Constructed triangular convolution steps — exact evidence

Exact theorem nodes and inherited prerequisites

• DT0001 dirichlet_convolution_entry_first_input_transport · actual bundle node 208
• DT0002 dirichlet_convolution_prefix_first_input_transport · actual bundle node 209
• DT0003 dirichlet_convolution_first_input_append_preserves · actual bundle node 210
• DT0004 dirichlet_convolution_table_first_input_append_preserves · actual bundle node 211
• DT0005 dirichlet_convolution_last_entry_iff · actual bundle node 212
• DT0006 dirichlet_convolution_strict_prefix_exists · actual bundle node 213
• DT0007 dirichlet_convolution_prefix_last_step · actual bundle node 214
• DT0008 dirichlet_convolution_first_input_append_step · actual bundle node 215
• DT0009 dirichlet_convolution_zero_prefix_sum · actual bundle node 216
• DT000A dirichlet_convolution_at_one_iff · actual bundle node 217
• arithmetic_signed_sum_append_transport · checked inherited prerequisite
  Exact statement in the checked dependency cone

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

• arithmetic_signed_sum_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

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

• arithmetic_signed_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_entry_omitted_value · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n d z. (d=0 \/ ~(exists pvs_factor_omitted_guard. (n) = (d) * pvs_factor_omitted_guard)) -> ((((~((d)=0)) /\ (exists dc_quotient_omitted_entry dc_left_omitted_entry dc_right_omitted_entry. (((n)=(d)*dc_quotient_omitted_entry) /\ (((exists dst_positive_code_omitted_entryleft dst_positive_scale_omitted_entryleft dst_negative_code_omitted_entryleft dst_negative_scale_omitted_entryleft dst_positive_omitted_entryleft dst_negative_omitted_entryleft. (((F) = (((((dst_positive_code_omitted_entryleft) + (dst_positive_scale_omitted_entryleft)) * S ((dst_positive_code_omitted_entryleft) + (dst_positive_scale_omitted_entryleft)) + ((dst_positive_scale_omitted_entryleft) + (dst_positive_scale_omitted_entryleft))) + (((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) * S ((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) + ((dst_negative_scale_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)))) * S ((((dst_positive_code_omitted_entryleft) + (dst_positive_scale_omitted_entryleft)) * S ((dst_positive_code_omitted_entryleft) + (dst_positive_scale_omitted_entryleft)) + ((dst_positive_scale_omitted_entryleft) + (dst_positive_scale_omitted_entryleft))) + (((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) * S ((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) + ((dst_negative_scale_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)))) + ((((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) * S ((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) + ((dst_negative_scale_omitted_entryleft) + (dst_negative_scale_omitted_entryleft))) + (((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) * S ((dst_negative_code_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)) + ((dst_negative_scale_omitted_entryleft) + (dst_negative_scale_omitted_entryleft)))))) /\ (((((exists ff_h_pvs_omitted_entryleftpositive. ff_h_pvs_omitted_entryleftpositive + S (dst_positive_omitted_entryleft) = S ((S (d)) * dst_positive_scale_omitted_entryleft)) /\ exists ff_q_pvs_omitted_entryleftpositive. dst_positive_code_omitted_entryleft = ff_q_pvs_omitted_entryleftpositive * S ((S (d)) * dst_positive_scale_omitted_entryleft) + (dst_positive_omitted_entryleft))) /\ (((((exists ff_h_pvs_omitted_entryleftnegative. ff_h_pvs_omitted_entryleftnegative + S (dst_negative_omitted_entryleft) = S ((S (d)) * dst_negative_scale_omitted_entryleft)) /\ exists ff_q_pvs_omitted_entryleftnegative. dst_negative_code_omitted_entryleft = ff_q_pvs_omitted_entryleftnegative * S ((S (d)) * dst_negative_scale_omitted_entryleft) + (dst_negative_omitted_entryleft))) /\ (exists ge_balance_positive_omitted_entryleftvalue ge_balance_negative_omitted_entryleftvalue. (((((dc_left_omitted_entry) = 2 * (ge_balance_positive_omitted_entryleftvalue) /\ (ge_balance_negative_omitted_entryleftvalue) = 0) \/ exists ge_signed_half_omitted_entryleftvaluedecode. (((dc_left_omitted_entry) = 2 * ge_signed_half_omitted_entryleftvaluedecode + 1 /\ (ge_balance_positive_omitted_entryleftvalue) = 0) /\ (ge_balance_negative_omitted_entryleftvalue) = S ge_signed_half_omitted_entryleftvaluedecode))) /\ ((dst_positive_omitted_entryleft) + ge_balance_negative_omitted_entryleftvalue = (dst_negative_omitted_entryleft) + ge_balance_positive_omitted_entryleftvalue))))))))) /\ (((exists dst_positive_code_omitted_entryright dst_positive_scale_omitted_entryright dst_negative_code_omitted_entryright dst_negative_scale_omitted_entryright dst_positive_omitted_entryright dst_negative_omitted_entryright. (((G) = (((((dst_positive_code_omitted_entryright) + (dst_positive_scale_omitted_entryright)) * S ((dst_positive_code_omitted_entryright) + (dst_positive_scale_omitted_entryright)) + ((dst_positive_scale_omitted_entryright) + (dst_positive_scale_omitted_entryright))) + (((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) * S ((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) + ((dst_negative_scale_omitted_entryright) + (dst_negative_scale_omitted_entryright)))) * S ((((dst_positive_code_omitted_entryright) + (dst_positive_scale_omitted_entryright)) * S ((dst_positive_code_omitted_entryright) + (dst_positive_scale_omitted_entryright)) + ((dst_positive_scale_omitted_entryright) + (dst_positive_scale_omitted_entryright))) + (((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) * S ((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) + ((dst_negative_scale_omitted_entryright) + (dst_negative_scale_omitted_entryright)))) + ((((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) * S ((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) + ((dst_negative_scale_omitted_entryright) + (dst_negative_scale_omitted_entryright))) + (((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) * S ((dst_negative_code_omitted_entryright) + (dst_negative_scale_omitted_entryright)) + ((dst_negative_scale_omitted_entryright) + (dst_negative_scale_omitted_entryright)))))) /\ (((((exists ff_h_pvs_omitted_entryrightpositive. ff_h_pvs_omitted_entryrightpositive + S (dst_positive_omitted_entryright) = S ((S (dc_quotient_omitted_entry)) * dst_positive_scale_omitted_entryright)) /\ exists ff_q_pvs_omitted_entryrightpositive. dst_positive_code_omitted_entryright = ff_q_pvs_omitted_entryrightpositive * S ((S (dc_quotient_omitted_entry)) * dst_positive_scale_omitted_entryright) + (dst_positive_omitted_entryright))) /\ (((((exists ff_h_pvs_omitted_entryrightnegative. ff_h_pvs_omitted_entryrightnegative + S (dst_negative_omitted_entryright) = S ((S (dc_quotient_omitted_entry)) * dst_negative_scale_omitted_entryright)) /\ exists ff_q_pvs_omitted_entryrightnegative. dst_negative_code_omitted_entryright = ff_q_pvs_omitted_entryrightnegative * S ((S (dc_quotient_omitted_entry)) * dst_negative_scale_omitted_entryright) + (dst_negative_omitted_entryright))) /\ (exists ge_balance_positive_omitted_entryrightvalue ge_balance_negative_omitted_entryrightvalue. (((((dc_right_omitted_entry) = 2 * (ge_balance_positive_omitted_entryrightvalue) /\ (ge_balance_negative_omitted_entryrightvalue) = 0) \/ exists ge_signed_half_omitted_entryrightvaluedecode. (((dc_right_omitted_entry) = 2 * ge_signed_half_omitted_entryrightvaluedecode + 1 /\ (ge_balance_positive_omitted_entryrightvalue) = 0) /\ (ge_balance_negative_omitted_entryrightvalue) = S ge_signed_half_omitted_entryrightvaluedecode))) /\ ((dst_positive_omitted_entryright) + ge_balance_negative_omitted_entryrightvalue = (dst_negative_omitted_entryright) + ge_balance_positive_omitted_entryrightvalue))))))))) /\ (exists sto_ap_omitted_entryproduct sto_an_omitted_entryproduct sto_bp_omitted_entryproduct sto_bn_omitted_entryproduct sto_cp_omitted_entryproduct sto_cn_omitted_entryproduct. (((((dc_left_omitted_entry) = 2 * (sto_ap_omitted_entryproduct) /\ (sto_an_omitted_entryproduct) = 0) \/ exists ge_signed_half_omitted_entryproductleft. (((dc_left_omitted_entry) = 2 * ge_signed_half_omitted_entryproductleft + 1 /\ (sto_ap_omitted_entryproduct) = 0) /\ (sto_an_omitted_entryproduct) = S ge_signed_half_omitted_entryproductleft))) /\ ((((((dc_right_omitted_entry) = 2 * (sto_bp_omitted_entryproduct) /\ (sto_bn_omitted_entryproduct) = 0) \/ exists ge_signed_half_omitted_entryproductright. (((dc_right_omitted_entry) = 2 * ge_signed_half_omitted_entryproductright + 1 /\ (sto_bp_omitted_entryproduct) = 0) /\ (sto_bn_omitted_entryproduct) = S ge_signed_half_omitted_entryproductright))) /\ ((((((z) = 2 * (sto_cp_omitted_entryproduct) /\ (sto_cn_omitted_entryproduct) = 0) \/ exists ge_signed_half_omitted_entryproductoutput. (((z) = 2 * ge_signed_half_omitted_entryproductoutput + 1 /\ (sto_cp_omitted_entryproduct) = 0) /\ (sto_cn_omitted_entryproduct) = S ge_signed_half_omitted_entryproductoutput))) /\ ((sto_ap_omitted_entryproduct * sto_bp_omitted_entryproduct + sto_an_omitted_entryproduct * sto_bn_omitted_entryproduct) + sto_cn_omitted_entryproduct = (sto_ap_omitted_entryproduct * sto_bn_omitted_entryproduct + sto_an_omitted_entryproduct * sto_bp_omitted_entryproduct) + sto_cp_omitted_entryproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_omitted_entrynondivisor. (n) = (d) * pvs_factor_omitted_entrynondivisor)) /\ ((z)=0)))) -> z=0

• dirichlet_convolution_entry_quotient_product · 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_read_left dst_positive_scale_read_left dst_negative_code_read_left dst_negative_scale_read_left dst_positive_read_left dst_negative_read_left. (((F) = (((((dst_positive_code_read_left) + (dst_positive_scale_read_left)) * S ((dst_positive_code_read_left) + (dst_positive_scale_read_left)) + ((dst_positive_scale_read_left) + (dst_positive_scale_read_left))) + (((dst_negative_code_read_left) + (dst_negative_scale_read_left)) * S ((dst_negative_code_read_left) + (dst_negative_scale_read_left)) + ((dst_negative_scale_read_left) + (dst_negative_scale_read_left)))) * S ((((dst_positive_code_read_left) + (dst_positive_scale_read_left)) * S ((dst_positive_code_read_left) + (dst_positive_scale_read_left)) + ((dst_positive_scale_read_left) + (dst_positive_scale_read_left))) + (((dst_negative_code_read_left) + (dst_negative_scale_read_left)) * S ((dst_negative_code_read_left) + (dst_negative_scale_read_left)) + ((dst_negative_scale_read_left) + (dst_negative_scale_read_left)))) + ((((dst_negative_code_read_left) + (dst_negative_scale_read_left)) * S ((dst_negative_code_read_left) + (dst_negative_scale_read_left)) + ((dst_negative_scale_read_left) + (dst_negative_scale_read_left))) + (((dst_negative_code_read_left) + (dst_negative_scale_read_left)) * S ((dst_negative_code_read_left) + (dst_negative_scale_read_left)) + ((dst_negative_scale_read_left) + (dst_negative_scale_read_left)))))) /\ (((((exists ff_h_pvs_read_leftpositive. ff_h_pvs_read_leftpositive + S (dst_positive_read_left) = S ((S (d)) * dst_positive_scale_read_left)) /\ exists ff_q_pvs_read_leftpositive. dst_positive_code_read_left = ff_q_pvs_read_leftpositive * S ((S (d)) * dst_positive_scale_read_left) + (dst_positive_read_left))) /\ (((((exists ff_h_pvs_read_leftnegative. ff_h_pvs_read_leftnegative + S (dst_negative_read_left) = S ((S (d)) * dst_negative_scale_read_left)) /\ exists ff_q_pvs_read_leftnegative. dst_negative_code_read_left = ff_q_pvs_read_leftnegative * S ((S (d)) * dst_negative_scale_read_left) + (dst_negative_read_left))) /\ (exists ge_balance_positive_read_leftvalue ge_balance_negative_read_leftvalue. (((((a) = 2 * (ge_balance_positive_read_leftvalue) /\ (ge_balance_negative_read_leftvalue) = 0) \/ exists ge_signed_half_read_leftvaluedecode. (((a) = 2 * ge_signed_half_read_leftvaluedecode + 1 /\ (ge_balance_positive_read_leftvalue) = 0) /\ (ge_balance_negative_read_leftvalue) = S ge_signed_half_read_leftvaluedecode))) /\ ((dst_positive_read_left) + ge_balance_negative_read_leftvalue = (dst_negative_read_left) + ge_balance_positive_read_leftvalue))))))))) -> (exists dst_positive_code_read_right dst_positive_scale_read_right dst_negative_code_read_right dst_negative_scale_read_right dst_positive_read_right dst_negative_read_right. (((G) = (((((dst_positive_code_read_right) + (dst_positive_scale_read_right)) * S ((dst_positive_code_read_right) + (dst_positive_scale_read_right)) + ((dst_positive_scale_read_right) + (dst_positive_scale_read_right))) + (((dst_negative_code_read_right) + (dst_negative_scale_read_right)) * S ((dst_negative_code_read_right) + (dst_negative_scale_read_right)) + ((dst_negative_scale_read_right) + (dst_negative_scale_read_right)))) * S ((((dst_positive_code_read_right) + (dst_positive_scale_read_right)) * S ((dst_positive_code_read_right) + (dst_positive_scale_read_right)) + ((dst_positive_scale_read_right) + (dst_positive_scale_read_right))) + (((dst_negative_code_read_right) + (dst_negative_scale_read_right)) * S ((dst_negative_code_read_right) + (dst_negative_scale_read_right)) + ((dst_negative_scale_read_right) + (dst_negative_scale_read_right)))) + ((((dst_negative_code_read_right) + (dst_negative_scale_read_right)) * S ((dst_negative_code_read_right) + (dst_negative_scale_read_right)) + ((dst_negative_scale_read_right) + (dst_negative_scale_read_right))) + (((dst_negative_code_read_right) + (dst_negative_scale_read_right)) * S ((dst_negative_code_read_right) + (dst_negative_scale_read_right)) + ((dst_negative_scale_read_right) + (dst_negative_scale_read_right)))))) /\ (((((exists ff_h_pvs_read_rightpositive. ff_h_pvs_read_rightpositive + S (dst_positive_read_right) = S ((S (q)) * dst_positive_scale_read_right)) /\ exists ff_q_pvs_read_rightpositive. dst_positive_code_read_right = ff_q_pvs_read_rightpositive * S ((S (q)) * dst_positive_scale_read_right) + (dst_positive_read_right))) /\ (((((exists ff_h_pvs_read_rightnegative. ff_h_pvs_read_rightnegative + S (dst_negative_read_right) = S ((S (q)) * dst_negative_scale_read_right)) /\ exists ff_q_pvs_read_rightnegative. dst_negative_code_read_right = ff_q_pvs_read_rightnegative * S ((S (q)) * dst_negative_scale_read_right) + (dst_negative_read_right))) /\ (exists ge_balance_positive_read_rightvalue ge_balance_negative_read_rightvalue. (((((b) = 2 * (ge_balance_positive_read_rightvalue) /\ (ge_balance_negative_read_rightvalue) = 0) \/ exists ge_signed_half_read_rightvaluedecode. (((b) = 2 * ge_signed_half_read_rightvaluedecode + 1 /\ (ge_balance_positive_read_rightvalue) = 0) /\ (ge_balance_negative_read_rightvalue) = S ge_signed_half_read_rightvaluedecode))) /\ ((dst_positive_read_right) + ge_balance_negative_read_rightvalue = (dst_negative_read_right) + ge_balance_positive_read_rightvalue))))))))) -> ((((~((d)=0)) /\ (exists dc_quotient_read_entry dc_left_read_entry dc_right_read_entry. (((n)=(d)*dc_quotient_read_entry) /\ (((exists dst_positive_code_read_entryleft dst_positive_scale_read_entryleft dst_negative_code_read_entryleft dst_negative_scale_read_entryleft dst_positive_read_entryleft dst_negative_read_entryleft. (((F) = (((((dst_positive_code_read_entryleft) + (dst_positive_scale_read_entryleft)) * S ((dst_positive_code_read_entryleft) + (dst_positive_scale_read_entryleft)) + ((dst_positive_scale_read_entryleft) + (dst_positive_scale_read_entryleft))) + (((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) * S ((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) + ((dst_negative_scale_read_entryleft) + (dst_negative_scale_read_entryleft)))) * S ((((dst_positive_code_read_entryleft) + (dst_positive_scale_read_entryleft)) * S ((dst_positive_code_read_entryleft) + (dst_positive_scale_read_entryleft)) + ((dst_positive_scale_read_entryleft) + (dst_positive_scale_read_entryleft))) + (((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) * S ((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) + ((dst_negative_scale_read_entryleft) + (dst_negative_scale_read_entryleft)))) + ((((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) * S ((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) + ((dst_negative_scale_read_entryleft) + (dst_negative_scale_read_entryleft))) + (((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) * S ((dst_negative_code_read_entryleft) + (dst_negative_scale_read_entryleft)) + ((dst_negative_scale_read_entryleft) + (dst_negative_scale_read_entryleft)))))) /\ (((((exists ff_h_pvs_read_entryleftpositive. ff_h_pvs_read_entryleftpositive + S (dst_positive_read_entryleft) = S ((S (d)) * dst_positive_scale_read_entryleft)) /\ exists ff_q_pvs_read_entryleftpositive. dst_positive_code_read_entryleft = ff_q_pvs_read_entryleftpositive * S ((S (d)) * dst_positive_scale_read_entryleft) + (dst_positive_read_entryleft))) /\ (((((exists ff_h_pvs_read_entryleftnegative. ff_h_pvs_read_entryleftnegative + S (dst_negative_read_entryleft) = S ((S (d)) * dst_negative_scale_read_entryleft)) /\ exists ff_q_pvs_read_entryleftnegative. dst_negative_code_read_entryleft = ff_q_pvs_read_entryleftnegative * S ((S (d)) * dst_negative_scale_read_entryleft) + (dst_negative_read_entryleft))) /\ (exists ge_balance_positive_read_entryleftvalue ge_balance_negative_read_entryleftvalue. (((((dc_left_read_entry) = 2 * (ge_balance_positive_read_entryleftvalue) /\ (ge_balance_negative_read_entryleftvalue) = 0) \/ exists ge_signed_half_read_entryleftvaluedecode. (((dc_left_read_entry) = 2 * ge_signed_half_read_entryleftvaluedecode + 1 /\ (ge_balance_positive_read_entryleftvalue) = 0) /\ (ge_balance_negative_read_entryleftvalue) = S ge_signed_half_read_entryleftvaluedecode))) /\ ((dst_positive_read_entryleft) + ge_balance_negative_read_entryleftvalue = (dst_negative_read_entryleft) + ge_balance_positive_read_entryleftvalue))))))))) /\ (((exists dst_positive_code_read_entryright dst_positive_scale_read_entryright dst_negative_code_read_entryright dst_negative_scale_read_entryright dst_positive_read_entryright dst_negative_read_entryright. (((G) = (((((dst_positive_code_read_entryright) + (dst_positive_scale_read_entryright)) * S ((dst_positive_code_read_entryright) + (dst_positive_scale_read_entryright)) + ((dst_positive_scale_read_entryright) + (dst_positive_scale_read_entryright))) + (((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) * S ((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) + ((dst_negative_scale_read_entryright) + (dst_negative_scale_read_entryright)))) * S ((((dst_positive_code_read_entryright) + (dst_positive_scale_read_entryright)) * S ((dst_positive_code_read_entryright) + (dst_positive_scale_read_entryright)) + ((dst_positive_scale_read_entryright) + (dst_positive_scale_read_entryright))) + (((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) * S ((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) + ((dst_negative_scale_read_entryright) + (dst_negative_scale_read_entryright)))) + ((((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) * S ((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) + ((dst_negative_scale_read_entryright) + (dst_negative_scale_read_entryright))) + (((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) * S ((dst_negative_code_read_entryright) + (dst_negative_scale_read_entryright)) + ((dst_negative_scale_read_entryright) + (dst_negative_scale_read_entryright)))))) /\ (((((exists ff_h_pvs_read_entryrightpositive. ff_h_pvs_read_entryrightpositive + S (dst_positive_read_entryright) = S ((S (dc_quotient_read_entry)) * dst_positive_scale_read_entryright)) /\ exists ff_q_pvs_read_entryrightpositive. dst_positive_code_read_entryright = ff_q_pvs_read_entryrightpositive * S ((S (dc_quotient_read_entry)) * dst_positive_scale_read_entryright) + (dst_positive_read_entryright))) /\ (((((exists ff_h_pvs_read_entryrightnegative. ff_h_pvs_read_entryrightnegative + S (dst_negative_read_entryright) = S ((S (dc_quotient_read_entry)) * dst_negative_scale_read_entryright)) /\ exists ff_q_pvs_read_entryrightnegative. dst_negative_code_read_entryright = ff_q_pvs_read_entryrightnegative * S ((S (dc_quotient_read_entry)) * dst_negative_scale_read_entryright) + (dst_negative_read_entryright))) /\ (exists ge_balance_positive_read_entryrightvalue ge_balance_negative_read_entryrightvalue. (((((dc_right_read_entry) = 2 * (ge_balance_positive_read_entryrightvalue) /\ (ge_balance_negative_read_entryrightvalue) = 0) \/ exists ge_signed_half_read_entryrightvaluedecode. (((dc_right_read_entry) = 2 * ge_signed_half_read_entryrightvaluedecode + 1 /\ (ge_balance_positive_read_entryrightvalue) = 0) /\ (ge_balance_negative_read_entryrightvalue) = S ge_signed_half_read_entryrightvaluedecode))) /\ ((dst_positive_read_entryright) + ge_balance_negative_read_entryrightvalue = (dst_negative_read_entryright) + ge_balance_positive_read_entryrightvalue))))))))) /\ (exists sto_ap_read_entryproduct sto_an_read_entryproduct sto_bp_read_entryproduct sto_bn_read_entryproduct sto_cp_read_entryproduct sto_cn_read_entryproduct. (((((dc_left_read_entry) = 2 * (sto_ap_read_entryproduct) /\ (sto_an_read_entryproduct) = 0) \/ exists ge_signed_half_read_entryproductleft. (((dc_left_read_entry) = 2 * ge_signed_half_read_entryproductleft + 1 /\ (sto_ap_read_entryproduct) = 0) /\ (sto_an_read_entryproduct) = S ge_signed_half_read_entryproductleft))) /\ ((((((dc_right_read_entry) = 2 * (sto_bp_read_entryproduct) /\ (sto_bn_read_entryproduct) = 0) \/ exists ge_signed_half_read_entryproductright. (((dc_right_read_entry) = 2 * ge_signed_half_read_entryproductright + 1 /\ (sto_bp_read_entryproduct) = 0) /\ (sto_bn_read_entryproduct) = S ge_signed_half_read_entryproductright))) /\ ((((((z) = 2 * (sto_cp_read_entryproduct) /\ (sto_cn_read_entryproduct) = 0) \/ exists ge_signed_half_read_entryproductoutput. (((z) = 2 * ge_signed_half_read_entryproductoutput + 1 /\ (sto_cp_read_entryproduct) = 0) /\ (sto_cn_read_entryproduct) = S ge_signed_half_read_entryproductoutput))) /\ ((sto_ap_read_entryproduct * sto_bp_read_entryproduct + sto_an_read_entryproduct * sto_bn_read_entryproduct) + sto_cn_read_entryproduct = (sto_ap_read_entryproduct * sto_bn_read_entryproduct + sto_an_read_entryproduct * sto_bp_read_entryproduct) + sto_cp_read_entryproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_read_entrynondivisor. (n) = (d) * pvs_factor_read_entrynondivisor)) /\ ((z)=0)))) -> (exists sto_ap_read_product sto_an_read_product sto_bp_read_product sto_bn_read_product sto_cp_read_product sto_cn_read_product. (((((a) = 2 * (sto_ap_read_product) /\ (sto_an_read_product) = 0) \/ exists ge_signed_half_read_productleft. (((a) = 2 * ge_signed_half_read_productleft + 1 /\ (sto_ap_read_product) = 0) /\ (sto_an_read_product) = S ge_signed_half_read_productleft))) /\ ((((((b) = 2 * (sto_bp_read_product) /\ (sto_bn_read_product) = 0) \/ exists ge_signed_half_read_productright. (((b) = 2 * ge_signed_half_read_productright + 1 /\ (sto_bp_read_product) = 0) /\ (sto_bn_read_product) = S ge_signed_half_read_productright))) /\ ((((((z) = 2 * (sto_cp_read_product) /\ (sto_cn_read_product) = 0) \/ exists ge_signed_half_read_productoutput. (((z) = 2 * ge_signed_half_read_productoutput + 1 /\ (sto_cp_read_product) = 0) /\ (sto_cn_read_product) = S ge_signed_half_read_productoutput))) /\ ((sto_ap_read_product * sto_bp_read_product + sto_an_read_product * sto_bn_read_product) + sto_cn_read_product = (sto_ap_read_product * sto_bn_read_product + sto_an_read_product * sto_bp_read_product) + sto_cp_read_product)))))))

• dirichlet_convolution_prefix_append · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n l M z. (((exists dst_positive_code_append_sourcetable dst_positive_scale_append_sourcetable dst_negative_code_append_sourcetable dst_negative_scale_append_sourcetable. (((M) = (((((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) * S ((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) + ((dst_positive_scale_append_sourcetable) + (dst_positive_scale_append_sourcetable))) + (((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable)))) * S ((((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) * S ((dst_positive_code_append_sourcetable) + (dst_positive_scale_append_sourcetable)) + ((dst_positive_scale_append_sourcetable) + (dst_positive_scale_append_sourcetable))) + (((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable)))) + ((((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable))) + (((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) * S ((dst_negative_code_append_sourcetable) + (dst_negative_scale_append_sourcetable)) + ((dst_negative_scale_append_sourcetable) + (dst_negative_scale_append_sourcetable)))))) /\ (forall dst_index_append_sourcetable. (exists pvs_le_gap_append_sourcetabledomain. pvs_le_gap_append_sourcetabledomain + (dst_index_append_sourcetable) = (l)) -> exists dst_positive_append_sourcetable dst_negative_append_sourcetable dst_value_append_sourcetable. ((((exists ff_h_pvs_append_sourcetableentrypositive. ff_h_pvs_append_sourcetableentrypositive + S (dst_positive_append_sourcetable) = S ((S (dst_index_append_sourcetable)) * dst_positive_scale_append_sourcetable)) /\ exists ff_q_pvs_append_sourcetableentrypositive. dst_positive_code_append_sourcetable = ff_q_pvs_append_sourcetableentrypositive * S ((S (dst_index_append_sourcetable)) * dst_positive_scale_append_sourcetable) + (dst_positive_append_sourcetable))) /\ (((((exists ff_h_pvs_append_sourcetableentrynegative. ff_h_pvs_append_sourcetableentrynegative + S (dst_negative_append_sourcetable) = S ((S (dst_index_append_sourcetable)) * dst_negative_scale_append_sourcetable)) /\ exists ff_q_pvs_append_sourcetableentrynegative. dst_negative_code_append_sourcetable = ff_q_pvs_append_sourcetableentrynegative * S ((S (dst_index_append_sourcetable)) * dst_negative_scale_append_sourcetable) + (dst_negative_append_sourcetable))) /\ (exists ge_balance_positive_append_sourcetableentryvalue ge_balance_negative_append_sourcetableentryvalue. (((((dst_value_append_sourcetable) = 2 * (ge_balance_positive_append_sourcetableentryvalue) /\ (ge_balance_negative_append_sourcetableentryvalue) = 0) \/ exists ge_signed_half_append_sourcetableentryvaluedecode. (((dst_value_append_sourcetable) = 2 * ge_signed_half_append_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_append_sourcetableentryvalue) = 0) /\ (ge_balance_negative_append_sourcetableentryvalue) = S ge_signed_half_append_sourcetableentryvaluedecode))) /\ ((dst_positive_append_sourcetable) + ge_balance_negative_append_sourcetableentryvalue = (dst_negative_append_sourcetable) + ge_balance_positive_append_sourcetableentryvalue))))))))) /\ (forall dc_index_append_source dc_value_append_source. (exists pvs_le_gap_append_sourcedomain. pvs_le_gap_append_sourcedomain + (dc_index_append_source) = (l)) -> (exists dst_positive_code_append_sourcelookup dst_positive_scale_append_sourcelookup dst_negative_code_append_sourcelookup dst_negative_scale_append_sourcelookup dst_positive_append_sourcelookup dst_negative_append_sourcelookup. (((M) = (((((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) * S ((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) + ((dst_positive_scale_append_sourcelookup) + (dst_positive_scale_append_sourcelookup))) + (((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)))) * S ((((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) * S ((dst_positive_code_append_sourcelookup) + (dst_positive_scale_append_sourcelookup)) + ((dst_positive_scale_append_sourcelookup) + (dst_positive_scale_append_sourcelookup))) + (((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)))) + ((((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup))) + (((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) * S ((dst_negative_code_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)) + ((dst_negative_scale_append_sourcelookup) + (dst_negative_scale_append_sourcelookup)))))) /\ (((((exists ff_h_pvs_append_sourcelookuppositive. ff_h_pvs_append_sourcelookuppositive + S (dst_positive_append_sourcelookup) = S ((S (dc_index_append_source)) * dst_positive_scale_append_sourcelookup)) /\ exists ff_q_pvs_append_sourcelookuppositive. dst_positive_code_append_sourcelookup = ff_q_pvs_append_sourcelookuppositive * S ((S (dc_index_append_source)) * dst_positive_scale_append_sourcelookup) + (dst_positive_append_sourcelookup))) /\ (((((exists ff_h_pvs_append_sourcelookupnegative. ff_h_pvs_append_sourcelookupnegative + S (dst_negative_append_sourcelookup) = S ((S (dc_index_append_source)) * dst_negative_scale_append_sourcelookup)) /\ exists ff_q_pvs_append_sourcelookupnegative. dst_negative_code_append_sourcelookup = ff_q_pvs_append_sourcelookupnegative * S ((S (dc_index_append_source)) * dst_negative_scale_append_sourcelookup) + (dst_negative_append_sourcelookup))) /\ (exists ge_balance_positive_append_sourcelookupvalue ge_balance_negative_append_sourcelookupvalue. (((((dc_value_append_source) = 2 * (ge_balance_positive_append_sourcelookupvalue) /\ (ge_balance_negative_append_sourcelookupvalue) = 0) \/ exists ge_signed_half_append_sourcelookupvaluedecode. (((dc_value_append_source) = 2 * ge_signed_half_append_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_append_sourcelookupvalue) = 0) /\ (ge_balance_negative_append_sourcelookupvalue) = S ge_signed_half_append_sourcelookupvaluedecode))) /\ ((dst_positive_append_sourcelookup) + ge_balance_negative_append_sourcelookupvalue = (dst_negative_append_sourcelookup) + ge_balance_positive_append_sourcelookupvalue))))))))) -> ((((~((dc_index_append_source)=0)) /\ (exists dc_quotient_append_sourceentry dc_left_append_sourceentry dc_right_append_sourceentry. (((n)=(dc_index_append_source)*dc_quotient_append_sourceentry) /\ (((exists dst_positive_code_append_sourceentryleft dst_positive_scale_append_sourceentryleft dst_negative_code_append_sourceentryleft dst_negative_scale_append_sourceentryleft dst_positive_append_sourceentryleft dst_negative_append_sourceentryleft. (((F) = (((((dst_positive_code_append_sourceentryleft) + (dst_positive_scale_append_sourceentryleft)) * S ((dst_positive_code_append_sourceentryleft) + (dst_positive_scale_append_sourceentryleft)) + ((dst_positive_scale_append_sourceentryleft) + (dst_positive_scale_append_sourceentryleft))) + (((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) * S ((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) + ((dst_negative_scale_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)))) * S ((((dst_positive_code_append_sourceentryleft) + (dst_positive_scale_append_sourceentryleft)) * S ((dst_positive_code_append_sourceentryleft) + (dst_positive_scale_append_sourceentryleft)) + ((dst_positive_scale_append_sourceentryleft) + (dst_positive_scale_append_sourceentryleft))) + (((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) * S ((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) + ((dst_negative_scale_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)))) + ((((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) * S ((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) + ((dst_negative_scale_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft))) + (((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) * S ((dst_negative_code_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)) + ((dst_negative_scale_append_sourceentryleft) + (dst_negative_scale_append_sourceentryleft)))))) /\ (((((exists ff_h_pvs_append_sourceentryleftpositive. ff_h_pvs_append_sourceentryleftpositive + S (dst_positive_append_sourceentryleft) = S ((S (dc_index_append_source)) * dst_positive_scale_append_sourceentryleft)) /\ exists ff_q_pvs_append_sourceentryleftpositive. dst_positive_code_append_sourceentryleft = ff_q_pvs_append_sourceentryleftpositive * S ((S (dc_index_append_source)) * dst_positive_scale_append_sourceentryleft) + (dst_positive_append_sourceentryleft))) /\ (((((exists ff_h_pvs_append_sourceentryleftnegative. ff_h_pvs_append_sourceentryleftnegative + S (dst_negative_append_sourceentryleft) = S ((S (dc_index_append_source)) * dst_negative_scale_append_sourceentryleft)) /\ exists ff_q_pvs_append_sourceentryleftnegative. dst_negative_code_append_sourceentryleft = ff_q_pvs_append_sourceentryleftnegative * S ((S (dc_index_append_source)) * dst_negative_scale_append_sourceentryleft) + (dst_negative_append_sourceentryleft))) /\ (exists ge_balance_positive_append_sourceentryleftvalue ge_balance_negative_append_sourceentryleftvalue. (((((dc_left_append_sourceentry) = 2 * (ge_balance_positive_append_sourceentryleftvalue) /\ (ge_balance_negative_append_sourceentryleftvalue) = 0) \/ exists ge_signed_half_append_sourceentryleftvaluedecode. (((dc_left_append_sourceentry) = 2 * ge_signed_half_append_sourceentryleftvaluedecode + 1 /\ (ge_balance_positive_append_sourceentryleftvalue) = 0) /\ (ge_balance_negative_append_sourceentryleftvalue) = S ge_signed_half_append_sourceentryleftvaluedecode))) /\ ((dst_positive_append_sourceentryleft) + ge_balance_negative_append_sourceentryleftvalue = (dst_negative_append_sourceentryleft) + ge_balance_positive_append_sourceentryleftvalue))))))))) /\ (((exists dst_positive_code_append_sourceentryright dst_positive_scale_append_sourceentryright dst_negative_code_append_sourceentryright dst_negative_scale_append_sourceentryright dst_positive_append_sourceentryright dst_negative_append_sourceentryright. (((G) = (((((dst_positive_code_append_sourceentryright) + (dst_positive_scale_append_sourceentryright)) * S ((dst_positive_code_append_sourceentryright) + (dst_positive_scale_append_sourceentryright)) + ((dst_positive_scale_append_sourceentryright) + (dst_positive_scale_append_sourceentryright))) + (((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) * S ((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) + ((dst_negative_scale_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)))) * S ((((dst_positive_code_append_sourceentryright) + (dst_positive_scale_append_sourceentryright)) * S ((dst_positive_code_append_sourceentryright) + (dst_positive_scale_append_sourceentryright)) + ((dst_positive_scale_append_sourceentryright) + (dst_positive_scale_append_sourceentryright))) + (((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) * S ((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) + ((dst_negative_scale_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)))) + ((((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) * S ((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) + ((dst_negative_scale_append_sourceentryright) + (dst_negative_scale_append_sourceentryright))) + (((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) * S ((dst_negative_code_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)) + ((dst_negative_scale_append_sourceentryright) + (dst_negative_scale_append_sourceentryright)))))) /\ (((((exists ff_h_pvs_append_sourceentryrightpositive. ff_h_pvs_append_sourceentryrightpositive + S (dst_positive_append_sourceentryright) = S ((S (dc_quotient_append_sourceentry)) * dst_positive_scale_append_sourceentryright)) /\ exists ff_q_pvs_append_sourceentryrightpositive. dst_positive_code_append_sourceentryright = ff_q_pvs_append_sourceentryrightpositive * S ((S (dc_quotient_append_sourceentry)) * dst_positive_scale_append_sourceentryright) + (dst_positive_append_sourceentryright))) /\ (((((exists ff_h_pvs_append_sourceentryrightnegative. ff_h_pvs_append_sourceentryrightnegative + S (dst_negative_append_sourceentryright) = S ((S (dc_quotient_append_sourceentry)) * dst_negative_scale_append_sourceentryright)) /\ exists ff_q_pvs_append_sourceentryrightnegative. dst_negative_code_append_sourceentryright = ff_q_pvs_append_sourceentryrightnegative * S ((S (dc_quotient_append_sourceentry)) * dst_negative_scale_append_sourceentryright) + (dst_negative_append_sourceentryright))) /\ (exists ge_balance_positive_append_sourceentryrightvalue ge_balance_negative_append_sourceentryrightvalue. (((((dc_right_append_sourceentry) = 2 * (ge_balance_positive_append_sourceentryrightvalue) /\ (ge_balance_negative_append_sourceentryrightvalue) = 0) \/ exists ge_signed_half_append_sourceentryrightvaluedecode. (((dc_right_append_sourceentry) = 2 * ge_signed_half_append_sourceentryrightvaluedecode + 1 /\ (ge_balance_positive_append_sourceentryrightvalue) = 0) /\ (ge_balance_negative_append_sourceentryrightvalue) = S ge_signed_half_append_sourceentryrightvaluedecode))) /\ ((dst_positive_append_sourceentryright) + ge_balance_negative_append_sourceentryrightvalue = (dst_negative_append_sourceentryright) + ge_balance_positive_append_sourceentryrightvalue))))))))) /\ (exists sto_ap_append_sourceentryproduct sto_an_append_sourceentryproduct sto_bp_append_sourceentryproduct sto_bn_append_sourceentryproduct sto_cp_append_sourceentryproduct sto_cn_append_sourceentryproduct. (((((dc_left_append_sourceentry) = 2 * (sto_ap_append_sourceentryproduct) /\ (sto_an_append_sourceentryproduct) = 0) \/ exists ge_signed_half_append_sourceentryproductleft. (((dc_left_append_sourceentry) = 2 * ge_signed_half_append_sourceentryproductleft + 1 /\ (sto_ap_append_sourceentryproduct) = 0) /\ (sto_an_append_sourceentryproduct) = S ge_signed_half_append_sourceentryproductleft))) /\ ((((((dc_right_append_sourceentry) = 2 * (sto_bp_append_sourceentryproduct) /\ (sto_bn_append_sourceentryproduct) = 0) \/ exists ge_signed_half_append_sourceentryproductright. (((dc_right_append_sourceentry) = 2 * ge_signed_half_append_sourceentryproductright + 1 /\ (sto_bp_append_sourceentryproduct) = 0) /\ (sto_bn_append_sourceentryproduct) = S ge_signed_half_append_sourceentryproductright))) /\ ((((((dc_value_append_source) = 2 * (sto_cp_append_sourceentryproduct) /\ (sto_cn_append_sourceentryproduct) = 0) \/ exists ge_signed_half_append_sourceentryproductoutput. (((dc_value_append_source) = 2 * ge_signed_half_append_sourceentryproductoutput + 1 /\ (sto_cp_append_sourceentryproduct) = 0) /\ (sto_cn_append_sourceentryproduct) = S ge_signed_half_append_sourceentryproductoutput))) /\ ((sto_ap_append_sourceentryproduct * sto_bp_append_sourceentryproduct + sto_an_append_sourceentryproduct * sto_bn_append_sourceentryproduct) + sto_cn_append_sourceentryproduct = (sto_ap_append_sourceentryproduct * sto_bn_append_sourceentryproduct + sto_an_append_sourceentryproduct * sto_bp_append_sourceentryproduct) + sto_cp_append_sourceentryproduct))))))))))))))) \/ ((((dc_index_append_source)=0 \/ ~(exists pvs_factor_append_sourceentrynondivisor. (n) = (dc_index_append_source) * pvs_factor_append_sourceentrynondivisor)) /\ ((dc_value_append_source)=0))))))) -> ((((~((S l)=0)) /\ (exists dc_quotient_append_last dc_left_append_last dc_right_append_last. (((n)=(S l)*dc_quotient_append_last) /\ (((exists dst_positive_code_append_lastleft dst_positive_scale_append_lastleft dst_negative_code_append_lastleft dst_negative_scale_append_lastleft dst_positive_append_lastleft dst_negative_append_lastleft. (((F) = (((((dst_positive_code_append_lastleft) + (dst_positive_scale_append_lastleft)) * S ((dst_positive_code_append_lastleft) + (dst_positive_scale_append_lastleft)) + ((dst_positive_scale_append_lastleft) + (dst_positive_scale_append_lastleft))) + (((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) * S ((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) + ((dst_negative_scale_append_lastleft) + (dst_negative_scale_append_lastleft)))) * S ((((dst_positive_code_append_lastleft) + (dst_positive_scale_append_lastleft)) * S ((dst_positive_code_append_lastleft) + (dst_positive_scale_append_lastleft)) + ((dst_positive_scale_append_lastleft) + (dst_positive_scale_append_lastleft))) + (((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) * S ((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) + ((dst_negative_scale_append_lastleft) + (dst_negative_scale_append_lastleft)))) + ((((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) * S ((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) + ((dst_negative_scale_append_lastleft) + (dst_negative_scale_append_lastleft))) + (((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) * S ((dst_negative_code_append_lastleft) + (dst_negative_scale_append_lastleft)) + ((dst_negative_scale_append_lastleft) + (dst_negative_scale_append_lastleft)))))) /\ (((((exists ff_h_pvs_append_lastleftpositive. ff_h_pvs_append_lastleftpositive + S (dst_positive_append_lastleft) = S ((S (S l)) * dst_positive_scale_append_lastleft)) /\ exists ff_q_pvs_append_lastleftpositive. dst_positive_code_append_lastleft = ff_q_pvs_append_lastleftpositive * S ((S (S l)) * dst_positive_scale_append_lastleft) + (dst_positive_append_lastleft))) /\ (((((exists ff_h_pvs_append_lastleftnegative. ff_h_pvs_append_lastleftnegative + S (dst_negative_append_lastleft) = S ((S (S l)) * dst_negative_scale_append_lastleft)) /\ exists ff_q_pvs_append_lastleftnegative. dst_negative_code_append_lastleft = ff_q_pvs_append_lastleftnegative * S ((S (S l)) * dst_negative_scale_append_lastleft) + (dst_negative_append_lastleft))) /\ (exists ge_balance_positive_append_lastleftvalue ge_balance_negative_append_lastleftvalue. (((((dc_left_append_last) = 2 * (ge_balance_positive_append_lastleftvalue) /\ (ge_balance_negative_append_lastleftvalue) = 0) \/ exists ge_signed_half_append_lastleftvaluedecode. (((dc_left_append_last) = 2 * ge_signed_half_append_lastleftvaluedecode + 1 /\ (ge_balance_positive_append_lastleftvalue) = 0) /\ (ge_balance_negative_append_lastleftvalue) = S ge_signed_half_append_lastleftvaluedecode))) /\ ((dst_positive_append_lastleft) + ge_balance_negative_append_lastleftvalue = (dst_negative_append_lastleft) + ge_balance_positive_append_lastleftvalue))))))))) /\ (((exists dst_positive_code_append_lastright dst_positive_scale_append_lastright dst_negative_code_append_lastright dst_negative_scale_append_lastright dst_positive_append_lastright dst_negative_append_lastright. (((G) = (((((dst_positive_code_append_lastright) + (dst_positive_scale_append_lastright)) * S ((dst_positive_code_append_lastright) + (dst_positive_scale_append_lastright)) + ((dst_positive_scale_append_lastright) + (dst_positive_scale_append_lastright))) + (((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) * S ((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) + ((dst_negative_scale_append_lastright) + (dst_negative_scale_append_lastright)))) * S ((((dst_positive_code_append_lastright) + (dst_positive_scale_append_lastright)) * S ((dst_positive_code_append_lastright) + (dst_positive_scale_append_lastright)) + ((dst_positive_scale_append_lastright) + (dst_positive_scale_append_lastright))) + (((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) * S ((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) + ((dst_negative_scale_append_lastright) + (dst_negative_scale_append_lastright)))) + ((((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) * S ((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) + ((dst_negative_scale_append_lastright) + (dst_negative_scale_append_lastright))) + (((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) * S ((dst_negative_code_append_lastright) + (dst_negative_scale_append_lastright)) + ((dst_negative_scale_append_lastright) + (dst_negative_scale_append_lastright)))))) /\ (((((exists ff_h_pvs_append_lastrightpositive. ff_h_pvs_append_lastrightpositive + S (dst_positive_append_lastright) = S ((S (dc_quotient_append_last)) * dst_positive_scale_append_lastright)) /\ exists ff_q_pvs_append_lastrightpositive. dst_positive_code_append_lastright = ff_q_pvs_append_lastrightpositive * S ((S (dc_quotient_append_last)) * dst_positive_scale_append_lastright) + (dst_positive_append_lastright))) /\ (((((exists ff_h_pvs_append_lastrightnegative. ff_h_pvs_append_lastrightnegative + S (dst_negative_append_lastright) = S ((S (dc_quotient_append_last)) * dst_negative_scale_append_lastright)) /\ exists ff_q_pvs_append_lastrightnegative. dst_negative_code_append_lastright = ff_q_pvs_append_lastrightnegative * S ((S (dc_quotient_append_last)) * dst_negative_scale_append_lastright) + (dst_negative_append_lastright))) /\ (exists ge_balance_positive_append_lastrightvalue ge_balance_negative_append_lastrightvalue. (((((dc_right_append_last) = 2 * (ge_balance_positive_append_lastrightvalue) /\ (ge_balance_negative_append_lastrightvalue) = 0) \/ exists ge_signed_half_append_lastrightvaluedecode. (((dc_right_append_last) = 2 * ge_signed_half_append_lastrightvaluedecode + 1 /\ (ge_balance_positive_append_lastrightvalue) = 0) /\ (ge_balance_negative_append_lastrightvalue) = S ge_signed_half_append_lastrightvaluedecode))) /\ ((dst_positive_append_lastright) + ge_balance_negative_append_lastrightvalue = (dst_negative_append_lastright) + ge_balance_positive_append_lastrightvalue))))))))) /\ (exists sto_ap_append_lastproduct sto_an_append_lastproduct sto_bp_append_lastproduct sto_bn_append_lastproduct sto_cp_append_lastproduct sto_cn_append_lastproduct. (((((dc_left_append_last) = 2 * (sto_ap_append_lastproduct) /\ (sto_an_append_lastproduct) = 0) \/ exists ge_signed_half_append_lastproductleft. (((dc_left_append_last) = 2 * ge_signed_half_append_lastproductleft + 1 /\ (sto_ap_append_lastproduct) = 0) /\ (sto_an_append_lastproduct) = S ge_signed_half_append_lastproductleft))) /\ ((((((dc_right_append_last) = 2 * (sto_bp_append_lastproduct) /\ (sto_bn_append_lastproduct) = 0) \/ exists ge_signed_half_append_lastproductright. (((dc_right_append_last) = 2 * ge_signed_half_append_lastproductright + 1 /\ (sto_bp_append_lastproduct) = 0) /\ (sto_bn_append_lastproduct) = S ge_signed_half_append_lastproductright))) /\ ((((((z) = 2 * (sto_cp_append_lastproduct) /\ (sto_cn_append_lastproduct) = 0) \/ exists ge_signed_half_append_lastproductoutput. (((z) = 2 * ge_signed_half_append_lastproductoutput + 1 /\ (sto_cp_append_lastproduct) = 0) /\ (sto_cn_append_lastproduct) = S ge_signed_half_append_lastproductoutput))) /\ ((sto_ap_append_lastproduct * sto_bp_append_lastproduct + sto_an_append_lastproduct * sto_bn_append_lastproduct) + sto_cn_append_lastproduct = (sto_ap_append_lastproduct * sto_bn_append_lastproduct + sto_an_append_lastproduct * sto_bp_append_lastproduct) + sto_cp_append_lastproduct))))))))))))))) \/ ((((S l)=0 \/ ~(exists pvs_factor_append_lastnondivisor. (n) = (S l) * pvs_factor_append_lastnondivisor)) /\ ((z)=0)))) -> exists H. (((exists dst_positive_code_append_resulttable dst_positive_scale_append_resulttable dst_negative_code_append_resulttable dst_negative_scale_append_resulttable. (((H) = (((((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) * S ((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) + ((dst_positive_scale_append_resulttable) + (dst_positive_scale_append_resulttable))) + (((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable)))) * S ((((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) * S ((dst_positive_code_append_resulttable) + (dst_positive_scale_append_resulttable)) + ((dst_positive_scale_append_resulttable) + (dst_positive_scale_append_resulttable))) + (((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable)))) + ((((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable))) + (((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) * S ((dst_negative_code_append_resulttable) + (dst_negative_scale_append_resulttable)) + ((dst_negative_scale_append_resulttable) + (dst_negative_scale_append_resulttable)))))) /\ (forall dst_index_append_resulttable. (exists pvs_le_gap_append_resulttabledomain. pvs_le_gap_append_resulttabledomain + (dst_index_append_resulttable) = (S l)) -> exists dst_positive_append_resulttable dst_negative_append_resulttable dst_value_append_resulttable. ((((exists ff_h_pvs_append_resulttableentrypositive. ff_h_pvs_append_resulttableentrypositive + S (dst_positive_append_resulttable) = S ((S (dst_index_append_resulttable)) * dst_positive_scale_append_resulttable)) /\ exists ff_q_pvs_append_resulttableentrypositive. dst_positive_code_append_resulttable = ff_q_pvs_append_resulttableentrypositive * S ((S (dst_index_append_resulttable)) * dst_positive_scale_append_resulttable) + (dst_positive_append_resulttable))) /\ (((((exists ff_h_pvs_append_resulttableentrynegative. ff_h_pvs_append_resulttableentrynegative + S (dst_negative_append_resulttable) = S ((S (dst_index_append_resulttable)) * dst_negative_scale_append_resulttable)) /\ exists ff_q_pvs_append_resulttableentrynegative. dst_negative_code_append_resulttable = ff_q_pvs_append_resulttableentrynegative * S ((S (dst_index_append_resulttable)) * dst_negative_scale_append_resulttable) + (dst_negative_append_resulttable))) /\ (exists ge_balance_positive_append_resulttableentryvalue ge_balance_negative_append_resulttableentryvalue. (((((dst_value_append_resulttable) = 2 * (ge_balance_positive_append_resulttableentryvalue) /\ (ge_balance_negative_append_resulttableentryvalue) = 0) \/ exists ge_signed_half_append_resulttableentryvaluedecode. (((dst_value_append_resulttable) = 2 * ge_signed_half_append_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_append_resulttableentryvalue) = 0) /\ (ge_balance_negative_append_resulttableentryvalue) = S ge_signed_half_append_resulttableentryvaluedecode))) /\ ((dst_positive_append_resulttable) + ge_balance_negative_append_resulttableentryvalue = (dst_negative_append_resulttable) + ge_balance_positive_append_resulttableentryvalue))))))))) /\ (forall dc_index_append_result dc_value_append_result. (exists pvs_le_gap_append_resultdomain. pvs_le_gap_append_resultdomain + (dc_index_append_result) = (S l)) -> (exists dst_positive_code_append_resultlookup dst_positive_scale_append_resultlookup dst_negative_code_append_resultlookup dst_negative_scale_append_resultlookup dst_positive_append_resultlookup dst_negative_append_resultlookup. (((H) = (((((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) * S ((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) + ((dst_positive_scale_append_resultlookup) + (dst_positive_scale_append_resultlookup))) + (((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup)))) * S ((((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) * S ((dst_positive_code_append_resultlookup) + (dst_positive_scale_append_resultlookup)) + ((dst_positive_scale_append_resultlookup) + (dst_positive_scale_append_resultlookup))) + (((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup)))) + ((((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup))) + (((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) * S ((dst_negative_code_append_resultlookup) + (dst_negative_scale_append_resultlookup)) + ((dst_negative_scale_append_resultlookup) + (dst_negative_scale_append_resultlookup)))))) /\ (((((exists ff_h_pvs_append_resultlookuppositive. ff_h_pvs_append_resultlookuppositive + S (dst_positive_append_resultlookup) = S ((S (dc_index_append_result)) * dst_positive_scale_append_resultlookup)) /\ exists ff_q_pvs_append_resultlookuppositive. dst_positive_code_append_resultlookup = ff_q_pvs_append_resultlookuppositive * S ((S (dc_index_append_result)) * dst_positive_scale_append_resultlookup) + (dst_positive_append_resultlookup))) /\ (((((exists ff_h_pvs_append_resultlookupnegative. ff_h_pvs_append_resultlookupnegative + S (dst_negative_append_resultlookup) = S ((S (dc_index_append_result)) * dst_negative_scale_append_resultlookup)) /\ exists ff_q_pvs_append_resultlookupnegative. dst_negative_code_append_resultlookup = ff_q_pvs_append_resultlookupnegative * S ((S (dc_index_append_result)) * dst_negative_scale_append_resultlookup) + (dst_negative_append_resultlookup))) /\ (exists ge_balance_positive_append_resultlookupvalue ge_balance_negative_append_resultlookupvalue. (((((dc_value_append_result) = 2 * (ge_balance_positive_append_resultlookupvalue) /\ (ge_balance_negative_append_resultlookupvalue) = 0) \/ exists ge_signed_half_append_resultlookupvaluedecode. (((dc_value_append_result) = 2 * ge_signed_half_append_resultlookupvaluedecode + 1 /\ (ge_balance_positive_append_resultlookupvalue) = 0) /\ (ge_balance_negative_append_resultlookupvalue) = S ge_signed_half_append_resultlookupvaluedecode))) /\ ((dst_positive_append_resultlookup) + ge_balance_negative_append_resultlookupvalue = (dst_negative_append_resultlookup) + ge_balance_positive_append_resultlookupvalue))))))))) -> ((((~((dc_index_append_result)=0)) /\ (exists dc_quotient_append_resultentry dc_left_append_resultentry dc_right_append_resultentry. (((n)=(dc_index_append_result)*dc_quotient_append_resultentry) /\ (((exists dst_positive_code_append_resultentryleft dst_positive_scale_append_resultentryleft dst_negative_code_append_resultentryleft dst_negative_scale_append_resultentryleft dst_positive_append_resultentryleft dst_negative_append_resultentryleft. (((F) = (((((dst_positive_code_append_resultentryleft) + (dst_positive_scale_append_resultentryleft)) * S ((dst_positive_code_append_resultentryleft) + (dst_positive_scale_append_resultentryleft)) + ((dst_positive_scale_append_resultentryleft) + (dst_positive_scale_append_resultentryleft))) + (((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) * S ((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) + ((dst_negative_scale_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)))) * S ((((dst_positive_code_append_resultentryleft) + (dst_positive_scale_append_resultentryleft)) * S ((dst_positive_code_append_resultentryleft) + (dst_positive_scale_append_resultentryleft)) + ((dst_positive_scale_append_resultentryleft) + (dst_positive_scale_append_resultentryleft))) + (((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) * S ((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) + ((dst_negative_scale_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)))) + ((((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) * S ((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) + ((dst_negative_scale_append_resultentryleft) + (dst_negative_scale_append_resultentryleft))) + (((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) * S ((dst_negative_code_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)) + ((dst_negative_scale_append_resultentryleft) + (dst_negative_scale_append_resultentryleft)))))) /\ (((((exists ff_h_pvs_append_resultentryleftpositive. ff_h_pvs_append_resultentryleftpositive + S (dst_positive_append_resultentryleft) = S ((S (dc_index_append_result)) * dst_positive_scale_append_resultentryleft)) /\ exists ff_q_pvs_append_resultentryleftpositive. dst_positive_code_append_resultentryleft = ff_q_pvs_append_resultentryleftpositive * S ((S (dc_index_append_result)) * dst_positive_scale_append_resultentryleft) + (dst_positive_append_resultentryleft))) /\ (((((exists ff_h_pvs_append_resultentryleftnegative. ff_h_pvs_append_resultentryleftnegative + S (dst_negative_append_resultentryleft) = S ((S (dc_index_append_result)) * dst_negative_scale_append_resultentryleft)) /\ exists ff_q_pvs_append_resultentryleftnegative. dst_negative_code_append_resultentryleft = ff_q_pvs_append_resultentryleftnegative * S ((S (dc_index_append_result)) * dst_negative_scale_append_resultentryleft) + (dst_negative_append_resultentryleft))) /\ (exists ge_balance_positive_append_resultentryleftvalue ge_balance_negative_append_resultentryleftvalue. (((((dc_left_append_resultentry) = 2 * (ge_balance_positive_append_resultentryleftvalue) /\ (ge_balance_negative_append_resultentryleftvalue) = 0) \/ exists ge_signed_half_append_resultentryleftvaluedecode. (((dc_left_append_resultentry) = 2 * ge_signed_half_append_resultentryleftvaluedecode + 1 /\ (ge_balance_positive_append_resultentryleftvalue) = 0) /\ (ge_balance_negative_append_resultentryleftvalue) = S ge_signed_half_append_resultentryleftvaluedecode))) /\ ((dst_positive_append_resultentryleft) + ge_balance_negative_append_resultentryleftvalue = (dst_negative_append_resultentryleft) + ge_balance_positive_append_resultentryleftvalue))))))))) /\ (((exists dst_positive_code_append_resultentryright dst_positive_scale_append_resultentryright dst_negative_code_append_resultentryright dst_negative_scale_append_resultentryright dst_positive_append_resultentryright dst_negative_append_resultentryright. (((G) = (((((dst_positive_code_append_resultentryright) + (dst_positive_scale_append_resultentryright)) * S ((dst_positive_code_append_resultentryright) + (dst_positive_scale_append_resultentryright)) + ((dst_positive_scale_append_resultentryright) + (dst_positive_scale_append_resultentryright))) + (((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) * S ((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) + ((dst_negative_scale_append_resultentryright) + (dst_negative_scale_append_resultentryright)))) * S ((((dst_positive_code_append_resultentryright) + (dst_positive_scale_append_resultentryright)) * S ((dst_positive_code_append_resultentryright) + (dst_positive_scale_append_resultentryright)) + ((dst_positive_scale_append_resultentryright) + (dst_positive_scale_append_resultentryright))) + (((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) * S ((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) + ((dst_negative_scale_append_resultentryright) + (dst_negative_scale_append_resultentryright)))) + ((((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) * S ((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) + ((dst_negative_scale_append_resultentryright) + (dst_negative_scale_append_resultentryright))) + (((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) * S ((dst_negative_code_append_resultentryright) + (dst_negative_scale_append_resultentryright)) + ((dst_negative_scale_append_resultentryright) + (dst_negative_scale_append_resultentryright)))))) /\ (((((exists ff_h_pvs_append_resultentryrightpositive. ff_h_pvs_append_resultentryrightpositive + S (dst_positive_append_resultentryright) = S ((S (dc_quotient_append_resultentry)) * dst_positive_scale_append_resultentryright)) /\ exists ff_q_pvs_append_resultentryrightpositive. dst_positive_code_append_resultentryright = ff_q_pvs_append_resultentryrightpositive * S ((S (dc_quotient_append_resultentry)) * dst_positive_scale_append_resultentryright) + (dst_positive_append_resultentryright))) /\ (((((exists ff_h_pvs_append_resultentryrightnegative. ff_h_pvs_append_resultentryrightnegative + S (dst_negative_append_resultentryright) = S ((S (dc_quotient_append_resultentry)) * dst_negative_scale_append_resultentryright)) /\ exists ff_q_pvs_append_resultentryrightnegative. dst_negative_code_append_resultentryright = ff_q_pvs_append_resultentryrightnegative * S ((S (dc_quotient_append_resultentry)) * dst_negative_scale_append_resultentryright) + (dst_negative_append_resultentryright))) /\ (exists ge_balance_positive_append_resultentryrightvalue ge_balance_negative_append_resultentryrightvalue. (((((dc_right_append_resultentry) = 2 * (ge_balance_positive_append_resultentryrightvalue) /\ (ge_balance_negative_append_resultentryrightvalue) = 0) \/ exists ge_signed_half_append_resultentryrightvaluedecode. (((dc_right_append_resultentry) = 2 * ge_signed_half_append_resultentryrightvaluedecode + 1 /\ (ge_balance_positive_append_resultentryrightvalue) = 0) /\ (ge_balance_negative_append_resultentryrightvalue) = S ge_signed_half_append_resultentryrightvaluedecode))) /\ ((dst_positive_append_resultentryright) + ge_balance_negative_append_resultentryrightvalue = (dst_negative_append_resultentryright) + ge_balance_positive_append_resultentryrightvalue))))))))) /\ (exists sto_ap_append_resultentryproduct sto_an_append_resultentryproduct sto_bp_append_resultentryproduct sto_bn_append_resultentryproduct sto_cp_append_resultentryproduct sto_cn_append_resultentryproduct. (((((dc_left_append_resultentry) = 2 * (sto_ap_append_resultentryproduct) /\ (sto_an_append_resultentryproduct) = 0) \/ exists ge_signed_half_append_resultentryproductleft. (((dc_left_append_resultentry) = 2 * ge_signed_half_append_resultentryproductleft + 1 /\ (sto_ap_append_resultentryproduct) = 0) /\ (sto_an_append_resultentryproduct) = S ge_signed_half_append_resultentryproductleft))) /\ ((((((dc_right_append_resultentry) = 2 * (sto_bp_append_resultentryproduct) /\ (sto_bn_append_resultentryproduct) = 0) \/ exists ge_signed_half_append_resultentryproductright. (((dc_right_append_resultentry) = 2 * ge_signed_half_append_resultentryproductright + 1 /\ (sto_bp_append_resultentryproduct) = 0) /\ (sto_bn_append_resultentryproduct) = S ge_signed_half_append_resultentryproductright))) /\ ((((((dc_value_append_result) = 2 * (sto_cp_append_resultentryproduct) /\ (sto_cn_append_resultentryproduct) = 0) \/ exists ge_signed_half_append_resultentryproductoutput. (((dc_value_append_result) = 2 * ge_signed_half_append_resultentryproductoutput + 1 /\ (sto_cp_append_resultentryproduct) = 0) /\ (sto_cn_append_resultentryproduct) = S ge_signed_half_append_resultentryproductoutput))) /\ ((sto_ap_append_resultentryproduct * sto_bp_append_resultentryproduct + sto_an_append_resultentryproduct * sto_bn_append_resultentryproduct) + sto_cn_append_resultentryproduct = (sto_ap_append_resultentryproduct * sto_bn_append_resultentryproduct + sto_an_append_resultentryproduct * sto_bp_append_resultentryproduct) + sto_cp_append_resultentryproduct))))))))))))))) \/ ((((dc_index_append_result)=0 \/ ~(exists pvs_factor_append_resultentrynondivisor. (n) = (dc_index_append_result) * pvs_factor_append_resultentrynondivisor)) /\ ((dc_value_append_result)=0))))))) /\ (forall dst_index_append_equal dst_first_append_equal dst_second_append_equal. (exists pvs_gap_append_equalbound. pvs_gap_append_equalbound + S (dst_index_append_equal) = (S l)) -> (exists dst_positive_code_append_equalfirst dst_positive_scale_append_equalfirst dst_negative_code_append_equalfirst dst_negative_scale_append_equalfirst dst_positive_append_equalfirst dst_negative_append_equalfirst. (((M) = (((((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) * S ((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) + ((dst_positive_scale_append_equalfirst) + (dst_positive_scale_append_equalfirst))) + (((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst)))) * S ((((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) * S ((dst_positive_code_append_equalfirst) + (dst_positive_scale_append_equalfirst)) + ((dst_positive_scale_append_equalfirst) + (dst_positive_scale_append_equalfirst))) + (((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst)))) + ((((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst))) + (((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) * S ((dst_negative_code_append_equalfirst) + (dst_negative_scale_append_equalfirst)) + ((dst_negative_scale_append_equalfirst) + (dst_negative_scale_append_equalfirst)))))) /\ (((((exists ff_h_pvs_append_equalfirstpositive. ff_h_pvs_append_equalfirstpositive + S (dst_positive_append_equalfirst) = S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalfirst)) /\ exists ff_q_pvs_append_equalfirstpositive. dst_positive_code_append_equalfirst = ff_q_pvs_append_equalfirstpositive * S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalfirst) + (dst_positive_append_equalfirst))) /\ (((((exists ff_h_pvs_append_equalfirstnegative. ff_h_pvs_append_equalfirstnegative + S (dst_negative_append_equalfirst) = S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalfirst)) /\ exists ff_q_pvs_append_equalfirstnegative. dst_negative_code_append_equalfirst = ff_q_pvs_append_equalfirstnegative * S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalfirst) + (dst_negative_append_equalfirst))) /\ (exists ge_balance_positive_append_equalfirstvalue ge_balance_negative_append_equalfirstvalue. (((((dst_first_append_equal) = 2 * (ge_balance_positive_append_equalfirstvalue) /\ (ge_balance_negative_append_equalfirstvalue) = 0) \/ exists ge_signed_half_append_equalfirstvaluedecode. (((dst_first_append_equal) = 2 * ge_signed_half_append_equalfirstvaluedecode + 1 /\ (ge_balance_positive_append_equalfirstvalue) = 0) /\ (ge_balance_negative_append_equalfirstvalue) = S ge_signed_half_append_equalfirstvaluedecode))) /\ ((dst_positive_append_equalfirst) + ge_balance_negative_append_equalfirstvalue = (dst_negative_append_equalfirst) + ge_balance_positive_append_equalfirstvalue))))))))) -> (exists dst_positive_code_append_equalsecond dst_positive_scale_append_equalsecond dst_negative_code_append_equalsecond dst_negative_scale_append_equalsecond dst_positive_append_equalsecond dst_negative_append_equalsecond. (((H) = (((((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) * S ((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) + ((dst_positive_scale_append_equalsecond) + (dst_positive_scale_append_equalsecond))) + (((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond)))) * S ((((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) * S ((dst_positive_code_append_equalsecond) + (dst_positive_scale_append_equalsecond)) + ((dst_positive_scale_append_equalsecond) + (dst_positive_scale_append_equalsecond))) + (((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond)))) + ((((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond))) + (((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) * S ((dst_negative_code_append_equalsecond) + (dst_negative_scale_append_equalsecond)) + ((dst_negative_scale_append_equalsecond) + (dst_negative_scale_append_equalsecond)))))) /\ (((((exists ff_h_pvs_append_equalsecondpositive. ff_h_pvs_append_equalsecondpositive + S (dst_positive_append_equalsecond) = S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalsecond)) /\ exists ff_q_pvs_append_equalsecondpositive. dst_positive_code_append_equalsecond = ff_q_pvs_append_equalsecondpositive * S ((S (dst_index_append_equal)) * dst_positive_scale_append_equalsecond) + (dst_positive_append_equalsecond))) /\ (((((exists ff_h_pvs_append_equalsecondnegative. ff_h_pvs_append_equalsecondnegative + S (dst_negative_append_equalsecond) = S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalsecond)) /\ exists ff_q_pvs_append_equalsecondnegative. dst_negative_code_append_equalsecond = ff_q_pvs_append_equalsecondnegative * S ((S (dst_index_append_equal)) * dst_negative_scale_append_equalsecond) + (dst_negative_append_equalsecond))) /\ (exists ge_balance_positive_append_equalsecondvalue ge_balance_negative_append_equalsecondvalue. (((((dst_second_append_equal) = 2 * (ge_balance_positive_append_equalsecondvalue) /\ (ge_balance_negative_append_equalsecondvalue) = 0) \/ exists ge_signed_half_append_equalsecondvaluedecode. (((dst_second_append_equal) = 2 * ge_signed_half_append_equalsecondvaluedecode + 1 /\ (ge_balance_positive_append_equalsecondvalue) = 0) /\ (ge_balance_negative_append_equalsecondvalue) = S ge_signed_half_append_equalsecondvaluedecode))) /\ ((dst_positive_append_equalsecond) + ge_balance_negative_append_equalsecondvalue = (dst_negative_append_equalsecond) + ge_balance_positive_append_equalsecondvalue))))))))) -> dst_first_append_equal = dst_second_append_equal)

• dirichlet_convolution_prefix_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n l. (exists dst_positive_code_exists_left dst_positive_scale_exists_left dst_negative_code_exists_left dst_negative_scale_exists_left. (((F) = (((((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) * S ((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) + ((dst_positive_scale_exists_left) + (dst_positive_scale_exists_left))) + (((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left)))) * S ((((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) * S ((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) + ((dst_positive_scale_exists_left) + (dst_positive_scale_exists_left))) + (((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left)))) + ((((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left))) + (((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left)))))) /\ (forall dst_index_exists_left. (exists pvs_le_gap_exists_leftdomain. pvs_le_gap_exists_leftdomain + (dst_index_exists_left) = (0)) -> exists dst_positive_exists_left dst_negative_exists_left dst_value_exists_left. ((((exists ff_h_pvs_exists_leftentrypositive. ff_h_pvs_exists_leftentrypositive + S (dst_positive_exists_left) = S ((S (dst_index_exists_left)) * dst_positive_scale_exists_left)) /\ exists ff_q_pvs_exists_leftentrypositive. dst_positive_code_exists_left = ff_q_pvs_exists_leftentrypositive * S ((S (dst_index_exists_left)) * dst_positive_scale_exists_left) + (dst_positive_exists_left))) /\ (((((exists ff_h_pvs_exists_leftentrynegative. ff_h_pvs_exists_leftentrynegative + S (dst_negative_exists_left) = S ((S (dst_index_exists_left)) * dst_negative_scale_exists_left)) /\ exists ff_q_pvs_exists_leftentrynegative. dst_negative_code_exists_left = ff_q_pvs_exists_leftentrynegative * S ((S (dst_index_exists_left)) * dst_negative_scale_exists_left) + (dst_negative_exists_left))) /\ (exists ge_balance_positive_exists_leftentryvalue ge_balance_negative_exists_leftentryvalue. (((((dst_value_exists_left) = 2 * (ge_balance_positive_exists_leftentryvalue) /\ (ge_balance_negative_exists_leftentryvalue) = 0) \/ exists ge_signed_half_exists_leftentryvaluedecode. (((dst_value_exists_left) = 2 * ge_signed_half_exists_leftentryvaluedecode + 1 /\ (ge_balance_positive_exists_leftentryvalue) = 0) /\ (ge_balance_negative_exists_leftentryvalue) = S ge_signed_half_exists_leftentryvaluedecode))) /\ ((dst_positive_exists_left) + ge_balance_negative_exists_leftentryvalue = (dst_negative_exists_left) + ge_balance_positive_exists_leftentryvalue))))))))) -> (exists dst_positive_code_exists_right dst_positive_scale_exists_right dst_negative_code_exists_right dst_negative_scale_exists_right. (((G) = (((((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) * S ((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) + ((dst_positive_scale_exists_right) + (dst_positive_scale_exists_right))) + (((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right)))) * S ((((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) * S ((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) + ((dst_positive_scale_exists_right) + (dst_positive_scale_exists_right))) + (((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right)))) + ((((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right))) + (((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right)))))) /\ (forall dst_index_exists_right. (exists pvs_le_gap_exists_rightdomain. pvs_le_gap_exists_rightdomain + (dst_index_exists_right) = (0)) -> exists dst_positive_exists_right dst_negative_exists_right dst_value_exists_right. ((((exists ff_h_pvs_exists_rightentrypositive. ff_h_pvs_exists_rightentrypositive + S (dst_positive_exists_right) = S ((S (dst_index_exists_right)) * dst_positive_scale_exists_right)) /\ exists ff_q_pvs_exists_rightentrypositive. dst_positive_code_exists_right = ff_q_pvs_exists_rightentrypositive * S ((S (dst_index_exists_right)) * dst_positive_scale_exists_right) + (dst_positive_exists_right))) /\ (((((exists ff_h_pvs_exists_rightentrynegative. ff_h_pvs_exists_rightentrynegative + S (dst_negative_exists_right) = S ((S (dst_index_exists_right)) * dst_negative_scale_exists_right)) /\ exists ff_q_pvs_exists_rightentrynegative. dst_negative_code_exists_right = ff_q_pvs_exists_rightentrynegative * S ((S (dst_index_exists_right)) * dst_negative_scale_exists_right) + (dst_negative_exists_right))) /\ (exists ge_balance_positive_exists_rightentryvalue ge_balance_negative_exists_rightentryvalue. (((((dst_value_exists_right) = 2 * (ge_balance_positive_exists_rightentryvalue) /\ (ge_balance_negative_exists_rightentryvalue) = 0) \/ exists ge_signed_half_exists_rightentryvaluedecode. (((dst_value_exists_right) = 2 * ge_signed_half_exists_rightentryvaluedecode + 1 /\ (ge_balance_positive_exists_rightentryvalue) = 0) /\ (ge_balance_negative_exists_rightentryvalue) = S ge_signed_half_exists_rightentryvaluedecode))) /\ ((dst_positive_exists_right) + ge_balance_negative_exists_rightentryvalue = (dst_negative_exists_right) + ge_balance_positive_exists_rightentryvalue))))))))) -> exists M. (((exists dst_positive_code_exists_resulttable dst_positive_scale_exists_resulttable dst_negative_code_exists_resulttable dst_negative_scale_exists_resulttable. (((M) = (((((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) * S ((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) + ((dst_positive_scale_exists_resulttable) + (dst_positive_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))) * S ((((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) * S ((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) + ((dst_positive_scale_exists_resulttable) + (dst_positive_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))) + ((((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))))) /\ (forall dst_index_exists_resulttable. (exists pvs_le_gap_exists_resulttabledomain. pvs_le_gap_exists_resulttabledomain + (dst_index_exists_resulttable) = (l)) -> exists dst_positive_exists_resulttable dst_negative_exists_resulttable dst_value_exists_resulttable. ((((exists ff_h_pvs_exists_resulttableentrypositive. ff_h_pvs_exists_resulttableentrypositive + S (dst_positive_exists_resulttable) = S ((S (dst_index_exists_resulttable)) * dst_positive_scale_exists_resulttable)) /\ exists ff_q_pvs_exists_resulttableentrypositive. dst_positive_code_exists_resulttable = ff_q_pvs_exists_resulttableentrypositive * S ((S (dst_index_exists_resulttable)) * dst_positive_scale_exists_resulttable) + (dst_positive_exists_resulttable))) /\ (((((exists ff_h_pvs_exists_resulttableentrynegative. ff_h_pvs_exists_resulttableentrynegative + S (dst_negative_exists_resulttable) = S ((S (dst_index_exists_resulttable)) * dst_negative_scale_exists_resulttable)) /\ exists ff_q_pvs_exists_resulttableentrynegative. dst_negative_code_exists_resulttable = ff_q_pvs_exists_resulttableentrynegative * S ((S (dst_index_exists_resulttable)) * dst_negative_scale_exists_resulttable) + (dst_negative_exists_resulttable))) /\ (exists ge_balance_positive_exists_resulttableentryvalue ge_balance_negative_exists_resulttableentryvalue. (((((dst_value_exists_resulttable) = 2 * (ge_balance_positive_exists_resulttableentryvalue) /\ (ge_balance_negative_exists_resulttableentryvalue) = 0) \/ exists ge_signed_half_exists_resulttableentryvaluedecode. (((dst_value_exists_resulttable) = 2 * ge_signed_half_exists_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_exists_resulttableentryvalue) = 0) /\ (ge_balance_negative_exists_resulttableentryvalue) = S ge_signed_half_exists_resulttableentryvaluedecode))) /\ ((dst_positive_exists_resulttable) + ge_balance_negative_exists_resulttableentryvalue = (dst_negative_exists_resulttable) + ge_balance_positive_exists_resulttableentryvalue))))))))) /\ (forall dc_index_exists_result dc_value_exists_result. (exists pvs_le_gap_exists_resultdomain. pvs_le_gap_exists_resultdomain + (dc_index_exists_result) = (l)) -> (exists dst_positive_code_exists_resultlookup dst_positive_scale_exists_resultlookup dst_negative_code_exists_resultlookup dst_negative_scale_exists_resultlookup dst_positive_exists_resultlookup dst_negative_exists_resultlookup. (((M) = (((((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) * S ((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) + ((dst_positive_scale_exists_resultlookup) + (dst_positive_scale_exists_resultlookup))) + (((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)))) * S ((((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) * S ((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) + ((dst_positive_scale_exists_resultlookup) + (dst_positive_scale_exists_resultlookup))) + (((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)))) + ((((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup))) + (((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)))))) /\ (((((exists ff_h_pvs_exists_resultlookuppositive. ff_h_pvs_exists_resultlookuppositive + S (dst_positive_exists_resultlookup) = S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultlookup)) /\ exists ff_q_pvs_exists_resultlookuppositive. dst_positive_code_exists_resultlookup = ff_q_pvs_exists_resultlookuppositive * S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultlookup) + (dst_positive_exists_resultlookup))) /\ (((((exists ff_h_pvs_exists_resultlookupnegative. ff_h_pvs_exists_resultlookupnegative + S (dst_negative_exists_resultlookup) = S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultlookup)) /\ exists ff_q_pvs_exists_resultlookupnegative. dst_negative_code_exists_resultlookup = ff_q_pvs_exists_resultlookupnegative * S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultlookup) + (dst_negative_exists_resultlookup))) /\ (exists ge_balance_positive_exists_resultlookupvalue ge_balance_negative_exists_resultlookupvalue. (((((dc_value_exists_result) = 2 * (ge_balance_positive_exists_resultlookupvalue) /\ (ge_balance_negative_exists_resultlookupvalue) = 0) \/ exists ge_signed_half_exists_resultlookupvaluedecode. (((dc_value_exists_result) = 2 * ge_signed_half_exists_resultlookupvaluedecode + 1 /\ (ge_balance_positive_exists_resultlookupvalue) = 0) /\ (ge_balance_negative_exists_resultlookupvalue) = S ge_signed_half_exists_resultlookupvaluedecode))) /\ ((dst_positive_exists_resultlookup) + ge_balance_negative_exists_resultlookupvalue = (dst_negative_exists_resultlookup) + ge_balance_positive_exists_resultlookupvalue))))))))) -> ((((~((dc_index_exists_result)=0)) /\ (exists dc_quotient_exists_resultentry dc_left_exists_resultentry dc_right_exists_resultentry. (((n)=(dc_index_exists_result)*dc_quotient_exists_resultentry) /\ (((exists dst_positive_code_exists_resultentryleft dst_positive_scale_exists_resultentryleft dst_negative_code_exists_resultentryleft dst_negative_scale_exists_resultentryleft dst_positive_exists_resultentryleft dst_negative_exists_resultentryleft. (((F) = (((((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) * S ((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) + ((dst_positive_scale_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft))) + (((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)))) * S ((((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) * S ((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) + ((dst_positive_scale_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft))) + (((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)))) + ((((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft))) + (((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)))))) /\ (((((exists ff_h_pvs_exists_resultentryleftpositive. ff_h_pvs_exists_resultentryleftpositive + S (dst_positive_exists_resultentryleft) = S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultentryleft)) /\ exists ff_q_pvs_exists_resultentryleftpositive. dst_positive_code_exists_resultentryleft = ff_q_pvs_exists_resultentryleftpositive * S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultentryleft) + (dst_positive_exists_resultentryleft))) /\ (((((exists ff_h_pvs_exists_resultentryleftnegative. ff_h_pvs_exists_resultentryleftnegative + S (dst_negative_exists_resultentryleft) = S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultentryleft)) /\ exists ff_q_pvs_exists_resultentryleftnegative. dst_negative_code_exists_resultentryleft = ff_q_pvs_exists_resultentryleftnegative * S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultentryleft) + (dst_negative_exists_resultentryleft))) /\ (exists ge_balance_positive_exists_resultentryleftvalue ge_balance_negative_exists_resultentryleftvalue. (((((dc_left_exists_resultentry) = 2 * (ge_balance_positive_exists_resultentryleftvalue) /\ (ge_balance_negative_exists_resultentryleftvalue) = 0) \/ exists ge_signed_half_exists_resultentryleftvaluedecode. (((dc_left_exists_resultentry) = 2 * ge_signed_half_exists_resultentryleftvaluedecode + 1 /\ (ge_balance_positive_exists_resultentryleftvalue) = 0) /\ (ge_balance_negative_exists_resultentryleftvalue) = S ge_signed_half_exists_resultentryleftvaluedecode))) /\ ((dst_positive_exists_resultentryleft) + ge_balance_negative_exists_resultentryleftvalue = (dst_negative_exists_resultentryleft) + ge_balance_positive_exists_resultentryleftvalue))))))))) /\ (((exists dst_positive_code_exists_resultentryright dst_positive_scale_exists_resultentryright dst_negative_code_exists_resultentryright dst_negative_scale_exists_resultentryright dst_positive_exists_resultentryright dst_negative_exists_resultentryright. (((G) = (((((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) * S ((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) + ((dst_positive_scale_exists_resultentryright) + (dst_positive_scale_exists_resultentryright))) + (((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)))) * S ((((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) * S ((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) + ((dst_positive_scale_exists_resultentryright) + (dst_positive_scale_exists_resultentryright))) + (((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)))) + ((((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright))) + (((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)))))) /\ (((((exists ff_h_pvs_exists_resultentryrightpositive. ff_h_pvs_exists_resultentryrightpositive + S (dst_positive_exists_resultentryright) = S ((S (dc_quotient_exists_resultentry)) * dst_positive_scale_exists_resultentryright)) /\ exists ff_q_pvs_exists_resultentryrightpositive. dst_positive_code_exists_resultentryright = ff_q_pvs_exists_resultentryrightpositive * S ((S (dc_quotient_exists_resultentry)) * dst_positive_scale_exists_resultentryright) + (dst_positive_exists_resultentryright))) /\ (((((exists ff_h_pvs_exists_resultentryrightnegative. ff_h_pvs_exists_resultentryrightnegative + S (dst_negative_exists_resultentryright) = S ((S (dc_quotient_exists_resultentry)) * dst_negative_scale_exists_resultentryright)) /\ exists ff_q_pvs_exists_resultentryrightnegative. dst_negative_code_exists_resultentryright = ff_q_pvs_exists_resultentryrightnegative * S ((S (dc_quotient_exists_resultentry)) * dst_negative_scale_exists_resultentryright) + (dst_negative_exists_resultentryright))) /\ (exists ge_balance_positive_exists_resultentryrightvalue ge_balance_negative_exists_resultentryrightvalue. (((((dc_right_exists_resultentry) = 2 * (ge_balance_positive_exists_resultentryrightvalue) /\ (ge_balance_negative_exists_resultentryrightvalue) = 0) \/ exists ge_signed_half_exists_resultentryrightvaluedecode. (((dc_right_exists_resultentry) = 2 * ge_signed_half_exists_resultentryrightvaluedecode + 1 /\ (ge_balance_positive_exists_resultentryrightvalue) = 0) /\ (ge_balance_negative_exists_resultentryrightvalue) = S ge_signed_half_exists_resultentryrightvaluedecode))) /\ ((dst_positive_exists_resultentryright) + ge_balance_negative_exists_resultentryrightvalue = (dst_negative_exists_resultentryright) + ge_balance_positive_exists_resultentryrightvalue))))))))) /\ (exists sto_ap_exists_resultentryproduct sto_an_exists_resultentryproduct sto_bp_exists_resultentryproduct sto_bn_exists_resultentryproduct sto_cp_exists_resultentryproduct sto_cn_exists_resultentryproduct. (((((dc_left_exists_resultentry) = 2 * (sto_ap_exists_resultentryproduct) /\ (sto_an_exists_resultentryproduct) = 0) \/ exists ge_signed_half_exists_resultentryproductleft. (((dc_left_exists_resultentry) = 2 * ge_signed_half_exists_resultentryproductleft + 1 /\ (sto_ap_exists_resultentryproduct) = 0) /\ (sto_an_exists_resultentryproduct) = S ge_signed_half_exists_resultentryproductleft))) /\ ((((((dc_right_exists_resultentry) = 2 * (sto_bp_exists_resultentryproduct) /\ (sto_bn_exists_resultentryproduct) = 0) \/ exists ge_signed_half_exists_resultentryproductright. (((dc_right_exists_resultentry) = 2 * ge_signed_half_exists_resultentryproductright + 1 /\ (sto_bp_exists_resultentryproduct) = 0) /\ (sto_bn_exists_resultentryproduct) = S ge_signed_half_exists_resultentryproductright))) /\ ((((((dc_value_exists_result) = 2 * (sto_cp_exists_resultentryproduct) /\ (sto_cn_exists_resultentryproduct) = 0) \/ exists ge_signed_half_exists_resultentryproductoutput. (((dc_value_exists_result) = 2 * ge_signed_half_exists_resultentryproductoutput + 1 /\ (sto_cp_exists_resultentryproduct) = 0) /\ (sto_cn_exists_resultentryproduct) = S ge_signed_half_exists_resultentryproductoutput))) /\ ((sto_ap_exists_resultentryproduct * sto_bp_exists_resultentryproduct + sto_an_exists_resultentryproduct * sto_bn_exists_resultentryproduct) + sto_cn_exists_resultentryproduct = (sto_ap_exists_resultentryproduct * sto_bn_exists_resultentryproduct + sto_an_exists_resultentryproduct * sto_bp_exists_resultentryproduct) + sto_cp_exists_resultentryproduct))))))))))))))) \/ ((((dc_index_exists_result)=0 \/ ~(exists pvs_factor_exists_resultentrynondivisor. (n) = (dc_index_exists_result) * pvs_factor_exists_resultentrynondivisor)) /\ ((dc_value_exists_result)=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_quotient_entry · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n l M d q a b z. (((exists dst_positive_code_keep_prefixtable dst_positive_scale_keep_prefixtable dst_negative_code_keep_prefixtable dst_negative_scale_keep_prefixtable. (((M) = (((((dst_positive_code_keep_prefixtable) + (dst_positive_scale_keep_prefixtable)) * S ((dst_positive_code_keep_prefixtable) + (dst_positive_scale_keep_prefixtable)) + ((dst_positive_scale_keep_prefixtable) + (dst_positive_scale_keep_prefixtable))) + (((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) * S ((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) + ((dst_negative_scale_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)))) * S ((((dst_positive_code_keep_prefixtable) + (dst_positive_scale_keep_prefixtable)) * S ((dst_positive_code_keep_prefixtable) + (dst_positive_scale_keep_prefixtable)) + ((dst_positive_scale_keep_prefixtable) + (dst_positive_scale_keep_prefixtable))) + (((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) * S ((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) + ((dst_negative_scale_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)))) + ((((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) * S ((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) + ((dst_negative_scale_keep_prefixtable) + (dst_negative_scale_keep_prefixtable))) + (((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) * S ((dst_negative_code_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)) + ((dst_negative_scale_keep_prefixtable) + (dst_negative_scale_keep_prefixtable)))))) /\ (forall dst_index_keep_prefixtable. (exists pvs_le_gap_keep_prefixtabledomain. pvs_le_gap_keep_prefixtabledomain + (dst_index_keep_prefixtable) = (l)) -> exists dst_positive_keep_prefixtable dst_negative_keep_prefixtable dst_value_keep_prefixtable. ((((exists ff_h_pvs_keep_prefixtableentrypositive. ff_h_pvs_keep_prefixtableentrypositive + S (dst_positive_keep_prefixtable) = S ((S (dst_index_keep_prefixtable)) * dst_positive_scale_keep_prefixtable)) /\ exists ff_q_pvs_keep_prefixtableentrypositive. dst_positive_code_keep_prefixtable = ff_q_pvs_keep_prefixtableentrypositive * S ((S (dst_index_keep_prefixtable)) * dst_positive_scale_keep_prefixtable) + (dst_positive_keep_prefixtable))) /\ (((((exists ff_h_pvs_keep_prefixtableentrynegative. ff_h_pvs_keep_prefixtableentrynegative + S (dst_negative_keep_prefixtable) = S ((S (dst_index_keep_prefixtable)) * dst_negative_scale_keep_prefixtable)) /\ exists ff_q_pvs_keep_prefixtableentrynegative. dst_negative_code_keep_prefixtable = ff_q_pvs_keep_prefixtableentrynegative * S ((S (dst_index_keep_prefixtable)) * dst_negative_scale_keep_prefixtable) + (dst_negative_keep_prefixtable))) /\ (exists ge_balance_positive_keep_prefixtableentryvalue ge_balance_negative_keep_prefixtableentryvalue. (((((dst_value_keep_prefixtable) = 2 * (ge_balance_positive_keep_prefixtableentryvalue) /\ (ge_balance_negative_keep_prefixtableentryvalue) = 0) \/ exists ge_signed_half_keep_prefixtableentryvaluedecode. (((dst_value_keep_prefixtable) = 2 * ge_signed_half_keep_prefixtableentryvaluedecode + 1 /\ (ge_balance_positive_keep_prefixtableentryvalue) = 0) /\ (ge_balance_negative_keep_prefixtableentryvalue) = S ge_signed_half_keep_prefixtableentryvaluedecode))) /\ ((dst_positive_keep_prefixtable) + ge_balance_negative_keep_prefixtableentryvalue = (dst_negative_keep_prefixtable) + ge_balance_positive_keep_prefixtableentryvalue))))))))) /\ (forall dc_index_keep_prefix dc_value_keep_prefix. (exists pvs_le_gap_keep_prefixdomain. pvs_le_gap_keep_prefixdomain + (dc_index_keep_prefix) = (l)) -> (exists dst_positive_code_keep_prefixlookup dst_positive_scale_keep_prefixlookup dst_negative_code_keep_prefixlookup dst_negative_scale_keep_prefixlookup dst_positive_keep_prefixlookup dst_negative_keep_prefixlookup. (((M) = (((((dst_positive_code_keep_prefixlookup) + (dst_positive_scale_keep_prefixlookup)) * S ((dst_positive_code_keep_prefixlookup) + (dst_positive_scale_keep_prefixlookup)) + ((dst_positive_scale_keep_prefixlookup) + (dst_positive_scale_keep_prefixlookup))) + (((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) * S ((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) + ((dst_negative_scale_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)))) * S ((((dst_positive_code_keep_prefixlookup) + (dst_positive_scale_keep_prefixlookup)) * S ((dst_positive_code_keep_prefixlookup) + (dst_positive_scale_keep_prefixlookup)) + ((dst_positive_scale_keep_prefixlookup) + (dst_positive_scale_keep_prefixlookup))) + (((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) * S ((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) + ((dst_negative_scale_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)))) + ((((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) * S ((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) + ((dst_negative_scale_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup))) + (((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) * S ((dst_negative_code_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)) + ((dst_negative_scale_keep_prefixlookup) + (dst_negative_scale_keep_prefixlookup)))))) /\ (((((exists ff_h_pvs_keep_prefixlookuppositive. ff_h_pvs_keep_prefixlookuppositive + S (dst_positive_keep_prefixlookup) = S ((S (dc_index_keep_prefix)) * dst_positive_scale_keep_prefixlookup)) /\ exists ff_q_pvs_keep_prefixlookuppositive. dst_positive_code_keep_prefixlookup = ff_q_pvs_keep_prefixlookuppositive * S ((S (dc_index_keep_prefix)) * dst_positive_scale_keep_prefixlookup) + (dst_positive_keep_prefixlookup))) /\ (((((exists ff_h_pvs_keep_prefixlookupnegative. ff_h_pvs_keep_prefixlookupnegative + S (dst_negative_keep_prefixlookup) = S ((S (dc_index_keep_prefix)) * dst_negative_scale_keep_prefixlookup)) /\ exists ff_q_pvs_keep_prefixlookupnegative. dst_negative_code_keep_prefixlookup = ff_q_pvs_keep_prefixlookupnegative * S ((S (dc_index_keep_prefix)) * dst_negative_scale_keep_prefixlookup) + (dst_negative_keep_prefixlookup))) /\ (exists ge_balance_positive_keep_prefixlookupvalue ge_balance_negative_keep_prefixlookupvalue. (((((dc_value_keep_prefix) = 2 * (ge_balance_positive_keep_prefixlookupvalue) /\ (ge_balance_negative_keep_prefixlookupvalue) = 0) \/ exists ge_signed_half_keep_prefixlookupvaluedecode. (((dc_value_keep_prefix) = 2 * ge_signed_half_keep_prefixlookupvaluedecode + 1 /\ (ge_balance_positive_keep_prefixlookupvalue) = 0) /\ (ge_balance_negative_keep_prefixlookupvalue) = S ge_signed_half_keep_prefixlookupvaluedecode))) /\ ((dst_positive_keep_prefixlookup) + ge_balance_negative_keep_prefixlookupvalue = (dst_negative_keep_prefixlookup) + ge_balance_positive_keep_prefixlookupvalue))))))))) -> ((((~((dc_index_keep_prefix)=0)) /\ (exists dc_quotient_keep_prefixentry dc_left_keep_prefixentry dc_right_keep_prefixentry. (((n)=(dc_index_keep_prefix)*dc_quotient_keep_prefixentry) /\ (((exists dst_positive_code_keep_prefixentryleft dst_positive_scale_keep_prefixentryleft dst_negative_code_keep_prefixentryleft dst_negative_scale_keep_prefixentryleft dst_positive_keep_prefixentryleft dst_negative_keep_prefixentryleft. (((F) = (((((dst_positive_code_keep_prefixentryleft) + (dst_positive_scale_keep_prefixentryleft)) * S ((dst_positive_code_keep_prefixentryleft) + (dst_positive_scale_keep_prefixentryleft)) + ((dst_positive_scale_keep_prefixentryleft) + (dst_positive_scale_keep_prefixentryleft))) + (((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) * S ((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) + ((dst_negative_scale_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)))) * S ((((dst_positive_code_keep_prefixentryleft) + (dst_positive_scale_keep_prefixentryleft)) * S ((dst_positive_code_keep_prefixentryleft) + (dst_positive_scale_keep_prefixentryleft)) + ((dst_positive_scale_keep_prefixentryleft) + (dst_positive_scale_keep_prefixentryleft))) + (((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) * S ((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) + ((dst_negative_scale_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)))) + ((((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) * S ((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) + ((dst_negative_scale_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft))) + (((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) * S ((dst_negative_code_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)) + ((dst_negative_scale_keep_prefixentryleft) + (dst_negative_scale_keep_prefixentryleft)))))) /\ (((((exists ff_h_pvs_keep_prefixentryleftpositive. ff_h_pvs_keep_prefixentryleftpositive + S (dst_positive_keep_prefixentryleft) = S ((S (dc_index_keep_prefix)) * dst_positive_scale_keep_prefixentryleft)) /\ exists ff_q_pvs_keep_prefixentryleftpositive. dst_positive_code_keep_prefixentryleft = ff_q_pvs_keep_prefixentryleftpositive * S ((S (dc_index_keep_prefix)) * dst_positive_scale_keep_prefixentryleft) + (dst_positive_keep_prefixentryleft))) /\ (((((exists ff_h_pvs_keep_prefixentryleftnegative. ff_h_pvs_keep_prefixentryleftnegative + S (dst_negative_keep_prefixentryleft) = S ((S (dc_index_keep_prefix)) * dst_negative_scale_keep_prefixentryleft)) /\ exists ff_q_pvs_keep_prefixentryleftnegative. dst_negative_code_keep_prefixentryleft = ff_q_pvs_keep_prefixentryleftnegative * S ((S (dc_index_keep_prefix)) * dst_negative_scale_keep_prefixentryleft) + (dst_negative_keep_prefixentryleft))) /\ (exists ge_balance_positive_keep_prefixentryleftvalue ge_balance_negative_keep_prefixentryleftvalue. (((((dc_left_keep_prefixentry) = 2 * (ge_balance_positive_keep_prefixentryleftvalue) /\ (ge_balance_negative_keep_prefixentryleftvalue) = 0) \/ exists ge_signed_half_keep_prefixentryleftvaluedecode. (((dc_left_keep_prefixentry) = 2 * ge_signed_half_keep_prefixentryleftvaluedecode + 1 /\ (ge_balance_positive_keep_prefixentryleftvalue) = 0) /\ (ge_balance_negative_keep_prefixentryleftvalue) = S ge_signed_half_keep_prefixentryleftvaluedecode))) /\ ((dst_positive_keep_prefixentryleft) + ge_balance_negative_keep_prefixentryleftvalue = (dst_negative_keep_prefixentryleft) + ge_balance_positive_keep_prefixentryleftvalue))))))))) /\ (((exists dst_positive_code_keep_prefixentryright dst_positive_scale_keep_prefixentryright dst_negative_code_keep_prefixentryright dst_negative_scale_keep_prefixentryright dst_positive_keep_prefixentryright dst_negative_keep_prefixentryright. (((G) = (((((dst_positive_code_keep_prefixentryright) + (dst_positive_scale_keep_prefixentryright)) * S ((dst_positive_code_keep_prefixentryright) + (dst_positive_scale_keep_prefixentryright)) + ((dst_positive_scale_keep_prefixentryright) + (dst_positive_scale_keep_prefixentryright))) + (((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) * S ((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) + ((dst_negative_scale_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)))) * S ((((dst_positive_code_keep_prefixentryright) + (dst_positive_scale_keep_prefixentryright)) * S ((dst_positive_code_keep_prefixentryright) + (dst_positive_scale_keep_prefixentryright)) + ((dst_positive_scale_keep_prefixentryright) + (dst_positive_scale_keep_prefixentryright))) + (((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) * S ((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) + ((dst_negative_scale_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)))) + ((((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) * S ((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) + ((dst_negative_scale_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright))) + (((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) * S ((dst_negative_code_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)) + ((dst_negative_scale_keep_prefixentryright) + (dst_negative_scale_keep_prefixentryright)))))) /\ (((((exists ff_h_pvs_keep_prefixentryrightpositive. ff_h_pvs_keep_prefixentryrightpositive + S (dst_positive_keep_prefixentryright) = S ((S (dc_quotient_keep_prefixentry)) * dst_positive_scale_keep_prefixentryright)) /\ exists ff_q_pvs_keep_prefixentryrightpositive. dst_positive_code_keep_prefixentryright = ff_q_pvs_keep_prefixentryrightpositive * S ((S (dc_quotient_keep_prefixentry)) * dst_positive_scale_keep_prefixentryright) + (dst_positive_keep_prefixentryright))) /\ (((((exists ff_h_pvs_keep_prefixentryrightnegative. ff_h_pvs_keep_prefixentryrightnegative + S (dst_negative_keep_prefixentryright) = S ((S (dc_quotient_keep_prefixentry)) * dst_negative_scale_keep_prefixentryright)) /\ exists ff_q_pvs_keep_prefixentryrightnegative. dst_negative_code_keep_prefixentryright = ff_q_pvs_keep_prefixentryrightnegative * S ((S (dc_quotient_keep_prefixentry)) * dst_negative_scale_keep_prefixentryright) + (dst_negative_keep_prefixentryright))) /\ (exists ge_balance_positive_keep_prefixentryrightvalue ge_balance_negative_keep_prefixentryrightvalue. (((((dc_right_keep_prefixentry) = 2 * (ge_balance_positive_keep_prefixentryrightvalue) /\ (ge_balance_negative_keep_prefixentryrightvalue) = 0) \/ exists ge_signed_half_keep_prefixentryrightvaluedecode. (((dc_right_keep_prefixentry) = 2 * ge_signed_half_keep_prefixentryrightvaluedecode + 1 /\ (ge_balance_positive_keep_prefixentryrightvalue) = 0) /\ (ge_balance_negative_keep_prefixentryrightvalue) = S ge_signed_half_keep_prefixentryrightvaluedecode))) /\ ((dst_positive_keep_prefixentryright) + ge_balance_negative_keep_prefixentryrightvalue = (dst_negative_keep_prefixentryright) + ge_balance_positive_keep_prefixentryrightvalue))))))))) /\ (exists sto_ap_keep_prefixentryproduct sto_an_keep_prefixentryproduct sto_bp_keep_prefixentryproduct sto_bn_keep_prefixentryproduct sto_cp_keep_prefixentryproduct sto_cn_keep_prefixentryproduct. (((((dc_left_keep_prefixentry) = 2 * (sto_ap_keep_prefixentryproduct) /\ (sto_an_keep_prefixentryproduct) = 0) \/ exists ge_signed_half_keep_prefixentryproductleft. (((dc_left_keep_prefixentry) = 2 * ge_signed_half_keep_prefixentryproductleft + 1 /\ (sto_ap_keep_prefixentryproduct) = 0) /\ (sto_an_keep_prefixentryproduct) = S ge_signed_half_keep_prefixentryproductleft))) /\ ((((((dc_right_keep_prefixentry) = 2 * (sto_bp_keep_prefixentryproduct) /\ (sto_bn_keep_prefixentryproduct) = 0) \/ exists ge_signed_half_keep_prefixentryproductright. (((dc_right_keep_prefixentry) = 2 * ge_signed_half_keep_prefixentryproductright + 1 /\ (sto_bp_keep_prefixentryproduct) = 0) /\ (sto_bn_keep_prefixentryproduct) = S ge_signed_half_keep_prefixentryproductright))) /\ ((((((dc_value_keep_prefix) = 2 * (sto_cp_keep_prefixentryproduct) /\ (sto_cn_keep_prefixentryproduct) = 0) \/ exists ge_signed_half_keep_prefixentryproductoutput. (((dc_value_keep_prefix) = 2 * ge_signed_half_keep_prefixentryproductoutput + 1 /\ (sto_cp_keep_prefixentryproduct) = 0) /\ (sto_cn_keep_prefixentryproduct) = S ge_signed_half_keep_prefixentryproductoutput))) /\ ((sto_ap_keep_prefixentryproduct * sto_bp_keep_prefixentryproduct + sto_an_keep_prefixentryproduct * sto_bn_keep_prefixentryproduct) + sto_cn_keep_prefixentryproduct = (sto_ap_keep_prefixentryproduct * sto_bn_keep_prefixentryproduct + sto_an_keep_prefixentryproduct * sto_bp_keep_prefixentryproduct) + sto_cp_keep_prefixentryproduct))))))))))))))) \/ ((((dc_index_keep_prefix)=0 \/ ~(exists pvs_factor_keep_prefixentrynondivisor. (n) = (dc_index_keep_prefix) * pvs_factor_keep_prefixentrynondivisor)) /\ ((dc_value_keep_prefix)=0))))))) -> (exists pvs_le_gap_keep_bound. pvs_le_gap_keep_bound + (d) = (l)) -> ~(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))))))) -> (exists dst_positive_code_keep_result dst_positive_scale_keep_result dst_negative_code_keep_result dst_negative_scale_keep_result dst_positive_keep_result dst_negative_keep_result. (((M) = (((((dst_positive_code_keep_result) + (dst_positive_scale_keep_result)) * S ((dst_positive_code_keep_result) + (dst_positive_scale_keep_result)) + ((dst_positive_scale_keep_result) + (dst_positive_scale_keep_result))) + (((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) * S ((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) + ((dst_negative_scale_keep_result) + (dst_negative_scale_keep_result)))) * S ((((dst_positive_code_keep_result) + (dst_positive_scale_keep_result)) * S ((dst_positive_code_keep_result) + (dst_positive_scale_keep_result)) + ((dst_positive_scale_keep_result) + (dst_positive_scale_keep_result))) + (((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) * S ((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) + ((dst_negative_scale_keep_result) + (dst_negative_scale_keep_result)))) + ((((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) * S ((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) + ((dst_negative_scale_keep_result) + (dst_negative_scale_keep_result))) + (((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) * S ((dst_negative_code_keep_result) + (dst_negative_scale_keep_result)) + ((dst_negative_scale_keep_result) + (dst_negative_scale_keep_result)))))) /\ (((((exists ff_h_pvs_keep_resultpositive. ff_h_pvs_keep_resultpositive + S (dst_positive_keep_result) = S ((S (d)) * dst_positive_scale_keep_result)) /\ exists ff_q_pvs_keep_resultpositive. dst_positive_code_keep_result = ff_q_pvs_keep_resultpositive * S ((S (d)) * dst_positive_scale_keep_result) + (dst_positive_keep_result))) /\ (((((exists ff_h_pvs_keep_resultnegative. ff_h_pvs_keep_resultnegative + S (dst_negative_keep_result) = S ((S (d)) * dst_negative_scale_keep_result)) /\ exists ff_q_pvs_keep_resultnegative. dst_negative_code_keep_result = ff_q_pvs_keep_resultnegative * S ((S (d)) * dst_negative_scale_keep_result) + (dst_negative_keep_result))) /\ (exists ge_balance_positive_keep_resultvalue ge_balance_negative_keep_resultvalue. (((((z) = 2 * (ge_balance_positive_keep_resultvalue) /\ (ge_balance_negative_keep_resultvalue) = 0) \/ exists ge_signed_half_keep_resultvaluedecode. (((z) = 2 * ge_signed_half_keep_resultvaluedecode + 1 /\ (ge_balance_positive_keep_resultvalue) = 0) /\ (ge_balance_negative_keep_resultvalue) = S ge_signed_half_keep_resultvaluedecode))) /\ ((dst_positive_keep_result) + ge_balance_negative_keep_resultvalue = (dst_negative_keep_result) + ge_balance_positive_keep_resultvalue)))))))))

• dirichlet_convolution_prefix_restrict · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n l k M. (((exists dst_positive_code_restrict_sourcetable dst_positive_scale_restrict_sourcetable dst_negative_code_restrict_sourcetable dst_negative_scale_restrict_sourcetable. (((M) = (((((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) * S ((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) + ((dst_positive_scale_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable))) + (((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)))) * S ((((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) * S ((dst_positive_code_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable)) + ((dst_positive_scale_restrict_sourcetable) + (dst_positive_scale_restrict_sourcetable))) + (((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)))) + ((((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable))) + (((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) * S ((dst_negative_code_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)) + ((dst_negative_scale_restrict_sourcetable) + (dst_negative_scale_restrict_sourcetable)))))) /\ (forall dst_index_restrict_sourcetable. (exists pvs_le_gap_restrict_sourcetabledomain. pvs_le_gap_restrict_sourcetabledomain + (dst_index_restrict_sourcetable) = (l)) -> exists dst_positive_restrict_sourcetable dst_negative_restrict_sourcetable dst_value_restrict_sourcetable. ((((exists ff_h_pvs_restrict_sourcetableentrypositive. ff_h_pvs_restrict_sourcetableentrypositive + S (dst_positive_restrict_sourcetable) = S ((S (dst_index_restrict_sourcetable)) * dst_positive_scale_restrict_sourcetable)) /\ exists ff_q_pvs_restrict_sourcetableentrypositive. dst_positive_code_restrict_sourcetable = ff_q_pvs_restrict_sourcetableentrypositive * S ((S (dst_index_restrict_sourcetable)) * dst_positive_scale_restrict_sourcetable) + (dst_positive_restrict_sourcetable))) /\ (((((exists ff_h_pvs_restrict_sourcetableentrynegative. ff_h_pvs_restrict_sourcetableentrynegative + S (dst_negative_restrict_sourcetable) = S ((S (dst_index_restrict_sourcetable)) * dst_negative_scale_restrict_sourcetable)) /\ exists ff_q_pvs_restrict_sourcetableentrynegative. dst_negative_code_restrict_sourcetable = ff_q_pvs_restrict_sourcetableentrynegative * S ((S (dst_index_restrict_sourcetable)) * dst_negative_scale_restrict_sourcetable) + (dst_negative_restrict_sourcetable))) /\ (exists ge_balance_positive_restrict_sourcetableentryvalue ge_balance_negative_restrict_sourcetableentryvalue. (((((dst_value_restrict_sourcetable) = 2 * (ge_balance_positive_restrict_sourcetableentryvalue) /\ (ge_balance_negative_restrict_sourcetableentryvalue) = 0) \/ exists ge_signed_half_restrict_sourcetableentryvaluedecode. (((dst_value_restrict_sourcetable) = 2 * ge_signed_half_restrict_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcetableentryvalue) = 0) /\ (ge_balance_negative_restrict_sourcetableentryvalue) = S ge_signed_half_restrict_sourcetableentryvaluedecode))) /\ ((dst_positive_restrict_sourcetable) + ge_balance_negative_restrict_sourcetableentryvalue = (dst_negative_restrict_sourcetable) + ge_balance_positive_restrict_sourcetableentryvalue))))))))) /\ (forall dc_index_restrict_source dc_value_restrict_source. (exists pvs_le_gap_restrict_sourcedomain. pvs_le_gap_restrict_sourcedomain + (dc_index_restrict_source) = (l)) -> (exists dst_positive_code_restrict_sourcelookup dst_positive_scale_restrict_sourcelookup dst_negative_code_restrict_sourcelookup dst_negative_scale_restrict_sourcelookup dst_positive_restrict_sourcelookup dst_negative_restrict_sourcelookup. (((M) = (((((dst_positive_code_restrict_sourcelookup) + (dst_positive_scale_restrict_sourcelookup)) * S ((dst_positive_code_restrict_sourcelookup) + (dst_positive_scale_restrict_sourcelookup)) + ((dst_positive_scale_restrict_sourcelookup) + (dst_positive_scale_restrict_sourcelookup))) + (((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) * S ((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) + ((dst_negative_scale_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)))) * S ((((dst_positive_code_restrict_sourcelookup) + (dst_positive_scale_restrict_sourcelookup)) * S ((dst_positive_code_restrict_sourcelookup) + (dst_positive_scale_restrict_sourcelookup)) + ((dst_positive_scale_restrict_sourcelookup) + (dst_positive_scale_restrict_sourcelookup))) + (((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) * S ((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) + ((dst_negative_scale_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)))) + ((((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) * S ((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) + ((dst_negative_scale_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup))) + (((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) * S ((dst_negative_code_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)) + ((dst_negative_scale_restrict_sourcelookup) + (dst_negative_scale_restrict_sourcelookup)))))) /\ (((((exists ff_h_pvs_restrict_sourcelookuppositive. ff_h_pvs_restrict_sourcelookuppositive + S (dst_positive_restrict_sourcelookup) = S ((S (dc_index_restrict_source)) * dst_positive_scale_restrict_sourcelookup)) /\ exists ff_q_pvs_restrict_sourcelookuppositive. dst_positive_code_restrict_sourcelookup = ff_q_pvs_restrict_sourcelookuppositive * S ((S (dc_index_restrict_source)) * dst_positive_scale_restrict_sourcelookup) + (dst_positive_restrict_sourcelookup))) /\ (((((exists ff_h_pvs_restrict_sourcelookupnegative. ff_h_pvs_restrict_sourcelookupnegative + S (dst_negative_restrict_sourcelookup) = S ((S (dc_index_restrict_source)) * dst_negative_scale_restrict_sourcelookup)) /\ exists ff_q_pvs_restrict_sourcelookupnegative. dst_negative_code_restrict_sourcelookup = ff_q_pvs_restrict_sourcelookupnegative * S ((S (dc_index_restrict_source)) * dst_negative_scale_restrict_sourcelookup) + (dst_negative_restrict_sourcelookup))) /\ (exists ge_balance_positive_restrict_sourcelookupvalue ge_balance_negative_restrict_sourcelookupvalue. (((((dc_value_restrict_source) = 2 * (ge_balance_positive_restrict_sourcelookupvalue) /\ (ge_balance_negative_restrict_sourcelookupvalue) = 0) \/ exists ge_signed_half_restrict_sourcelookupvaluedecode. (((dc_value_restrict_source) = 2 * ge_signed_half_restrict_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_restrict_sourcelookupvalue) = 0) /\ (ge_balance_negative_restrict_sourcelookupvalue) = S ge_signed_half_restrict_sourcelookupvaluedecode))) /\ ((dst_positive_restrict_sourcelookup) + ge_balance_negative_restrict_sourcelookupvalue = (dst_negative_restrict_sourcelookup) + ge_balance_positive_restrict_sourcelookupvalue))))))))) -> ((((~((dc_index_restrict_source)=0)) /\ (exists dc_quotient_restrict_sourceentry dc_left_restrict_sourceentry dc_right_restrict_sourceentry. (((n)=(dc_index_restrict_source)*dc_quotient_restrict_sourceentry) /\ (((exists dst_positive_code_restrict_sourceentryleft dst_positive_scale_restrict_sourceentryleft dst_negative_code_restrict_sourceentryleft dst_negative_scale_restrict_sourceentryleft dst_positive_restrict_sourceentryleft dst_negative_restrict_sourceentryleft. (((F) = (((((dst_positive_code_restrict_sourceentryleft) + (dst_positive_scale_restrict_sourceentryleft)) * S ((dst_positive_code_restrict_sourceentryleft) + (dst_positive_scale_restrict_sourceentryleft)) + ((dst_positive_scale_restrict_sourceentryleft) + (dst_positive_scale_restrict_sourceentryleft))) + (((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) * S ((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) + ((dst_negative_scale_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)))) * S ((((dst_positive_code_restrict_sourceentryleft) + (dst_positive_scale_restrict_sourceentryleft)) * S ((dst_positive_code_restrict_sourceentryleft) + (dst_positive_scale_restrict_sourceentryleft)) + ((dst_positive_scale_restrict_sourceentryleft) + (dst_positive_scale_restrict_sourceentryleft))) + (((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) * S ((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) + ((dst_negative_scale_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)))) + ((((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) * S ((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) + ((dst_negative_scale_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft))) + (((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) * S ((dst_negative_code_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)) + ((dst_negative_scale_restrict_sourceentryleft) + (dst_negative_scale_restrict_sourceentryleft)))))) /\ (((((exists ff_h_pvs_restrict_sourceentryleftpositive. ff_h_pvs_restrict_sourceentryleftpositive + S (dst_positive_restrict_sourceentryleft) = S ((S (dc_index_restrict_source)) * dst_positive_scale_restrict_sourceentryleft)) /\ exists ff_q_pvs_restrict_sourceentryleftpositive. dst_positive_code_restrict_sourceentryleft = ff_q_pvs_restrict_sourceentryleftpositive * S ((S (dc_index_restrict_source)) * dst_positive_scale_restrict_sourceentryleft) + (dst_positive_restrict_sourceentryleft))) /\ (((((exists ff_h_pvs_restrict_sourceentryleftnegative. ff_h_pvs_restrict_sourceentryleftnegative + S (dst_negative_restrict_sourceentryleft) = S ((S (dc_index_restrict_source)) * dst_negative_scale_restrict_sourceentryleft)) /\ exists ff_q_pvs_restrict_sourceentryleftnegative. dst_negative_code_restrict_sourceentryleft = ff_q_pvs_restrict_sourceentryleftnegative * S ((S (dc_index_restrict_source)) * dst_negative_scale_restrict_sourceentryleft) + (dst_negative_restrict_sourceentryleft))) /\ (exists ge_balance_positive_restrict_sourceentryleftvalue ge_balance_negative_restrict_sourceentryleftvalue. (((((dc_left_restrict_sourceentry) = 2 * (ge_balance_positive_restrict_sourceentryleftvalue) /\ (ge_balance_negative_restrict_sourceentryleftvalue) = 0) \/ exists ge_signed_half_restrict_sourceentryleftvaluedecode. (((dc_left_restrict_sourceentry) = 2 * ge_signed_half_restrict_sourceentryleftvaluedecode + 1 /\ (ge_balance_positive_restrict_sourceentryleftvalue) = 0) /\ (ge_balance_negative_restrict_sourceentryleftvalue) = S ge_signed_half_restrict_sourceentryleftvaluedecode))) /\ ((dst_positive_restrict_sourceentryleft) + ge_balance_negative_restrict_sourceentryleftvalue = (dst_negative_restrict_sourceentryleft) + ge_balance_positive_restrict_sourceentryleftvalue))))))))) /\ (((exists dst_positive_code_restrict_sourceentryright dst_positive_scale_restrict_sourceentryright dst_negative_code_restrict_sourceentryright dst_negative_scale_restrict_sourceentryright dst_positive_restrict_sourceentryright dst_negative_restrict_sourceentryright. (((G) = (((((dst_positive_code_restrict_sourceentryright) + (dst_positive_scale_restrict_sourceentryright)) * S ((dst_positive_code_restrict_sourceentryright) + (dst_positive_scale_restrict_sourceentryright)) + ((dst_positive_scale_restrict_sourceentryright) + (dst_positive_scale_restrict_sourceentryright))) + (((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) * S ((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) + ((dst_negative_scale_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)))) * S ((((dst_positive_code_restrict_sourceentryright) + (dst_positive_scale_restrict_sourceentryright)) * S ((dst_positive_code_restrict_sourceentryright) + (dst_positive_scale_restrict_sourceentryright)) + ((dst_positive_scale_restrict_sourceentryright) + (dst_positive_scale_restrict_sourceentryright))) + (((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) * S ((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) + ((dst_negative_scale_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)))) + ((((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) * S ((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) + ((dst_negative_scale_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright))) + (((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) * S ((dst_negative_code_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)) + ((dst_negative_scale_restrict_sourceentryright) + (dst_negative_scale_restrict_sourceentryright)))))) /\ (((((exists ff_h_pvs_restrict_sourceentryrightpositive. ff_h_pvs_restrict_sourceentryrightpositive + S (dst_positive_restrict_sourceentryright) = S ((S (dc_quotient_restrict_sourceentry)) * dst_positive_scale_restrict_sourceentryright)) /\ exists ff_q_pvs_restrict_sourceentryrightpositive. dst_positive_code_restrict_sourceentryright = ff_q_pvs_restrict_sourceentryrightpositive * S ((S (dc_quotient_restrict_sourceentry)) * dst_positive_scale_restrict_sourceentryright) + (dst_positive_restrict_sourceentryright))) /\ (((((exists ff_h_pvs_restrict_sourceentryrightnegative. ff_h_pvs_restrict_sourceentryrightnegative + S (dst_negative_restrict_sourceentryright) = S ((S (dc_quotient_restrict_sourceentry)) * dst_negative_scale_restrict_sourceentryright)) /\ exists ff_q_pvs_restrict_sourceentryrightnegative. dst_negative_code_restrict_sourceentryright = ff_q_pvs_restrict_sourceentryrightnegative * S ((S (dc_quotient_restrict_sourceentry)) * dst_negative_scale_restrict_sourceentryright) + (dst_negative_restrict_sourceentryright))) /\ (exists ge_balance_positive_restrict_sourceentryrightvalue ge_balance_negative_restrict_sourceentryrightvalue. (((((dc_right_restrict_sourceentry) = 2 * (ge_balance_positive_restrict_sourceentryrightvalue) /\ (ge_balance_negative_restrict_sourceentryrightvalue) = 0) \/ exists ge_signed_half_restrict_sourceentryrightvaluedecode. (((dc_right_restrict_sourceentry) = 2 * ge_signed_half_restrict_sourceentryrightvaluedecode + 1 /\ (ge_balance_positive_restrict_sourceentryrightvalue) = 0) /\ (ge_balance_negative_restrict_sourceentryrightvalue) = S ge_signed_half_restrict_sourceentryrightvaluedecode))) /\ ((dst_positive_restrict_sourceentryright) + ge_balance_negative_restrict_sourceentryrightvalue = (dst_negative_restrict_sourceentryright) + ge_balance_positive_restrict_sourceentryrightvalue))))))))) /\ (exists sto_ap_restrict_sourceentryproduct sto_an_restrict_sourceentryproduct sto_bp_restrict_sourceentryproduct sto_bn_restrict_sourceentryproduct sto_cp_restrict_sourceentryproduct sto_cn_restrict_sourceentryproduct. (((((dc_left_restrict_sourceentry) = 2 * (sto_ap_restrict_sourceentryproduct) /\ (sto_an_restrict_sourceentryproduct) = 0) \/ exists ge_signed_half_restrict_sourceentryproductleft. (((dc_left_restrict_sourceentry) = 2 * ge_signed_half_restrict_sourceentryproductleft + 1 /\ (sto_ap_restrict_sourceentryproduct) = 0) /\ (sto_an_restrict_sourceentryproduct) = S ge_signed_half_restrict_sourceentryproductleft))) /\ ((((((dc_right_restrict_sourceentry) = 2 * (sto_bp_restrict_sourceentryproduct) /\ (sto_bn_restrict_sourceentryproduct) = 0) \/ exists ge_signed_half_restrict_sourceentryproductright. (((dc_right_restrict_sourceentry) = 2 * ge_signed_half_restrict_sourceentryproductright + 1 /\ (sto_bp_restrict_sourceentryproduct) = 0) /\ (sto_bn_restrict_sourceentryproduct) = S ge_signed_half_restrict_sourceentryproductright))) /\ ((((((dc_value_restrict_source) = 2 * (sto_cp_restrict_sourceentryproduct) /\ (sto_cn_restrict_sourceentryproduct) = 0) \/ exists ge_signed_half_restrict_sourceentryproductoutput. (((dc_value_restrict_source) = 2 * ge_signed_half_restrict_sourceentryproductoutput + 1 /\ (sto_cp_restrict_sourceentryproduct) = 0) /\ (sto_cn_restrict_sourceentryproduct) = S ge_signed_half_restrict_sourceentryproductoutput))) /\ ((sto_ap_restrict_sourceentryproduct * sto_bp_restrict_sourceentryproduct + sto_an_restrict_sourceentryproduct * sto_bn_restrict_sourceentryproduct) + sto_cn_restrict_sourceentryproduct = (sto_ap_restrict_sourceentryproduct * sto_bn_restrict_sourceentryproduct + sto_an_restrict_sourceentryproduct * sto_bp_restrict_sourceentryproduct) + sto_cp_restrict_sourceentryproduct))))))))))))))) \/ ((((dc_index_restrict_source)=0 \/ ~(exists pvs_factor_restrict_sourceentrynondivisor. (n) = (dc_index_restrict_source) * pvs_factor_restrict_sourceentrynondivisor)) /\ ((dc_value_restrict_source)=0))))))) -> (exists pvs_le_gap_restrict_bound. pvs_le_gap_restrict_bound + (k) = (l)) -> (((exists dst_positive_code_restrict_resulttable dst_positive_scale_restrict_resulttable dst_negative_code_restrict_resulttable dst_negative_scale_restrict_resulttable. (((M) = (((((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) * S ((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) + ((dst_positive_scale_restrict_resulttable) + (dst_positive_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))) * S ((((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) * S ((dst_positive_code_restrict_resulttable) + (dst_positive_scale_restrict_resulttable)) + ((dst_positive_scale_restrict_resulttable) + (dst_positive_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))) + ((((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable))) + (((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) * S ((dst_negative_code_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)) + ((dst_negative_scale_restrict_resulttable) + (dst_negative_scale_restrict_resulttable)))))) /\ (forall dst_index_restrict_resulttable. (exists pvs_le_gap_restrict_resulttabledomain. pvs_le_gap_restrict_resulttabledomain + (dst_index_restrict_resulttable) = (k)) -> exists dst_positive_restrict_resulttable dst_negative_restrict_resulttable dst_value_restrict_resulttable. ((((exists ff_h_pvs_restrict_resulttableentrypositive. ff_h_pvs_restrict_resulttableentrypositive + S (dst_positive_restrict_resulttable) = S ((S (dst_index_restrict_resulttable)) * dst_positive_scale_restrict_resulttable)) /\ exists ff_q_pvs_restrict_resulttableentrypositive. dst_positive_code_restrict_resulttable = ff_q_pvs_restrict_resulttableentrypositive * S ((S (dst_index_restrict_resulttable)) * dst_positive_scale_restrict_resulttable) + (dst_positive_restrict_resulttable))) /\ (((((exists ff_h_pvs_restrict_resulttableentrynegative. ff_h_pvs_restrict_resulttableentrynegative + S (dst_negative_restrict_resulttable) = S ((S (dst_index_restrict_resulttable)) * dst_negative_scale_restrict_resulttable)) /\ exists ff_q_pvs_restrict_resulttableentrynegative. dst_negative_code_restrict_resulttable = ff_q_pvs_restrict_resulttableentrynegative * S ((S (dst_index_restrict_resulttable)) * dst_negative_scale_restrict_resulttable) + (dst_negative_restrict_resulttable))) /\ (exists ge_balance_positive_restrict_resulttableentryvalue ge_balance_negative_restrict_resulttableentryvalue. (((((dst_value_restrict_resulttable) = 2 * (ge_balance_positive_restrict_resulttableentryvalue) /\ (ge_balance_negative_restrict_resulttableentryvalue) = 0) \/ exists ge_signed_half_restrict_resulttableentryvaluedecode. (((dst_value_restrict_resulttable) = 2 * ge_signed_half_restrict_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_restrict_resulttableentryvalue) = 0) /\ (ge_balance_negative_restrict_resulttableentryvalue) = S ge_signed_half_restrict_resulttableentryvaluedecode))) /\ ((dst_positive_restrict_resulttable) + ge_balance_negative_restrict_resulttableentryvalue = (dst_negative_restrict_resulttable) + ge_balance_positive_restrict_resulttableentryvalue))))))))) /\ (forall dc_index_restrict_result dc_value_restrict_result. (exists pvs_le_gap_restrict_resultdomain. pvs_le_gap_restrict_resultdomain + (dc_index_restrict_result) = (k)) -> (exists dst_positive_code_restrict_resultlookup dst_positive_scale_restrict_resultlookup dst_negative_code_restrict_resultlookup dst_negative_scale_restrict_resultlookup dst_positive_restrict_resultlookup dst_negative_restrict_resultlookup. (((M) = (((((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) * S ((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) + ((dst_positive_scale_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))) * S ((((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) * S ((dst_positive_code_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup)) + ((dst_positive_scale_restrict_resultlookup) + (dst_positive_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))) + ((((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup))) + (((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) * S ((dst_negative_code_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)) + ((dst_negative_scale_restrict_resultlookup) + (dst_negative_scale_restrict_resultlookup)))))) /\ (((((exists ff_h_pvs_restrict_resultlookuppositive. ff_h_pvs_restrict_resultlookuppositive + S (dst_positive_restrict_resultlookup) = S ((S (dc_index_restrict_result)) * dst_positive_scale_restrict_resultlookup)) /\ exists ff_q_pvs_restrict_resultlookuppositive. dst_positive_code_restrict_resultlookup = ff_q_pvs_restrict_resultlookuppositive * S ((S (dc_index_restrict_result)) * dst_positive_scale_restrict_resultlookup) + (dst_positive_restrict_resultlookup))) /\ (((((exists ff_h_pvs_restrict_resultlookupnegative. ff_h_pvs_restrict_resultlookupnegative + S (dst_negative_restrict_resultlookup) = S ((S (dc_index_restrict_result)) * dst_negative_scale_restrict_resultlookup)) /\ exists ff_q_pvs_restrict_resultlookupnegative. dst_negative_code_restrict_resultlookup = ff_q_pvs_restrict_resultlookupnegative * S ((S (dc_index_restrict_result)) * dst_negative_scale_restrict_resultlookup) + (dst_negative_restrict_resultlookup))) /\ (exists ge_balance_positive_restrict_resultlookupvalue ge_balance_negative_restrict_resultlookupvalue. (((((dc_value_restrict_result) = 2 * (ge_balance_positive_restrict_resultlookupvalue) /\ (ge_balance_negative_restrict_resultlookupvalue) = 0) \/ exists ge_signed_half_restrict_resultlookupvaluedecode. (((dc_value_restrict_result) = 2 * ge_signed_half_restrict_resultlookupvaluedecode + 1 /\ (ge_balance_positive_restrict_resultlookupvalue) = 0) /\ (ge_balance_negative_restrict_resultlookupvalue) = S ge_signed_half_restrict_resultlookupvaluedecode))) /\ ((dst_positive_restrict_resultlookup) + ge_balance_negative_restrict_resultlookupvalue = (dst_negative_restrict_resultlookup) + ge_balance_positive_restrict_resultlookupvalue))))))))) -> ((((~((dc_index_restrict_result)=0)) /\ (exists dc_quotient_restrict_resultentry dc_left_restrict_resultentry dc_right_restrict_resultentry. (((n)=(dc_index_restrict_result)*dc_quotient_restrict_resultentry) /\ (((exists dst_positive_code_restrict_resultentryleft dst_positive_scale_restrict_resultentryleft dst_negative_code_restrict_resultentryleft dst_negative_scale_restrict_resultentryleft dst_positive_restrict_resultentryleft dst_negative_restrict_resultentryleft. (((F) = (((((dst_positive_code_restrict_resultentryleft) + (dst_positive_scale_restrict_resultentryleft)) * S ((dst_positive_code_restrict_resultentryleft) + (dst_positive_scale_restrict_resultentryleft)) + ((dst_positive_scale_restrict_resultentryleft) + (dst_positive_scale_restrict_resultentryleft))) + (((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) * S ((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) + ((dst_negative_scale_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)))) * S ((((dst_positive_code_restrict_resultentryleft) + (dst_positive_scale_restrict_resultentryleft)) * S ((dst_positive_code_restrict_resultentryleft) + (dst_positive_scale_restrict_resultentryleft)) + ((dst_positive_scale_restrict_resultentryleft) + (dst_positive_scale_restrict_resultentryleft))) + (((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) * S ((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) + ((dst_negative_scale_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)))) + ((((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) * S ((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) + ((dst_negative_scale_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft))) + (((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) * S ((dst_negative_code_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)) + ((dst_negative_scale_restrict_resultentryleft) + (dst_negative_scale_restrict_resultentryleft)))))) /\ (((((exists ff_h_pvs_restrict_resultentryleftpositive. ff_h_pvs_restrict_resultentryleftpositive + S (dst_positive_restrict_resultentryleft) = S ((S (dc_index_restrict_result)) * dst_positive_scale_restrict_resultentryleft)) /\ exists ff_q_pvs_restrict_resultentryleftpositive. dst_positive_code_restrict_resultentryleft = ff_q_pvs_restrict_resultentryleftpositive * S ((S (dc_index_restrict_result)) * dst_positive_scale_restrict_resultentryleft) + (dst_positive_restrict_resultentryleft))) /\ (((((exists ff_h_pvs_restrict_resultentryleftnegative. ff_h_pvs_restrict_resultentryleftnegative + S (dst_negative_restrict_resultentryleft) = S ((S (dc_index_restrict_result)) * dst_negative_scale_restrict_resultentryleft)) /\ exists ff_q_pvs_restrict_resultentryleftnegative. dst_negative_code_restrict_resultentryleft = ff_q_pvs_restrict_resultentryleftnegative * S ((S (dc_index_restrict_result)) * dst_negative_scale_restrict_resultentryleft) + (dst_negative_restrict_resultentryleft))) /\ (exists ge_balance_positive_restrict_resultentryleftvalue ge_balance_negative_restrict_resultentryleftvalue. (((((dc_left_restrict_resultentry) = 2 * (ge_balance_positive_restrict_resultentryleftvalue) /\ (ge_balance_negative_restrict_resultentryleftvalue) = 0) \/ exists ge_signed_half_restrict_resultentryleftvaluedecode. (((dc_left_restrict_resultentry) = 2 * ge_signed_half_restrict_resultentryleftvaluedecode + 1 /\ (ge_balance_positive_restrict_resultentryleftvalue) = 0) /\ (ge_balance_negative_restrict_resultentryleftvalue) = S ge_signed_half_restrict_resultentryleftvaluedecode))) /\ ((dst_positive_restrict_resultentryleft) + ge_balance_negative_restrict_resultentryleftvalue = (dst_negative_restrict_resultentryleft) + ge_balance_positive_restrict_resultentryleftvalue))))))))) /\ (((exists dst_positive_code_restrict_resultentryright dst_positive_scale_restrict_resultentryright dst_negative_code_restrict_resultentryright dst_negative_scale_restrict_resultentryright dst_positive_restrict_resultentryright dst_negative_restrict_resultentryright. (((G) = (((((dst_positive_code_restrict_resultentryright) + (dst_positive_scale_restrict_resultentryright)) * S ((dst_positive_code_restrict_resultentryright) + (dst_positive_scale_restrict_resultentryright)) + ((dst_positive_scale_restrict_resultentryright) + (dst_positive_scale_restrict_resultentryright))) + (((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) * S ((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) + ((dst_negative_scale_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)))) * S ((((dst_positive_code_restrict_resultentryright) + (dst_positive_scale_restrict_resultentryright)) * S ((dst_positive_code_restrict_resultentryright) + (dst_positive_scale_restrict_resultentryright)) + ((dst_positive_scale_restrict_resultentryright) + (dst_positive_scale_restrict_resultentryright))) + (((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) * S ((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) + ((dst_negative_scale_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)))) + ((((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) * S ((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) + ((dst_negative_scale_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright))) + (((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) * S ((dst_negative_code_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)) + ((dst_negative_scale_restrict_resultentryright) + (dst_negative_scale_restrict_resultentryright)))))) /\ (((((exists ff_h_pvs_restrict_resultentryrightpositive. ff_h_pvs_restrict_resultentryrightpositive + S (dst_positive_restrict_resultentryright) = S ((S (dc_quotient_restrict_resultentry)) * dst_positive_scale_restrict_resultentryright)) /\ exists ff_q_pvs_restrict_resultentryrightpositive. dst_positive_code_restrict_resultentryright = ff_q_pvs_restrict_resultentryrightpositive * S ((S (dc_quotient_restrict_resultentry)) * dst_positive_scale_restrict_resultentryright) + (dst_positive_restrict_resultentryright))) /\ (((((exists ff_h_pvs_restrict_resultentryrightnegative. ff_h_pvs_restrict_resultentryrightnegative + S (dst_negative_restrict_resultentryright) = S ((S (dc_quotient_restrict_resultentry)) * dst_negative_scale_restrict_resultentryright)) /\ exists ff_q_pvs_restrict_resultentryrightnegative. dst_negative_code_restrict_resultentryright = ff_q_pvs_restrict_resultentryrightnegative * S ((S (dc_quotient_restrict_resultentry)) * dst_negative_scale_restrict_resultentryright) + (dst_negative_restrict_resultentryright))) /\ (exists ge_balance_positive_restrict_resultentryrightvalue ge_balance_negative_restrict_resultentryrightvalue. (((((dc_right_restrict_resultentry) = 2 * (ge_balance_positive_restrict_resultentryrightvalue) /\ (ge_balance_negative_restrict_resultentryrightvalue) = 0) \/ exists ge_signed_half_restrict_resultentryrightvaluedecode. (((dc_right_restrict_resultentry) = 2 * ge_signed_half_restrict_resultentryrightvaluedecode + 1 /\ (ge_balance_positive_restrict_resultentryrightvalue) = 0) /\ (ge_balance_negative_restrict_resultentryrightvalue) = S ge_signed_half_restrict_resultentryrightvaluedecode))) /\ ((dst_positive_restrict_resultentryright) + ge_balance_negative_restrict_resultentryrightvalue = (dst_negative_restrict_resultentryright) + ge_balance_positive_restrict_resultentryrightvalue))))))))) /\ (exists sto_ap_restrict_resultentryproduct sto_an_restrict_resultentryproduct sto_bp_restrict_resultentryproduct sto_bn_restrict_resultentryproduct sto_cp_restrict_resultentryproduct sto_cn_restrict_resultentryproduct. (((((dc_left_restrict_resultentry) = 2 * (sto_ap_restrict_resultentryproduct) /\ (sto_an_restrict_resultentryproduct) = 0) \/ exists ge_signed_half_restrict_resultentryproductleft. (((dc_left_restrict_resultentry) = 2 * ge_signed_half_restrict_resultentryproductleft + 1 /\ (sto_ap_restrict_resultentryproduct) = 0) /\ (sto_an_restrict_resultentryproduct) = S ge_signed_half_restrict_resultentryproductleft))) /\ ((((((dc_right_restrict_resultentry) = 2 * (sto_bp_restrict_resultentryproduct) /\ (sto_bn_restrict_resultentryproduct) = 0) \/ exists ge_signed_half_restrict_resultentryproductright. (((dc_right_restrict_resultentry) = 2 * ge_signed_half_restrict_resultentryproductright + 1 /\ (sto_bp_restrict_resultentryproduct) = 0) /\ (sto_bn_restrict_resultentryproduct) = S ge_signed_half_restrict_resultentryproductright))) /\ ((((((dc_value_restrict_result) = 2 * (sto_cp_restrict_resultentryproduct) /\ (sto_cn_restrict_resultentryproduct) = 0) \/ exists ge_signed_half_restrict_resultentryproductoutput. (((dc_value_restrict_result) = 2 * ge_signed_half_restrict_resultentryproductoutput + 1 /\ (sto_cp_restrict_resultentryproduct) = 0) /\ (sto_cn_restrict_resultentryproduct) = S ge_signed_half_restrict_resultentryproductoutput))) /\ ((sto_ap_restrict_resultentryproduct * sto_bp_restrict_resultentryproduct + sto_an_restrict_resultentryproduct * sto_bn_restrict_resultentryproduct) + sto_cn_restrict_resultentryproduct = (sto_ap_restrict_resultentryproduct * sto_bn_restrict_resultentryproduct + sto_an_restrict_resultentryproduct * sto_bp_restrict_resultentryproduct) + sto_cp_restrict_resultentryproduct))))))))))))))) \/ ((((dc_index_restrict_result)=0 \/ ~(exists pvs_factor_restrict_resultentrynondivisor. (n) = (dc_index_restrict_result) * pvs_factor_restrict_resultentrynondivisor)) /\ ((dc_value_restrict_result)=0)))))))

• dirichlet_convolution_prefix_zero_constructor · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n M. (exists dst_positive_code_base_table dst_positive_scale_base_table dst_negative_code_base_table dst_negative_scale_base_table. (((M) = (((((dst_positive_code_base_table) + (dst_positive_scale_base_table)) * S ((dst_positive_code_base_table) + (dst_positive_scale_base_table)) + ((dst_positive_scale_base_table) + (dst_positive_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))) * S ((((dst_positive_code_base_table) + (dst_positive_scale_base_table)) * S ((dst_positive_code_base_table) + (dst_positive_scale_base_table)) + ((dst_positive_scale_base_table) + (dst_positive_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))) + ((((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table))) + (((dst_negative_code_base_table) + (dst_negative_scale_base_table)) * S ((dst_negative_code_base_table) + (dst_negative_scale_base_table)) + ((dst_negative_scale_base_table) + (dst_negative_scale_base_table)))))) /\ (forall dst_index_base_table. (exists pvs_le_gap_base_tabledomain. pvs_le_gap_base_tabledomain + (dst_index_base_table) = (0)) -> exists dst_positive_base_table dst_negative_base_table dst_value_base_table. ((((exists ff_h_pvs_base_tableentrypositive. ff_h_pvs_base_tableentrypositive + S (dst_positive_base_table) = S ((S (dst_index_base_table)) * dst_positive_scale_base_table)) /\ exists ff_q_pvs_base_tableentrypositive. dst_positive_code_base_table = ff_q_pvs_base_tableentrypositive * S ((S (dst_index_base_table)) * dst_positive_scale_base_table) + (dst_positive_base_table))) /\ (((((exists ff_h_pvs_base_tableentrynegative. ff_h_pvs_base_tableentrynegative + S (dst_negative_base_table) = S ((S (dst_index_base_table)) * dst_negative_scale_base_table)) /\ exists ff_q_pvs_base_tableentrynegative. dst_negative_code_base_table = ff_q_pvs_base_tableentrynegative * S ((S (dst_index_base_table)) * dst_negative_scale_base_table) + (dst_negative_base_table))) /\ (exists ge_balance_positive_base_tableentryvalue ge_balance_negative_base_tableentryvalue. (((((dst_value_base_table) = 2 * (ge_balance_positive_base_tableentryvalue) /\ (ge_balance_negative_base_tableentryvalue) = 0) \/ exists ge_signed_half_base_tableentryvaluedecode. (((dst_value_base_table) = 2 * ge_signed_half_base_tableentryvaluedecode + 1 /\ (ge_balance_positive_base_tableentryvalue) = 0) /\ (ge_balance_negative_base_tableentryvalue) = S ge_signed_half_base_tableentryvaluedecode))) /\ ((dst_positive_base_table) + ge_balance_negative_base_tableentryvalue = (dst_negative_base_table) + ge_balance_positive_base_tableentryvalue))))))))) -> (exists dst_positive_code_base_entry dst_positive_scale_base_entry dst_negative_code_base_entry dst_negative_scale_base_entry dst_positive_base_entry dst_negative_base_entry. (((M) = (((((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) * S ((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) + ((dst_positive_scale_base_entry) + (dst_positive_scale_base_entry))) + (((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry)))) * S ((((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) * S ((dst_positive_code_base_entry) + (dst_positive_scale_base_entry)) + ((dst_positive_scale_base_entry) + (dst_positive_scale_base_entry))) + (((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry)))) + ((((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry))) + (((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) * S ((dst_negative_code_base_entry) + (dst_negative_scale_base_entry)) + ((dst_negative_scale_base_entry) + (dst_negative_scale_base_entry)))))) /\ (((((exists ff_h_pvs_base_entrypositive. ff_h_pvs_base_entrypositive + S (dst_positive_base_entry) = S ((S (0)) * dst_positive_scale_base_entry)) /\ exists ff_q_pvs_base_entrypositive. dst_positive_code_base_entry = ff_q_pvs_base_entrypositive * S ((S (0)) * dst_positive_scale_base_entry) + (dst_positive_base_entry))) /\ (((((exists ff_h_pvs_base_entrynegative. ff_h_pvs_base_entrynegative + S (dst_negative_base_entry) = S ((S (0)) * dst_negative_scale_base_entry)) /\ exists ff_q_pvs_base_entrynegative. dst_negative_code_base_entry = ff_q_pvs_base_entrynegative * S ((S (0)) * dst_negative_scale_base_entry) + (dst_negative_base_entry))) /\ (exists ge_balance_positive_base_entryvalue ge_balance_negative_base_entryvalue. (((((0) = 2 * (ge_balance_positive_base_entryvalue) /\ (ge_balance_negative_base_entryvalue) = 0) \/ exists ge_signed_half_base_entryvaluedecode. (((0) = 2 * ge_signed_half_base_entryvaluedecode + 1 /\ (ge_balance_positive_base_entryvalue) = 0) /\ (ge_balance_negative_base_entryvalue) = S ge_signed_half_base_entryvaluedecode))) /\ ((dst_positive_base_entry) + ge_balance_negative_base_entryvalue = (dst_negative_base_entry) + ge_balance_positive_base_entryvalue))))))))) -> (((exists dst_positive_code_base_resulttable dst_positive_scale_base_resulttable dst_negative_code_base_resulttable dst_negative_scale_base_resulttable. (((M) = (((((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) * S ((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) + ((dst_positive_scale_base_resulttable) + (dst_positive_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))) * S ((((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) * S ((dst_positive_code_base_resulttable) + (dst_positive_scale_base_resulttable)) + ((dst_positive_scale_base_resulttable) + (dst_positive_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))) + ((((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable))) + (((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) * S ((dst_negative_code_base_resulttable) + (dst_negative_scale_base_resulttable)) + ((dst_negative_scale_base_resulttable) + (dst_negative_scale_base_resulttable)))))) /\ (forall dst_index_base_resulttable. (exists pvs_le_gap_base_resulttabledomain. pvs_le_gap_base_resulttabledomain + (dst_index_base_resulttable) = (0)) -> exists dst_positive_base_resulttable dst_negative_base_resulttable dst_value_base_resulttable. ((((exists ff_h_pvs_base_resulttableentrypositive. ff_h_pvs_base_resulttableentrypositive + S (dst_positive_base_resulttable) = S ((S (dst_index_base_resulttable)) * dst_positive_scale_base_resulttable)) /\ exists ff_q_pvs_base_resulttableentrypositive. dst_positive_code_base_resulttable = ff_q_pvs_base_resulttableentrypositive * S ((S (dst_index_base_resulttable)) * dst_positive_scale_base_resulttable) + (dst_positive_base_resulttable))) /\ (((((exists ff_h_pvs_base_resulttableentrynegative. ff_h_pvs_base_resulttableentrynegative + S (dst_negative_base_resulttable) = S ((S (dst_index_base_resulttable)) * dst_negative_scale_base_resulttable)) /\ exists ff_q_pvs_base_resulttableentrynegative. dst_negative_code_base_resulttable = ff_q_pvs_base_resulttableentrynegative * S ((S (dst_index_base_resulttable)) * dst_negative_scale_base_resulttable) + (dst_negative_base_resulttable))) /\ (exists ge_balance_positive_base_resulttableentryvalue ge_balance_negative_base_resulttableentryvalue. (((((dst_value_base_resulttable) = 2 * (ge_balance_positive_base_resulttableentryvalue) /\ (ge_balance_negative_base_resulttableentryvalue) = 0) \/ exists ge_signed_half_base_resulttableentryvaluedecode. (((dst_value_base_resulttable) = 2 * ge_signed_half_base_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_base_resulttableentryvalue) = 0) /\ (ge_balance_negative_base_resulttableentryvalue) = S ge_signed_half_base_resulttableentryvaluedecode))) /\ ((dst_positive_base_resulttable) + ge_balance_negative_base_resulttableentryvalue = (dst_negative_base_resulttable) + ge_balance_positive_base_resulttableentryvalue))))))))) /\ (forall dc_index_base_result dc_value_base_result. (exists pvs_le_gap_base_resultdomain. pvs_le_gap_base_resultdomain + (dc_index_base_result) = (0)) -> (exists dst_positive_code_base_resultlookup dst_positive_scale_base_resultlookup dst_negative_code_base_resultlookup dst_negative_scale_base_resultlookup dst_positive_base_resultlookup dst_negative_base_resultlookup. (((M) = (((((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) * S ((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) + ((dst_positive_scale_base_resultlookup) + (dst_positive_scale_base_resultlookup))) + (((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup)))) * S ((((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) * S ((dst_positive_code_base_resultlookup) + (dst_positive_scale_base_resultlookup)) + ((dst_positive_scale_base_resultlookup) + (dst_positive_scale_base_resultlookup))) + (((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup)))) + ((((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup))) + (((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) * S ((dst_negative_code_base_resultlookup) + (dst_negative_scale_base_resultlookup)) + ((dst_negative_scale_base_resultlookup) + (dst_negative_scale_base_resultlookup)))))) /\ (((((exists ff_h_pvs_base_resultlookuppositive. ff_h_pvs_base_resultlookuppositive + S (dst_positive_base_resultlookup) = S ((S (dc_index_base_result)) * dst_positive_scale_base_resultlookup)) /\ exists ff_q_pvs_base_resultlookuppositive. dst_positive_code_base_resultlookup = ff_q_pvs_base_resultlookuppositive * S ((S (dc_index_base_result)) * dst_positive_scale_base_resultlookup) + (dst_positive_base_resultlookup))) /\ (((((exists ff_h_pvs_base_resultlookupnegative. ff_h_pvs_base_resultlookupnegative + S (dst_negative_base_resultlookup) = S ((S (dc_index_base_result)) * dst_negative_scale_base_resultlookup)) /\ exists ff_q_pvs_base_resultlookupnegative. dst_negative_code_base_resultlookup = ff_q_pvs_base_resultlookupnegative * S ((S (dc_index_base_result)) * dst_negative_scale_base_resultlookup) + (dst_negative_base_resultlookup))) /\ (exists ge_balance_positive_base_resultlookupvalue ge_balance_negative_base_resultlookupvalue. (((((dc_value_base_result) = 2 * (ge_balance_positive_base_resultlookupvalue) /\ (ge_balance_negative_base_resultlookupvalue) = 0) \/ exists ge_signed_half_base_resultlookupvaluedecode. (((dc_value_base_result) = 2 * ge_signed_half_base_resultlookupvaluedecode + 1 /\ (ge_balance_positive_base_resultlookupvalue) = 0) /\ (ge_balance_negative_base_resultlookupvalue) = S ge_signed_half_base_resultlookupvaluedecode))) /\ ((dst_positive_base_resultlookup) + ge_balance_negative_base_resultlookupvalue = (dst_negative_base_resultlookup) + ge_balance_positive_base_resultlookupvalue))))))))) -> ((((~((dc_index_base_result)=0)) /\ (exists dc_quotient_base_resultentry dc_left_base_resultentry dc_right_base_resultentry. (((n)=(dc_index_base_result)*dc_quotient_base_resultentry) /\ (((exists dst_positive_code_base_resultentryleft dst_positive_scale_base_resultentryleft dst_negative_code_base_resultentryleft dst_negative_scale_base_resultentryleft dst_positive_base_resultentryleft dst_negative_base_resultentryleft. (((F) = (((((dst_positive_code_base_resultentryleft) + (dst_positive_scale_base_resultentryleft)) * S ((dst_positive_code_base_resultentryleft) + (dst_positive_scale_base_resultentryleft)) + ((dst_positive_scale_base_resultentryleft) + (dst_positive_scale_base_resultentryleft))) + (((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) * S ((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) + ((dst_negative_scale_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)))) * S ((((dst_positive_code_base_resultentryleft) + (dst_positive_scale_base_resultentryleft)) * S ((dst_positive_code_base_resultentryleft) + (dst_positive_scale_base_resultentryleft)) + ((dst_positive_scale_base_resultentryleft) + (dst_positive_scale_base_resultentryleft))) + (((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) * S ((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) + ((dst_negative_scale_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)))) + ((((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) * S ((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) + ((dst_negative_scale_base_resultentryleft) + (dst_negative_scale_base_resultentryleft))) + (((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) * S ((dst_negative_code_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)) + ((dst_negative_scale_base_resultentryleft) + (dst_negative_scale_base_resultentryleft)))))) /\ (((((exists ff_h_pvs_base_resultentryleftpositive. ff_h_pvs_base_resultentryleftpositive + S (dst_positive_base_resultentryleft) = S ((S (dc_index_base_result)) * dst_positive_scale_base_resultentryleft)) /\ exists ff_q_pvs_base_resultentryleftpositive. dst_positive_code_base_resultentryleft = ff_q_pvs_base_resultentryleftpositive * S ((S (dc_index_base_result)) * dst_positive_scale_base_resultentryleft) + (dst_positive_base_resultentryleft))) /\ (((((exists ff_h_pvs_base_resultentryleftnegative. ff_h_pvs_base_resultentryleftnegative + S (dst_negative_base_resultentryleft) = S ((S (dc_index_base_result)) * dst_negative_scale_base_resultentryleft)) /\ exists ff_q_pvs_base_resultentryleftnegative. dst_negative_code_base_resultentryleft = ff_q_pvs_base_resultentryleftnegative * S ((S (dc_index_base_result)) * dst_negative_scale_base_resultentryleft) + (dst_negative_base_resultentryleft))) /\ (exists ge_balance_positive_base_resultentryleftvalue ge_balance_negative_base_resultentryleftvalue. (((((dc_left_base_resultentry) = 2 * (ge_balance_positive_base_resultentryleftvalue) /\ (ge_balance_negative_base_resultentryleftvalue) = 0) \/ exists ge_signed_half_base_resultentryleftvaluedecode. (((dc_left_base_resultentry) = 2 * ge_signed_half_base_resultentryleftvaluedecode + 1 /\ (ge_balance_positive_base_resultentryleftvalue) = 0) /\ (ge_balance_negative_base_resultentryleftvalue) = S ge_signed_half_base_resultentryleftvaluedecode))) /\ ((dst_positive_base_resultentryleft) + ge_balance_negative_base_resultentryleftvalue = (dst_negative_base_resultentryleft) + ge_balance_positive_base_resultentryleftvalue))))))))) /\ (((exists dst_positive_code_base_resultentryright dst_positive_scale_base_resultentryright dst_negative_code_base_resultentryright dst_negative_scale_base_resultentryright dst_positive_base_resultentryright dst_negative_base_resultentryright. (((G) = (((((dst_positive_code_base_resultentryright) + (dst_positive_scale_base_resultentryright)) * S ((dst_positive_code_base_resultentryright) + (dst_positive_scale_base_resultentryright)) + ((dst_positive_scale_base_resultentryright) + (dst_positive_scale_base_resultentryright))) + (((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) * S ((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) + ((dst_negative_scale_base_resultentryright) + (dst_negative_scale_base_resultentryright)))) * S ((((dst_positive_code_base_resultentryright) + (dst_positive_scale_base_resultentryright)) * S ((dst_positive_code_base_resultentryright) + (dst_positive_scale_base_resultentryright)) + ((dst_positive_scale_base_resultentryright) + (dst_positive_scale_base_resultentryright))) + (((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) * S ((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) + ((dst_negative_scale_base_resultentryright) + (dst_negative_scale_base_resultentryright)))) + ((((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) * S ((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) + ((dst_negative_scale_base_resultentryright) + (dst_negative_scale_base_resultentryright))) + (((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) * S ((dst_negative_code_base_resultentryright) + (dst_negative_scale_base_resultentryright)) + ((dst_negative_scale_base_resultentryright) + (dst_negative_scale_base_resultentryright)))))) /\ (((((exists ff_h_pvs_base_resultentryrightpositive. ff_h_pvs_base_resultentryrightpositive + S (dst_positive_base_resultentryright) = S ((S (dc_quotient_base_resultentry)) * dst_positive_scale_base_resultentryright)) /\ exists ff_q_pvs_base_resultentryrightpositive. dst_positive_code_base_resultentryright = ff_q_pvs_base_resultentryrightpositive * S ((S (dc_quotient_base_resultentry)) * dst_positive_scale_base_resultentryright) + (dst_positive_base_resultentryright))) /\ (((((exists ff_h_pvs_base_resultentryrightnegative. ff_h_pvs_base_resultentryrightnegative + S (dst_negative_base_resultentryright) = S ((S (dc_quotient_base_resultentry)) * dst_negative_scale_base_resultentryright)) /\ exists ff_q_pvs_base_resultentryrightnegative. dst_negative_code_base_resultentryright = ff_q_pvs_base_resultentryrightnegative * S ((S (dc_quotient_base_resultentry)) * dst_negative_scale_base_resultentryright) + (dst_negative_base_resultentryright))) /\ (exists ge_balance_positive_base_resultentryrightvalue ge_balance_negative_base_resultentryrightvalue. (((((dc_right_base_resultentry) = 2 * (ge_balance_positive_base_resultentryrightvalue) /\ (ge_balance_negative_base_resultentryrightvalue) = 0) \/ exists ge_signed_half_base_resultentryrightvaluedecode. (((dc_right_base_resultentry) = 2 * ge_signed_half_base_resultentryrightvaluedecode + 1 /\ (ge_balance_positive_base_resultentryrightvalue) = 0) /\ (ge_balance_negative_base_resultentryrightvalue) = S ge_signed_half_base_resultentryrightvaluedecode))) /\ ((dst_positive_base_resultentryright) + ge_balance_negative_base_resultentryrightvalue = (dst_negative_base_resultentryright) + ge_balance_positive_base_resultentryrightvalue))))))))) /\ (exists sto_ap_base_resultentryproduct sto_an_base_resultentryproduct sto_bp_base_resultentryproduct sto_bn_base_resultentryproduct sto_cp_base_resultentryproduct sto_cn_base_resultentryproduct. (((((dc_left_base_resultentry) = 2 * (sto_ap_base_resultentryproduct) /\ (sto_an_base_resultentryproduct) = 0) \/ exists ge_signed_half_base_resultentryproductleft. (((dc_left_base_resultentry) = 2 * ge_signed_half_base_resultentryproductleft + 1 /\ (sto_ap_base_resultentryproduct) = 0) /\ (sto_an_base_resultentryproduct) = S ge_signed_half_base_resultentryproductleft))) /\ ((((((dc_right_base_resultentry) = 2 * (sto_bp_base_resultentryproduct) /\ (sto_bn_base_resultentryproduct) = 0) \/ exists ge_signed_half_base_resultentryproductright. (((dc_right_base_resultentry) = 2 * ge_signed_half_base_resultentryproductright + 1 /\ (sto_bp_base_resultentryproduct) = 0) /\ (sto_bn_base_resultentryproduct) = S ge_signed_half_base_resultentryproductright))) /\ ((((((dc_value_base_result) = 2 * (sto_cp_base_resultentryproduct) /\ (sto_cn_base_resultentryproduct) = 0) \/ exists ge_signed_half_base_resultentryproductoutput. (((dc_value_base_result) = 2 * ge_signed_half_base_resultentryproductoutput + 1 /\ (sto_cp_base_resultentryproduct) = 0) /\ (sto_cn_base_resultentryproduct) = S ge_signed_half_base_resultentryproductoutput))) /\ ((sto_ap_base_resultentryproduct * sto_bp_base_resultentryproduct + sto_an_base_resultentryproduct * sto_bn_base_resultentryproduct) + sto_cn_base_resultentryproduct = (sto_ap_base_resultentryproduct * sto_bn_base_resultentryproduct + sto_an_base_resultentryproduct * sto_bp_base_resultentryproduct) + sto_cp_base_resultentryproduct))))))))))))))) \/ ((((dc_index_base_result)=0 \/ ~(exists pvs_factor_base_resultentrynondivisor. (n) = (dc_index_base_result) * pvs_factor_base_resultentrynondivisor)) /\ ((dc_value_base_result)=0)))))))

• divisor_signed_sum_functional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F l a b. (exists dst_positive_code_sum_unique_first dst_positive_scale_sum_unique_first dst_negative_code_sum_unique_first dst_negative_scale_sum_unique_first dst_positive_sum_sum_unique_first dst_negative_sum_sum_unique_first. (((F) = (((((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) * S ((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) + ((dst_positive_scale_sum_unique_first) + (dst_positive_scale_sum_unique_first))) + (((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first)))) * S ((((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) * S ((dst_positive_code_sum_unique_first) + (dst_positive_scale_sum_unique_first)) + ((dst_positive_scale_sum_unique_first) + (dst_positive_scale_sum_unique_first))) + (((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first)))) + ((((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first))) + (((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) * S ((dst_negative_code_sum_unique_first) + (dst_negative_scale_sum_unique_first)) + ((dst_negative_scale_sum_unique_first) + (dst_negative_scale_sum_unique_first)))))) /\ (((exists fs_u_dst_sum_unique_firstpositive fs_v_dst_sum_unique_firstpositive. ((((exists fs_h_dst_sum_unique_firstpositive_body_start. fs_h_dst_sum_unique_firstpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_start. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstpositive_body_terminal. fs_h_dst_sum_unique_firstpositive_body_terminal + S (dst_positive_sum_sum_unique_first) = S ((S (l)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_terminal. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_firstpositive) + (dst_positive_sum_sum_unique_first))) /\ forall fs_i_dst_sum_unique_firstpositive_body_steps. (exists fs_lt_dst_sum_unique_firstpositive_body_steps_bound. fs_lt_dst_sum_unique_firstpositive_body_steps_bound + S fs_i_dst_sum_unique_firstpositive_body_steps = l) -> exists fs_a_dst_sum_unique_firstpositive_body_steps fs_r_dst_sum_unique_firstpositive_body_steps fs_s_dst_sum_unique_firstpositive_body_steps. ((((exists fs_h_dst_sum_unique_firstpositive_body_steps_summand. fs_h_dst_sum_unique_firstpositive_body_steps_summand + S (fs_a_dst_sum_unique_firstpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * dst_positive_scale_sum_unique_first)) /\ exists fs_q_dst_sum_unique_firstpositive_body_steps_summand. dst_positive_code_sum_unique_first = fs_q_dst_sum_unique_firstpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * dst_positive_scale_sum_unique_first) + (fs_a_dst_sum_unique_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstpositive_body_steps_partial. fs_h_dst_sum_unique_firstpositive_body_steps_partial + S (fs_r_dst_sum_unique_firstpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_steps_partial. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive) + (fs_r_dst_sum_unique_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstpositive_body_steps_successor. fs_h_dst_sum_unique_firstpositive_body_steps_successor + S (fs_s_dst_sum_unique_firstpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive)) /\ exists fs_q_dst_sum_unique_firstpositive_body_steps_successor. fs_u_dst_sum_unique_firstpositive = fs_q_dst_sum_unique_firstpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstpositive_body_steps)) * fs_v_dst_sum_unique_firstpositive) + (fs_s_dst_sum_unique_firstpositive_body_steps))) /\ fs_s_dst_sum_unique_firstpositive_body_steps = fs_r_dst_sum_unique_firstpositive_body_steps + fs_a_dst_sum_unique_firstpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_firstnegative fs_v_dst_sum_unique_firstnegative. ((((exists fs_h_dst_sum_unique_firstnegative_body_start. fs_h_dst_sum_unique_firstnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_start. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstnegative_body_terminal. fs_h_dst_sum_unique_firstnegative_body_terminal + S (dst_negative_sum_sum_unique_first) = S ((S (l)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_terminal. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_firstnegative) + (dst_negative_sum_sum_unique_first))) /\ forall fs_i_dst_sum_unique_firstnegative_body_steps. (exists fs_lt_dst_sum_unique_firstnegative_body_steps_bound. fs_lt_dst_sum_unique_firstnegative_body_steps_bound + S fs_i_dst_sum_unique_firstnegative_body_steps = l) -> exists fs_a_dst_sum_unique_firstnegative_body_steps fs_r_dst_sum_unique_firstnegative_body_steps fs_s_dst_sum_unique_firstnegative_body_steps. ((((exists fs_h_dst_sum_unique_firstnegative_body_steps_summand. fs_h_dst_sum_unique_firstnegative_body_steps_summand + S (fs_a_dst_sum_unique_firstnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * dst_negative_scale_sum_unique_first)) /\ exists fs_q_dst_sum_unique_firstnegative_body_steps_summand. dst_negative_code_sum_unique_first = fs_q_dst_sum_unique_firstnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * dst_negative_scale_sum_unique_first) + (fs_a_dst_sum_unique_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstnegative_body_steps_partial. fs_h_dst_sum_unique_firstnegative_body_steps_partial + S (fs_r_dst_sum_unique_firstnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_steps_partial. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative) + (fs_r_dst_sum_unique_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstnegative_body_steps_successor. fs_h_dst_sum_unique_firstnegative_body_steps_successor + S (fs_s_dst_sum_unique_firstnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative)) /\ exists fs_q_dst_sum_unique_firstnegative_body_steps_successor. fs_u_dst_sum_unique_firstnegative = fs_q_dst_sum_unique_firstnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstnegative_body_steps)) * fs_v_dst_sum_unique_firstnegative) + (fs_s_dst_sum_unique_firstnegative_body_steps))) /\ fs_s_dst_sum_unique_firstnegative_body_steps = fs_r_dst_sum_unique_firstnegative_body_steps + fs_a_dst_sum_unique_firstnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_firstresult ge_balance_negative_sum_unique_firstresult. (((((a) = 2 * (ge_balance_positive_sum_unique_firstresult) /\ (ge_balance_negative_sum_unique_firstresult) = 0) \/ exists ge_signed_half_sum_unique_firstresultdecode. (((a) = 2 * ge_signed_half_sum_unique_firstresultdecode + 1 /\ (ge_balance_positive_sum_unique_firstresult) = 0) /\ (ge_balance_negative_sum_unique_firstresult) = S ge_signed_half_sum_unique_firstresultdecode))) /\ ((dst_positive_sum_sum_unique_first) + ge_balance_negative_sum_unique_firstresult = (dst_negative_sum_sum_unique_first) + ge_balance_positive_sum_unique_firstresult))))))))) -> (exists dst_positive_code_sum_unique_second dst_positive_scale_sum_unique_second dst_negative_code_sum_unique_second dst_negative_scale_sum_unique_second dst_positive_sum_sum_unique_second dst_negative_sum_sum_unique_second. (((F) = (((((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) * S ((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) + ((dst_positive_scale_sum_unique_second) + (dst_positive_scale_sum_unique_second))) + (((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second)))) * S ((((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) * S ((dst_positive_code_sum_unique_second) + (dst_positive_scale_sum_unique_second)) + ((dst_positive_scale_sum_unique_second) + (dst_positive_scale_sum_unique_second))) + (((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second)))) + ((((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second))) + (((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) * S ((dst_negative_code_sum_unique_second) + (dst_negative_scale_sum_unique_second)) + ((dst_negative_scale_sum_unique_second) + (dst_negative_scale_sum_unique_second)))))) /\ (((exists fs_u_dst_sum_unique_secondpositive fs_v_dst_sum_unique_secondpositive. ((((exists fs_h_dst_sum_unique_secondpositive_body_start. fs_h_dst_sum_unique_secondpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_start. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondpositive_body_terminal. fs_h_dst_sum_unique_secondpositive_body_terminal + S (dst_positive_sum_sum_unique_second) = S ((S (l)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_terminal. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_secondpositive) + (dst_positive_sum_sum_unique_second))) /\ forall fs_i_dst_sum_unique_secondpositive_body_steps. (exists fs_lt_dst_sum_unique_secondpositive_body_steps_bound. fs_lt_dst_sum_unique_secondpositive_body_steps_bound + S fs_i_dst_sum_unique_secondpositive_body_steps = l) -> exists fs_a_dst_sum_unique_secondpositive_body_steps fs_r_dst_sum_unique_secondpositive_body_steps fs_s_dst_sum_unique_secondpositive_body_steps. ((((exists fs_h_dst_sum_unique_secondpositive_body_steps_summand. fs_h_dst_sum_unique_secondpositive_body_steps_summand + S (fs_a_dst_sum_unique_secondpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * dst_positive_scale_sum_unique_second)) /\ exists fs_q_dst_sum_unique_secondpositive_body_steps_summand. dst_positive_code_sum_unique_second = fs_q_dst_sum_unique_secondpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * dst_positive_scale_sum_unique_second) + (fs_a_dst_sum_unique_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondpositive_body_steps_partial. fs_h_dst_sum_unique_secondpositive_body_steps_partial + S (fs_r_dst_sum_unique_secondpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_steps_partial. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive) + (fs_r_dst_sum_unique_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondpositive_body_steps_successor. fs_h_dst_sum_unique_secondpositive_body_steps_successor + S (fs_s_dst_sum_unique_secondpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive)) /\ exists fs_q_dst_sum_unique_secondpositive_body_steps_successor. fs_u_dst_sum_unique_secondpositive = fs_q_dst_sum_unique_secondpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondpositive_body_steps)) * fs_v_dst_sum_unique_secondpositive) + (fs_s_dst_sum_unique_secondpositive_body_steps))) /\ fs_s_dst_sum_unique_secondpositive_body_steps = fs_r_dst_sum_unique_secondpositive_body_steps + fs_a_dst_sum_unique_secondpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_secondnegative fs_v_dst_sum_unique_secondnegative. ((((exists fs_h_dst_sum_unique_secondnegative_body_start. fs_h_dst_sum_unique_secondnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_start. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondnegative_body_terminal. fs_h_dst_sum_unique_secondnegative_body_terminal + S (dst_negative_sum_sum_unique_second) = S ((S (l)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_terminal. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_unique_secondnegative) + (dst_negative_sum_sum_unique_second))) /\ forall fs_i_dst_sum_unique_secondnegative_body_steps. (exists fs_lt_dst_sum_unique_secondnegative_body_steps_bound. fs_lt_dst_sum_unique_secondnegative_body_steps_bound + S fs_i_dst_sum_unique_secondnegative_body_steps = l) -> exists fs_a_dst_sum_unique_secondnegative_body_steps fs_r_dst_sum_unique_secondnegative_body_steps fs_s_dst_sum_unique_secondnegative_body_steps. ((((exists fs_h_dst_sum_unique_secondnegative_body_steps_summand. fs_h_dst_sum_unique_secondnegative_body_steps_summand + S (fs_a_dst_sum_unique_secondnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * dst_negative_scale_sum_unique_second)) /\ exists fs_q_dst_sum_unique_secondnegative_body_steps_summand. dst_negative_code_sum_unique_second = fs_q_dst_sum_unique_secondnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * dst_negative_scale_sum_unique_second) + (fs_a_dst_sum_unique_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondnegative_body_steps_partial. fs_h_dst_sum_unique_secondnegative_body_steps_partial + S (fs_r_dst_sum_unique_secondnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_steps_partial. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative) + (fs_r_dst_sum_unique_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondnegative_body_steps_successor. fs_h_dst_sum_unique_secondnegative_body_steps_successor + S (fs_s_dst_sum_unique_secondnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative)) /\ exists fs_q_dst_sum_unique_secondnegative_body_steps_successor. fs_u_dst_sum_unique_secondnegative = fs_q_dst_sum_unique_secondnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondnegative_body_steps)) * fs_v_dst_sum_unique_secondnegative) + (fs_s_dst_sum_unique_secondnegative_body_steps))) /\ fs_s_dst_sum_unique_secondnegative_body_steps = fs_r_dst_sum_unique_secondnegative_body_steps + fs_a_dst_sum_unique_secondnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_secondresult ge_balance_negative_sum_unique_secondresult. (((((b) = 2 * (ge_balance_positive_sum_unique_secondresult) /\ (ge_balance_negative_sum_unique_secondresult) = 0) \/ exists ge_signed_half_sum_unique_secondresultdecode. (((b) = 2 * ge_signed_half_sum_unique_secondresultdecode + 1 /\ (ge_balance_positive_sum_unique_secondresult) = 0) /\ (ge_balance_negative_sum_unique_secondresult) = S ge_signed_half_sum_unique_secondresultdecode))) /\ ((dst_positive_sum_sum_unique_second) + ge_balance_negative_sum_unique_secondresult = (dst_negative_sum_sum_unique_second) + ge_balance_positive_sum_unique_secondresult))))))))) -> a = b

• divisor_signed_sum_successor_decompose · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F l z. (exists dst_positive_code_decomp_sum dst_positive_scale_decomp_sum dst_negative_code_decomp_sum dst_negative_scale_decomp_sum dst_positive_sum_decomp_sum dst_negative_sum_decomp_sum. (((F) = (((((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) * S ((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) + ((dst_positive_scale_decomp_sum) + (dst_positive_scale_decomp_sum))) + (((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum)))) * S ((((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) * S ((dst_positive_code_decomp_sum) + (dst_positive_scale_decomp_sum)) + ((dst_positive_scale_decomp_sum) + (dst_positive_scale_decomp_sum))) + (((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum)))) + ((((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum))) + (((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) * S ((dst_negative_code_decomp_sum) + (dst_negative_scale_decomp_sum)) + ((dst_negative_scale_decomp_sum) + (dst_negative_scale_decomp_sum)))))) /\ (((exists fs_u_dst_decomp_sumpositive fs_v_dst_decomp_sumpositive. ((((exists fs_h_dst_decomp_sumpositive_body_start. fs_h_dst_decomp_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_start. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_start * S ((S (0)) * fs_v_dst_decomp_sumpositive) + (0))) /\ ((((exists fs_h_dst_decomp_sumpositive_body_terminal. fs_h_dst_decomp_sumpositive_body_terminal + S (dst_positive_sum_decomp_sum) = S ((S (S l)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_terminal. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_terminal * S ((S (S l)) * fs_v_dst_decomp_sumpositive) + (dst_positive_sum_decomp_sum))) /\ forall fs_i_dst_decomp_sumpositive_body_steps. (exists fs_lt_dst_decomp_sumpositive_body_steps_bound. fs_lt_dst_decomp_sumpositive_body_steps_bound + S fs_i_dst_decomp_sumpositive_body_steps = S l) -> exists fs_a_dst_decomp_sumpositive_body_steps fs_r_dst_decomp_sumpositive_body_steps fs_s_dst_decomp_sumpositive_body_steps. ((((exists fs_h_dst_decomp_sumpositive_body_steps_summand. fs_h_dst_decomp_sumpositive_body_steps_summand + S (fs_a_dst_decomp_sumpositive_body_steps) = S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * dst_positive_scale_decomp_sum)) /\ exists fs_q_dst_decomp_sumpositive_body_steps_summand. dst_positive_code_decomp_sum = fs_q_dst_decomp_sumpositive_body_steps_summand * S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * dst_positive_scale_decomp_sum) + (fs_a_dst_decomp_sumpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_sumpositive_body_steps_partial. fs_h_dst_decomp_sumpositive_body_steps_partial + S (fs_r_dst_decomp_sumpositive_body_steps) = S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_steps_partial. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_steps_partial * S ((S (fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive) + (fs_r_dst_decomp_sumpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_sumpositive_body_steps_successor. fs_h_dst_decomp_sumpositive_body_steps_successor + S (fs_s_dst_decomp_sumpositive_body_steps) = S ((S (S fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive)) /\ exists fs_q_dst_decomp_sumpositive_body_steps_successor. fs_u_dst_decomp_sumpositive = fs_q_dst_decomp_sumpositive_body_steps_successor * S ((S (S fs_i_dst_decomp_sumpositive_body_steps)) * fs_v_dst_decomp_sumpositive) + (fs_s_dst_decomp_sumpositive_body_steps))) /\ fs_s_dst_decomp_sumpositive_body_steps = fs_r_dst_decomp_sumpositive_body_steps + fs_a_dst_decomp_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_decomp_sumnegative fs_v_dst_decomp_sumnegative. ((((exists fs_h_dst_decomp_sumnegative_body_start. fs_h_dst_decomp_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_start. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_start * S ((S (0)) * fs_v_dst_decomp_sumnegative) + (0))) /\ ((((exists fs_h_dst_decomp_sumnegative_body_terminal. fs_h_dst_decomp_sumnegative_body_terminal + S (dst_negative_sum_decomp_sum) = S ((S (S l)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_terminal. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_terminal * S ((S (S l)) * fs_v_dst_decomp_sumnegative) + (dst_negative_sum_decomp_sum))) /\ forall fs_i_dst_decomp_sumnegative_body_steps. (exists fs_lt_dst_decomp_sumnegative_body_steps_bound. fs_lt_dst_decomp_sumnegative_body_steps_bound + S fs_i_dst_decomp_sumnegative_body_steps = S l) -> exists fs_a_dst_decomp_sumnegative_body_steps fs_r_dst_decomp_sumnegative_body_steps fs_s_dst_decomp_sumnegative_body_steps. ((((exists fs_h_dst_decomp_sumnegative_body_steps_summand. fs_h_dst_decomp_sumnegative_body_steps_summand + S (fs_a_dst_decomp_sumnegative_body_steps) = S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * dst_negative_scale_decomp_sum)) /\ exists fs_q_dst_decomp_sumnegative_body_steps_summand. dst_negative_code_decomp_sum = fs_q_dst_decomp_sumnegative_body_steps_summand * S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * dst_negative_scale_decomp_sum) + (fs_a_dst_decomp_sumnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_sumnegative_body_steps_partial. fs_h_dst_decomp_sumnegative_body_steps_partial + S (fs_r_dst_decomp_sumnegative_body_steps) = S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_steps_partial. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_steps_partial * S ((S (fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative) + (fs_r_dst_decomp_sumnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_sumnegative_body_steps_successor. fs_h_dst_decomp_sumnegative_body_steps_successor + S (fs_s_dst_decomp_sumnegative_body_steps) = S ((S (S fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative)) /\ exists fs_q_dst_decomp_sumnegative_body_steps_successor. fs_u_dst_decomp_sumnegative = fs_q_dst_decomp_sumnegative_body_steps_successor * S ((S (S fs_i_dst_decomp_sumnegative_body_steps)) * fs_v_dst_decomp_sumnegative) + (fs_s_dst_decomp_sumnegative_body_steps))) /\ fs_s_dst_decomp_sumnegative_body_steps = fs_r_dst_decomp_sumnegative_body_steps + fs_a_dst_decomp_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_decomp_sumresult ge_balance_negative_decomp_sumresult. (((((z) = 2 * (ge_balance_positive_decomp_sumresult) /\ (ge_balance_negative_decomp_sumresult) = 0) \/ exists ge_signed_half_decomp_sumresultdecode. (((z) = 2 * ge_signed_half_decomp_sumresultdecode + 1 /\ (ge_balance_positive_decomp_sumresult) = 0) /\ (ge_balance_negative_decomp_sumresult) = S ge_signed_half_decomp_sumresultdecode))) /\ ((dst_positive_sum_decomp_sum) + ge_balance_negative_decomp_sumresult = (dst_negative_sum_decomp_sum) + ge_balance_positive_decomp_sumresult))))))))) -> exists a b. ((exists dst_positive_code_decomp_prefix dst_positive_scale_decomp_prefix dst_negative_code_decomp_prefix dst_negative_scale_decomp_prefix dst_positive_sum_decomp_prefix dst_negative_sum_decomp_prefix. (((F) = (((((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) * S ((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) + ((dst_positive_scale_decomp_prefix) + (dst_positive_scale_decomp_prefix))) + (((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix)))) * S ((((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) * S ((dst_positive_code_decomp_prefix) + (dst_positive_scale_decomp_prefix)) + ((dst_positive_scale_decomp_prefix) + (dst_positive_scale_decomp_prefix))) + (((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix)))) + ((((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix))) + (((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) * S ((dst_negative_code_decomp_prefix) + (dst_negative_scale_decomp_prefix)) + ((dst_negative_scale_decomp_prefix) + (dst_negative_scale_decomp_prefix)))))) /\ (((exists fs_u_dst_decomp_prefixpositive fs_v_dst_decomp_prefixpositive. ((((exists fs_h_dst_decomp_prefixpositive_body_start. fs_h_dst_decomp_prefixpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_start. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_start * S ((S (0)) * fs_v_dst_decomp_prefixpositive) + (0))) /\ ((((exists fs_h_dst_decomp_prefixpositive_body_terminal. fs_h_dst_decomp_prefixpositive_body_terminal + S (dst_positive_sum_decomp_prefix) = S ((S (l)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_terminal. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_terminal * S ((S (l)) * fs_v_dst_decomp_prefixpositive) + (dst_positive_sum_decomp_prefix))) /\ forall fs_i_dst_decomp_prefixpositive_body_steps. (exists fs_lt_dst_decomp_prefixpositive_body_steps_bound. fs_lt_dst_decomp_prefixpositive_body_steps_bound + S fs_i_dst_decomp_prefixpositive_body_steps = l) -> exists fs_a_dst_decomp_prefixpositive_body_steps fs_r_dst_decomp_prefixpositive_body_steps fs_s_dst_decomp_prefixpositive_body_steps. ((((exists fs_h_dst_decomp_prefixpositive_body_steps_summand. fs_h_dst_decomp_prefixpositive_body_steps_summand + S (fs_a_dst_decomp_prefixpositive_body_steps) = S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * dst_positive_scale_decomp_prefix)) /\ exists fs_q_dst_decomp_prefixpositive_body_steps_summand. dst_positive_code_decomp_prefix = fs_q_dst_decomp_prefixpositive_body_steps_summand * S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * dst_positive_scale_decomp_prefix) + (fs_a_dst_decomp_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixpositive_body_steps_partial. fs_h_dst_decomp_prefixpositive_body_steps_partial + S (fs_r_dst_decomp_prefixpositive_body_steps) = S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_steps_partial. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_steps_partial * S ((S (fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive) + (fs_r_dst_decomp_prefixpositive_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixpositive_body_steps_successor. fs_h_dst_decomp_prefixpositive_body_steps_successor + S (fs_s_dst_decomp_prefixpositive_body_steps) = S ((S (S fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive)) /\ exists fs_q_dst_decomp_prefixpositive_body_steps_successor. fs_u_dst_decomp_prefixpositive = fs_q_dst_decomp_prefixpositive_body_steps_successor * S ((S (S fs_i_dst_decomp_prefixpositive_body_steps)) * fs_v_dst_decomp_prefixpositive) + (fs_s_dst_decomp_prefixpositive_body_steps))) /\ fs_s_dst_decomp_prefixpositive_body_steps = fs_r_dst_decomp_prefixpositive_body_steps + fs_a_dst_decomp_prefixpositive_body_steps)))))) /\ (((exists fs_u_dst_decomp_prefixnegative fs_v_dst_decomp_prefixnegative. ((((exists fs_h_dst_decomp_prefixnegative_body_start. fs_h_dst_decomp_prefixnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_start. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_start * S ((S (0)) * fs_v_dst_decomp_prefixnegative) + (0))) /\ ((((exists fs_h_dst_decomp_prefixnegative_body_terminal. fs_h_dst_decomp_prefixnegative_body_terminal + S (dst_negative_sum_decomp_prefix) = S ((S (l)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_terminal. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_terminal * S ((S (l)) * fs_v_dst_decomp_prefixnegative) + (dst_negative_sum_decomp_prefix))) /\ forall fs_i_dst_decomp_prefixnegative_body_steps. (exists fs_lt_dst_decomp_prefixnegative_body_steps_bound. fs_lt_dst_decomp_prefixnegative_body_steps_bound + S fs_i_dst_decomp_prefixnegative_body_steps = l) -> exists fs_a_dst_decomp_prefixnegative_body_steps fs_r_dst_decomp_prefixnegative_body_steps fs_s_dst_decomp_prefixnegative_body_steps. ((((exists fs_h_dst_decomp_prefixnegative_body_steps_summand. fs_h_dst_decomp_prefixnegative_body_steps_summand + S (fs_a_dst_decomp_prefixnegative_body_steps) = S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * dst_negative_scale_decomp_prefix)) /\ exists fs_q_dst_decomp_prefixnegative_body_steps_summand. dst_negative_code_decomp_prefix = fs_q_dst_decomp_prefixnegative_body_steps_summand * S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * dst_negative_scale_decomp_prefix) + (fs_a_dst_decomp_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixnegative_body_steps_partial. fs_h_dst_decomp_prefixnegative_body_steps_partial + S (fs_r_dst_decomp_prefixnegative_body_steps) = S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_steps_partial. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_steps_partial * S ((S (fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative) + (fs_r_dst_decomp_prefixnegative_body_steps))) /\ ((((exists fs_h_dst_decomp_prefixnegative_body_steps_successor. fs_h_dst_decomp_prefixnegative_body_steps_successor + S (fs_s_dst_decomp_prefixnegative_body_steps) = S ((S (S fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative)) /\ exists fs_q_dst_decomp_prefixnegative_body_steps_successor. fs_u_dst_decomp_prefixnegative = fs_q_dst_decomp_prefixnegative_body_steps_successor * S ((S (S fs_i_dst_decomp_prefixnegative_body_steps)) * fs_v_dst_decomp_prefixnegative) + (fs_s_dst_decomp_prefixnegative_body_steps))) /\ fs_s_dst_decomp_prefixnegative_body_steps = fs_r_dst_decomp_prefixnegative_body_steps + fs_a_dst_decomp_prefixnegative_body_steps)))))) /\ (exists ge_balance_positive_decomp_prefixresult ge_balance_negative_decomp_prefixresult. (((((a) = 2 * (ge_balance_positive_decomp_prefixresult) /\ (ge_balance_negative_decomp_prefixresult) = 0) \/ exists ge_signed_half_decomp_prefixresultdecode. (((a) = 2 * ge_signed_half_decomp_prefixresultdecode + 1 /\ (ge_balance_positive_decomp_prefixresult) = 0) /\ (ge_balance_negative_decomp_prefixresult) = S ge_signed_half_decomp_prefixresultdecode))) /\ ((dst_positive_sum_decomp_prefix) + ge_balance_negative_decomp_prefixresult = (dst_negative_sum_decomp_prefix) + ge_balance_positive_decomp_prefixresult))))))))) /\ (((exists dst_positive_code_decomp_entry dst_positive_scale_decomp_entry dst_negative_code_decomp_entry dst_negative_scale_decomp_entry dst_positive_decomp_entry dst_negative_decomp_entry. (((F) = (((((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) * S ((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) + ((dst_positive_scale_decomp_entry) + (dst_positive_scale_decomp_entry))) + (((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry)))) * S ((((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) * S ((dst_positive_code_decomp_entry) + (dst_positive_scale_decomp_entry)) + ((dst_positive_scale_decomp_entry) + (dst_positive_scale_decomp_entry))) + (((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry)))) + ((((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry))) + (((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) * S ((dst_negative_code_decomp_entry) + (dst_negative_scale_decomp_entry)) + ((dst_negative_scale_decomp_entry) + (dst_negative_scale_decomp_entry)))))) /\ (((((exists ff_h_pvs_decomp_entrypositive. ff_h_pvs_decomp_entrypositive + S (dst_positive_decomp_entry) = S ((S (l)) * dst_positive_scale_decomp_entry)) /\ exists ff_q_pvs_decomp_entrypositive. dst_positive_code_decomp_entry = ff_q_pvs_decomp_entrypositive * S ((S (l)) * dst_positive_scale_decomp_entry) + (dst_positive_decomp_entry))) /\ (((((exists ff_h_pvs_decomp_entrynegative. ff_h_pvs_decomp_entrynegative + S (dst_negative_decomp_entry) = S ((S (l)) * dst_negative_scale_decomp_entry)) /\ exists ff_q_pvs_decomp_entrynegative. dst_negative_code_decomp_entry = ff_q_pvs_decomp_entrynegative * S ((S (l)) * dst_negative_scale_decomp_entry) + (dst_negative_decomp_entry))) /\ (exists ge_balance_positive_decomp_entryvalue ge_balance_negative_decomp_entryvalue. (((((b) = 2 * (ge_balance_positive_decomp_entryvalue) /\ (ge_balance_negative_decomp_entryvalue) = 0) \/ exists ge_signed_half_decomp_entryvaluedecode. (((b) = 2 * ge_signed_half_decomp_entryvaluedecode + 1 /\ (ge_balance_positive_decomp_entryvalue) = 0) /\ (ge_balance_negative_decomp_entryvalue) = S ge_signed_half_decomp_entryvaluedecode))) /\ ((dst_positive_decomp_entry) + ge_balance_negative_decomp_entryvalue = (dst_negative_decomp_entry) + ge_balance_positive_decomp_entryvalue))))))))) /\ (exists dsa_ap_decomp_add dsa_an_decomp_add dsa_bp_decomp_add dsa_bn_decomp_add dsa_cp_decomp_add dsa_cn_decomp_add. (((((a) = 2 * (dsa_ap_decomp_add) /\ (dsa_an_decomp_add) = 0) \/ exists ge_signed_half_decomp_addleft. (((a) = 2 * ge_signed_half_decomp_addleft + 1 /\ (dsa_ap_decomp_add) = 0) /\ (dsa_an_decomp_add) = S ge_signed_half_decomp_addleft))) /\ ((((((b) = 2 * (dsa_bp_decomp_add) /\ (dsa_bn_decomp_add) = 0) \/ exists ge_signed_half_decomp_addright. (((b) = 2 * ge_signed_half_decomp_addright + 1 /\ (dsa_bp_decomp_add) = 0) /\ (dsa_bn_decomp_add) = S ge_signed_half_decomp_addright))) /\ ((((((z) = 2 * (dsa_cp_decomp_add) /\ (dsa_cn_decomp_add) = 0) \/ exists ge_signed_half_decomp_addoutput. (((z) = 2 * ge_signed_half_decomp_addoutput + 1 /\ (dsa_cp_decomp_add) = 0) /\ (dsa_cn_decomp_add) = S ge_signed_half_decomp_addoutput))) /\ ((dsa_ap_decomp_add + dsa_bp_decomp_add) + dsa_cn_decomp_add = (dsa_an_decomp_add + dsa_bn_decomp_add) + dsa_cp_decomp_add))))))))))

• 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_zero · checked inherited prerequisite
  Exact statement in the checked dependency cone

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

• lt_of_le_of_lt · checked inherited prerequisite
  Exact statement in the checked dependency cone

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

• mul_one · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n. n * 1 = n

• signed_add_functional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall left right output1 output2. (exists sa_lp_functional_left sa_ln_functional_left sa_rp_functional_left sa_rn_functional_left sa_op_functional_left sa_on_functional_left. (((left = 2 * sa_lp_functional_left /\ sa_ln_functional_left = 0) \/ exists sd_half_functional_left_left. ((left = 2 * sd_half_functional_left_left + 1 /\ sa_lp_functional_left = 0) /\ sa_ln_functional_left = S sd_half_functional_left_left)) /\ (((right = 2 * sa_rp_functional_left /\ sa_rn_functional_left = 0) \/ exists sd_half_functional_left_right. ((right = 2 * sd_half_functional_left_right + 1 /\ sa_rp_functional_left = 0) /\ sa_rn_functional_left = S sd_half_functional_left_right)) /\ (((output1 = 2 * sa_op_functional_left /\ sa_on_functional_left = 0) \/ exists sd_half_functional_left_output. ((output1 = 2 * sd_half_functional_left_output + 1 /\ sa_op_functional_left = 0) /\ sa_on_functional_left = S sd_half_functional_left_output)) /\ (sa_lp_functional_left + sa_rp_functional_left) + sa_on_functional_left = (sa_ln_functional_left + sa_rn_functional_left) + sa_op_functional_left)))) -> (exists sa_lp_functional_right sa_ln_functional_right sa_rp_functional_right sa_rn_functional_right sa_op_functional_right sa_on_functional_right. (((left = 2 * sa_lp_functional_right /\ sa_ln_functional_right = 0) \/ exists sd_half_functional_right_left. ((left = 2 * sd_half_functional_right_left + 1 /\ sa_lp_functional_right = 0) /\ sa_ln_functional_right = S sd_half_functional_right_left)) /\ (((right = 2 * sa_rp_functional_right /\ sa_rn_functional_right = 0) \/ exists sd_half_functional_right_right. ((right = 2 * sd_half_functional_right_right + 1 /\ sa_rp_functional_right = 0) /\ sa_rn_functional_right = S sd_half_functional_right_right)) /\ (((output2 = 2 * sa_op_functional_right /\ sa_on_functional_right = 0) \/ exists sd_half_functional_right_output. ((output2 = 2 * sd_half_functional_right_output + 1 /\ sa_op_functional_right = 0) /\ sa_on_functional_right = S sd_half_functional_right_output)) /\ (sa_lp_functional_right + sa_rp_functional_right) + sa_on_functional_right = (sa_ln_functional_right + sa_rn_functional_right) + sa_op_functional_right)))) -> output1 = output2

• signed_add_zero_left · checked inherited prerequisite
  Exact statement in the checked dependency cone

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

• signed_prefix_sum_zero_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F l. (exists dst_positive_code_zero_source dst_positive_scale_zero_source dst_negative_code_zero_source dst_negative_scale_zero_source. (((F) = (((((dst_positive_code_zero_source) + (dst_positive_scale_zero_source)) * S ((dst_positive_code_zero_source) + (dst_positive_scale_zero_source)) + ((dst_positive_scale_zero_source) + (dst_positive_scale_zero_source))) + (((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) * S ((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) + ((dst_negative_scale_zero_source) + (dst_negative_scale_zero_source)))) * S ((((dst_positive_code_zero_source) + (dst_positive_scale_zero_source)) * S ((dst_positive_code_zero_source) + (dst_positive_scale_zero_source)) + ((dst_positive_scale_zero_source) + (dst_positive_scale_zero_source))) + (((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) * S ((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) + ((dst_negative_scale_zero_source) + (dst_negative_scale_zero_source)))) + ((((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) * S ((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) + ((dst_negative_scale_zero_source) + (dst_negative_scale_zero_source))) + (((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) * S ((dst_negative_code_zero_source) + (dst_negative_scale_zero_source)) + ((dst_negative_scale_zero_source) + (dst_negative_scale_zero_source)))))) /\ (forall dst_index_zero_source. (exists pvs_le_gap_zero_sourcedomain. pvs_le_gap_zero_sourcedomain + (dst_index_zero_source) = (0)) -> exists dst_positive_zero_source dst_negative_zero_source dst_value_zero_source. ((((exists ff_h_pvs_zero_sourceentrypositive. ff_h_pvs_zero_sourceentrypositive + S (dst_positive_zero_source) = S ((S (dst_index_zero_source)) * dst_positive_scale_zero_source)) /\ exists ff_q_pvs_zero_sourceentrypositive. dst_positive_code_zero_source = ff_q_pvs_zero_sourceentrypositive * S ((S (dst_index_zero_source)) * dst_positive_scale_zero_source) + (dst_positive_zero_source))) /\ (((((exists ff_h_pvs_zero_sourceentrynegative. ff_h_pvs_zero_sourceentrynegative + S (dst_negative_zero_source) = S ((S (dst_index_zero_source)) * dst_negative_scale_zero_source)) /\ exists ff_q_pvs_zero_sourceentrynegative. dst_negative_code_zero_source = ff_q_pvs_zero_sourceentrynegative * S ((S (dst_index_zero_source)) * dst_negative_scale_zero_source) + (dst_negative_zero_source))) /\ (exists ge_balance_positive_zero_sourceentryvalue ge_balance_negative_zero_sourceentryvalue. (((((dst_value_zero_source) = 2 * (ge_balance_positive_zero_sourceentryvalue) /\ (ge_balance_negative_zero_sourceentryvalue) = 0) \/ exists ge_signed_half_zero_sourceentryvaluedecode. (((dst_value_zero_source) = 2 * ge_signed_half_zero_sourceentryvaluedecode + 1 /\ (ge_balance_positive_zero_sourceentryvalue) = 0) /\ (ge_balance_negative_zero_sourceentryvalue) = S ge_signed_half_zero_sourceentryvaluedecode))) /\ ((dst_positive_zero_source) + ge_balance_negative_zero_sourceentryvalue = (dst_negative_zero_source) + ge_balance_positive_zero_sourceentryvalue))))))))) -> (forall sfs_index_zero_window sfs_value_zero_window. (exists pvs_le_gap_zero_windowlower. pvs_le_gap_zero_windowlower + (0) = (sfs_index_zero_window)) -> (exists pvs_gap_zero_windowupper. pvs_gap_zero_windowupper + S (sfs_index_zero_window) = (l)) -> (exists dst_positive_code_zero_windowentry dst_positive_scale_zero_windowentry dst_negative_code_zero_windowentry dst_negative_scale_zero_windowentry dst_positive_zero_windowentry dst_negative_zero_windowentry. (((F) = (((((dst_positive_code_zero_windowentry) + (dst_positive_scale_zero_windowentry)) * S ((dst_positive_code_zero_windowentry) + (dst_positive_scale_zero_windowentry)) + ((dst_positive_scale_zero_windowentry) + (dst_positive_scale_zero_windowentry))) + (((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) * S ((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) + ((dst_negative_scale_zero_windowentry) + (dst_negative_scale_zero_windowentry)))) * S ((((dst_positive_code_zero_windowentry) + (dst_positive_scale_zero_windowentry)) * S ((dst_positive_code_zero_windowentry) + (dst_positive_scale_zero_windowentry)) + ((dst_positive_scale_zero_windowentry) + (dst_positive_scale_zero_windowentry))) + (((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) * S ((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) + ((dst_negative_scale_zero_windowentry) + (dst_negative_scale_zero_windowentry)))) + ((((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) * S ((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) + ((dst_negative_scale_zero_windowentry) + (dst_negative_scale_zero_windowentry))) + (((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) * S ((dst_negative_code_zero_windowentry) + (dst_negative_scale_zero_windowentry)) + ((dst_negative_scale_zero_windowentry) + (dst_negative_scale_zero_windowentry)))))) /\ (((((exists ff_h_pvs_zero_windowentrypositive. ff_h_pvs_zero_windowentrypositive + S (dst_positive_zero_windowentry) = S ((S (sfs_index_zero_window)) * dst_positive_scale_zero_windowentry)) /\ exists ff_q_pvs_zero_windowentrypositive. dst_positive_code_zero_windowentry = ff_q_pvs_zero_windowentrypositive * S ((S (sfs_index_zero_window)) * dst_positive_scale_zero_windowentry) + (dst_positive_zero_windowentry))) /\ (((((exists ff_h_pvs_zero_windowentrynegative. ff_h_pvs_zero_windowentrynegative + S (dst_negative_zero_windowentry) = S ((S (sfs_index_zero_window)) * dst_negative_scale_zero_windowentry)) /\ exists ff_q_pvs_zero_windowentrynegative. dst_negative_code_zero_windowentry = ff_q_pvs_zero_windowentrynegative * S ((S (sfs_index_zero_window)) * dst_negative_scale_zero_windowentry) + (dst_negative_zero_windowentry))) /\ (exists ge_balance_positive_zero_windowentryvalue ge_balance_negative_zero_windowentryvalue. (((((sfs_value_zero_window) = 2 * (ge_balance_positive_zero_windowentryvalue) /\ (ge_balance_negative_zero_windowentryvalue) = 0) \/ exists ge_signed_half_zero_windowentryvaluedecode. (((sfs_value_zero_window) = 2 * ge_signed_half_zero_windowentryvaluedecode + 1 /\ (ge_balance_positive_zero_windowentryvalue) = 0) /\ (ge_balance_negative_zero_windowentryvalue) = S ge_signed_half_zero_windowentryvaluedecode))) /\ ((dst_positive_zero_windowentry) + ge_balance_negative_zero_windowentryvalue = (dst_negative_zero_windowentry) + ge_balance_positive_zero_windowentryvalue))))))))) -> sfs_value_zero_window=0) -> (exists dst_positive_code_zero_result dst_positive_scale_zero_result dst_negative_code_zero_result dst_negative_scale_zero_result dst_positive_sum_zero_result dst_negative_sum_zero_result. (((F) = (((((dst_positive_code_zero_result) + (dst_positive_scale_zero_result)) * S ((dst_positive_code_zero_result) + (dst_positive_scale_zero_result)) + ((dst_positive_scale_zero_result) + (dst_positive_scale_zero_result))) + (((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) * S ((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) + ((dst_negative_scale_zero_result) + (dst_negative_scale_zero_result)))) * S ((((dst_positive_code_zero_result) + (dst_positive_scale_zero_result)) * S ((dst_positive_code_zero_result) + (dst_positive_scale_zero_result)) + ((dst_positive_scale_zero_result) + (dst_positive_scale_zero_result))) + (((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) * S ((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) + ((dst_negative_scale_zero_result) + (dst_negative_scale_zero_result)))) + ((((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) * S ((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) + ((dst_negative_scale_zero_result) + (dst_negative_scale_zero_result))) + (((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) * S ((dst_negative_code_zero_result) + (dst_negative_scale_zero_result)) + ((dst_negative_scale_zero_result) + (dst_negative_scale_zero_result)))))) /\ (((exists fs_u_dst_zero_resultpositive fs_v_dst_zero_resultpositive. ((((exists fs_h_dst_zero_resultpositive_body_start. fs_h_dst_zero_resultpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_resultpositive)) /\ exists fs_q_dst_zero_resultpositive_body_start. fs_u_dst_zero_resultpositive = fs_q_dst_zero_resultpositive_body_start * S ((S (0)) * fs_v_dst_zero_resultpositive) + (0))) /\ ((((exists fs_h_dst_zero_resultpositive_body_terminal. fs_h_dst_zero_resultpositive_body_terminal + S (dst_positive_sum_zero_result) = S ((S (l)) * fs_v_dst_zero_resultpositive)) /\ exists fs_q_dst_zero_resultpositive_body_terminal. fs_u_dst_zero_resultpositive = fs_q_dst_zero_resultpositive_body_terminal * S ((S (l)) * fs_v_dst_zero_resultpositive) + (dst_positive_sum_zero_result))) /\ forall fs_i_dst_zero_resultpositive_body_steps. (exists fs_lt_dst_zero_resultpositive_body_steps_bound. fs_lt_dst_zero_resultpositive_body_steps_bound + S fs_i_dst_zero_resultpositive_body_steps = l) -> exists fs_a_dst_zero_resultpositive_body_steps fs_r_dst_zero_resultpositive_body_steps fs_s_dst_zero_resultpositive_body_steps. ((((exists fs_h_dst_zero_resultpositive_body_steps_summand. fs_h_dst_zero_resultpositive_body_steps_summand + S (fs_a_dst_zero_resultpositive_body_steps) = S ((S (fs_i_dst_zero_resultpositive_body_steps)) * dst_positive_scale_zero_result)) /\ exists fs_q_dst_zero_resultpositive_body_steps_summand. dst_positive_code_zero_result = fs_q_dst_zero_resultpositive_body_steps_summand * S ((S (fs_i_dst_zero_resultpositive_body_steps)) * dst_positive_scale_zero_result) + (fs_a_dst_zero_resultpositive_body_steps))) /\ ((((exists fs_h_dst_zero_resultpositive_body_steps_partial. fs_h_dst_zero_resultpositive_body_steps_partial + S (fs_r_dst_zero_resultpositive_body_steps) = S ((S (fs_i_dst_zero_resultpositive_body_steps)) * fs_v_dst_zero_resultpositive)) /\ exists fs_q_dst_zero_resultpositive_body_steps_partial. fs_u_dst_zero_resultpositive = fs_q_dst_zero_resultpositive_body_steps_partial * S ((S (fs_i_dst_zero_resultpositive_body_steps)) * fs_v_dst_zero_resultpositive) + (fs_r_dst_zero_resultpositive_body_steps))) /\ ((((exists fs_h_dst_zero_resultpositive_body_steps_successor. fs_h_dst_zero_resultpositive_body_steps_successor + S (fs_s_dst_zero_resultpositive_body_steps) = S ((S (S fs_i_dst_zero_resultpositive_body_steps)) * fs_v_dst_zero_resultpositive)) /\ exists fs_q_dst_zero_resultpositive_body_steps_successor. fs_u_dst_zero_resultpositive = fs_q_dst_zero_resultpositive_body_steps_successor * S ((S (S fs_i_dst_zero_resultpositive_body_steps)) * fs_v_dst_zero_resultpositive) + (fs_s_dst_zero_resultpositive_body_steps))) /\ fs_s_dst_zero_resultpositive_body_steps = fs_r_dst_zero_resultpositive_body_steps + fs_a_dst_zero_resultpositive_body_steps)))))) /\ (((exists fs_u_dst_zero_resultnegative fs_v_dst_zero_resultnegative. ((((exists fs_h_dst_zero_resultnegative_body_start. fs_h_dst_zero_resultnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_resultnegative)) /\ exists fs_q_dst_zero_resultnegative_body_start. fs_u_dst_zero_resultnegative = fs_q_dst_zero_resultnegative_body_start * S ((S (0)) * fs_v_dst_zero_resultnegative) + (0))) /\ ((((exists fs_h_dst_zero_resultnegative_body_terminal. fs_h_dst_zero_resultnegative_body_terminal + S (dst_negative_sum_zero_result) = S ((S (l)) * fs_v_dst_zero_resultnegative)) /\ exists fs_q_dst_zero_resultnegative_body_terminal. fs_u_dst_zero_resultnegative = fs_q_dst_zero_resultnegative_body_terminal * S ((S (l)) * fs_v_dst_zero_resultnegative) + (dst_negative_sum_zero_result))) /\ forall fs_i_dst_zero_resultnegative_body_steps. (exists fs_lt_dst_zero_resultnegative_body_steps_bound. fs_lt_dst_zero_resultnegative_body_steps_bound + S fs_i_dst_zero_resultnegative_body_steps = l) -> exists fs_a_dst_zero_resultnegative_body_steps fs_r_dst_zero_resultnegative_body_steps fs_s_dst_zero_resultnegative_body_steps. ((((exists fs_h_dst_zero_resultnegative_body_steps_summand. fs_h_dst_zero_resultnegative_body_steps_summand + S (fs_a_dst_zero_resultnegative_body_steps) = S ((S (fs_i_dst_zero_resultnegative_body_steps)) * dst_negative_scale_zero_result)) /\ exists fs_q_dst_zero_resultnegative_body_steps_summand. dst_negative_code_zero_result = fs_q_dst_zero_resultnegative_body_steps_summand * S ((S (fs_i_dst_zero_resultnegative_body_steps)) * dst_negative_scale_zero_result) + (fs_a_dst_zero_resultnegative_body_steps))) /\ ((((exists fs_h_dst_zero_resultnegative_body_steps_partial. fs_h_dst_zero_resultnegative_body_steps_partial + S (fs_r_dst_zero_resultnegative_body_steps) = S ((S (fs_i_dst_zero_resultnegative_body_steps)) * fs_v_dst_zero_resultnegative)) /\ exists fs_q_dst_zero_resultnegative_body_steps_partial. fs_u_dst_zero_resultnegative = fs_q_dst_zero_resultnegative_body_steps_partial * S ((S (fs_i_dst_zero_resultnegative_body_steps)) * fs_v_dst_zero_resultnegative) + (fs_r_dst_zero_resultnegative_body_steps))) /\ ((((exists fs_h_dst_zero_resultnegative_body_steps_successor. fs_h_dst_zero_resultnegative_body_steps_successor + S (fs_s_dst_zero_resultnegative_body_steps) = S ((S (S fs_i_dst_zero_resultnegative_body_steps)) * fs_v_dst_zero_resultnegative)) /\ exists fs_q_dst_zero_resultnegative_body_steps_successor. fs_u_dst_zero_resultnegative = fs_q_dst_zero_resultnegative_body_steps_successor * S ((S (S fs_i_dst_zero_resultnegative_body_steps)) * fs_v_dst_zero_resultnegative) + (fs_s_dst_zero_resultnegative_body_steps))) /\ fs_s_dst_zero_resultnegative_body_steps = fs_r_dst_zero_resultnegative_body_steps + fs_a_dst_zero_resultnegative_body_steps)))))) /\ (exists ge_balance_positive_zero_resultresult ge_balance_negative_zero_resultresult. (((((0) = 2 * (ge_balance_positive_zero_resultresult) /\ (ge_balance_negative_zero_resultresult) = 0) \/ exists ge_signed_half_zero_resultresultdecode. (((0) = 2 * ge_signed_half_zero_resultresultdecode + 1 /\ (ge_balance_positive_zero_resultresult) = 0) /\ (ge_balance_negative_zero_resultresult) = S ge_signed_half_zero_resultresultdecode))) /\ ((dst_positive_sum_zero_result) + ge_balance_negative_zero_resultresult = (dst_negative_sum_zero_result) + ge_balance_positive_zero_resultresult)))))))))

• signed_table_domain_resize · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall N M F. (exists dst_positive_code_resize_input dst_positive_scale_resize_input dst_negative_code_resize_input dst_negative_scale_resize_input. (((F) = (((((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) * S ((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) + ((dst_positive_scale_resize_input) + (dst_positive_scale_resize_input))) + (((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input)))) * S ((((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) * S ((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) + ((dst_positive_scale_resize_input) + (dst_positive_scale_resize_input))) + (((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input)))) + ((((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input))) + (((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input)))))) /\ (forall dst_index_resize_input. (exists pvs_le_gap_resize_inputdomain. pvs_le_gap_resize_inputdomain + (dst_index_resize_input) = (N)) -> exists dst_positive_resize_input dst_negative_resize_input dst_value_resize_input. ((((exists ff_h_pvs_resize_inputentrypositive. ff_h_pvs_resize_inputentrypositive + S (dst_positive_resize_input) = S ((S (dst_index_resize_input)) * dst_positive_scale_resize_input)) /\ exists ff_q_pvs_resize_inputentrypositive. dst_positive_code_resize_input = ff_q_pvs_resize_inputentrypositive * S ((S (dst_index_resize_input)) * dst_positive_scale_resize_input) + (dst_positive_resize_input))) /\ (((((exists ff_h_pvs_resize_inputentrynegative. ff_h_pvs_resize_inputentrynegative + S (dst_negative_resize_input) = S ((S (dst_index_resize_input)) * dst_negative_scale_resize_input)) /\ exists ff_q_pvs_resize_inputentrynegative. dst_negative_code_resize_input = ff_q_pvs_resize_inputentrynegative * S ((S (dst_index_resize_input)) * dst_negative_scale_resize_input) + (dst_negative_resize_input))) /\ (exists ge_balance_positive_resize_inputentryvalue ge_balance_negative_resize_inputentryvalue. (((((dst_value_resize_input) = 2 * (ge_balance_positive_resize_inputentryvalue) /\ (ge_balance_negative_resize_inputentryvalue) = 0) \/ exists ge_signed_half_resize_inputentryvaluedecode. (((dst_value_resize_input) = 2 * ge_signed_half_resize_inputentryvaluedecode + 1 /\ (ge_balance_positive_resize_inputentryvalue) = 0) /\ (ge_balance_negative_resize_inputentryvalue) = S ge_signed_half_resize_inputentryvaluedecode))) /\ ((dst_positive_resize_input) + ge_balance_negative_resize_inputentryvalue = (dst_negative_resize_input) + ge_balance_positive_resize_inputentryvalue))))))))) -> (exists dst_positive_code_resize_output dst_positive_scale_resize_output dst_negative_code_resize_output dst_negative_scale_resize_output. (((F) = (((((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) * S ((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) + ((dst_positive_scale_resize_output) + (dst_positive_scale_resize_output))) + (((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output)))) * S ((((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) * S ((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) + ((dst_positive_scale_resize_output) + (dst_positive_scale_resize_output))) + (((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output)))) + ((((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output))) + (((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output)))))) /\ (forall dst_index_resize_output. (exists pvs_le_gap_resize_outputdomain. pvs_le_gap_resize_outputdomain + (dst_index_resize_output) = (M)) -> exists dst_positive_resize_output dst_negative_resize_output dst_value_resize_output. ((((exists ff_h_pvs_resize_outputentrypositive. ff_h_pvs_resize_outputentrypositive + S (dst_positive_resize_output) = S ((S (dst_index_resize_output)) * dst_positive_scale_resize_output)) /\ exists ff_q_pvs_resize_outputentrypositive. dst_positive_code_resize_output = ff_q_pvs_resize_outputentrypositive * S ((S (dst_index_resize_output)) * dst_positive_scale_resize_output) + (dst_positive_resize_output))) /\ (((((exists ff_h_pvs_resize_outputentrynegative. ff_h_pvs_resize_outputentrynegative + S (dst_negative_resize_output) = S ((S (dst_index_resize_output)) * dst_negative_scale_resize_output)) /\ exists ff_q_pvs_resize_outputentrynegative. dst_negative_code_resize_output = ff_q_pvs_resize_outputentrynegative * S ((S (dst_index_resize_output)) * dst_negative_scale_resize_output) + (dst_negative_resize_output))) /\ (exists ge_balance_positive_resize_outputentryvalue ge_balance_negative_resize_outputentryvalue. (((((dst_value_resize_output) = 2 * (ge_balance_positive_resize_outputentryvalue) /\ (ge_balance_negative_resize_outputentryvalue) = 0) \/ exists ge_signed_half_resize_outputentryvaluedecode. (((dst_value_resize_output) = 2 * ge_signed_half_resize_outputentryvaluedecode + 1 /\ (ge_balance_positive_resize_outputentryvalue) = 0) /\ (ge_balance_negative_resize_outputentryvalue) = S ge_signed_half_resize_outputentryvaluedecode))) /\ ((dst_positive_resize_output) + ge_balance_negative_resize_outputentryvalue = (dst_negative_resize_output) + ge_balance_positive_resize_outputentryvalue)))))))))

• 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