists fs_q_dst_last_sumnegative_body_steps_partial. fs_u_dst_last_sumnegative = fs_q_dst_last_sumnegative_body_steps_partial * S ((S (fs_i_dst_last_sumnegative_body_steps)) * fs_v_dst_last_sumnegative) + (fs_r_dst_last_sumnegative_body_steps))) /\ ((((exists fs_h_dst_last_sumnegative_body_steps_successor. fs_h_dst_last_sumnegative_body_steps_successor + S (fs_s_dst_last_sumnegative_body_steps) = S ((S (S fs_i_dst_last_sumnegative_body_steps)) * fs_v_dst_last_sumnegative)) /\ exists fs_q_dst_last_sumnegative_body_steps_successor. fs_u_dst_last_sumnegative = fs_q_dst_last_sumnegative_body_steps_successor * S ((S (S fs_i_dst_last_sumnegative_body_steps)) * fs_v_dst_last_sumnegative) + (fs_s_dst_last_sumnegative_body_steps))) /\ fs_s_dst_last_sumnegative_body_steps = fs_r_dst_last_sumnegative_body_steps + fs_a_dst_last_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_last_sumresult ge_balance_negative_last_sumresult. (((((z) = 2 * (ge_balance_positive_last_sumresult) /\ (ge_balance_negative_last_sumresult) = 0) \/ exists ge_signed_half_last_sumresultdecode. (((z) = 2 * ge_signed_half_last_sumresultdecode + 1 /\ (ge_balance_positive_last_sumresult) = 0) /\ (ge_balance_negative_last_sumresult) = S ge_signed_half_last_sumresultdecode))) /\ ((dst_positive_sum_last_sum) + ge_balance_negative_last_sumresult = (dst_negative_sum_last_sum) + ge_balance_positive_last_sumresult))))))))) -> z=a

succ_le_succ · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + a = b) -> exists r. r + S a = S b
```
zero_le · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. 0 <= n
```