prime_field_convolution_prefix_right_subtract

forall p ab ac bb bc cb cc L db dc M ub uc vb vc wb wc N. (forall pfs_index_prefix_subtract_right_source. (exists pfa_gap_prefix_subtract_right_sourceindex. pfa_gap_prefix_subtract_right_sourceindex + S (pfs_index_prefix_subtract_right_source) = (L)) -> exists pfs_left_prefix_subtract_right_source pfs_right_prefix_subtract_right_source pfs_result_prefix_subtract_right_source. ((((exists ff_h_pfp_prefix_subtract_right_sourceleft. ff_h_pfp_prefix_subtract_right_sourceleft + S (pfs_left_prefix_subtract_right_source) = S ((S (pfs_index_prefix_subtract_right_source)) * ac)) /\ exists ff_q_pfp_prefix_subtract_right_sourceleft. ab = ff_q_pfp_prefix_subtract_right_sourceleft * S ((S (pfs_index_prefix_subtract_right_source)) * ac) + (pfs_left_prefix_subtract_right_source))) /\ (((((exists ff_h_pfp_prefix_subtract_right_sourceright. ff_h_pfp_prefix_subtract_right_sourceright + S (pfs_right_prefix_subtract_right_source) = S ((S (pfs_index_prefix_subtract_right_source)) * bc)) /\ exists ff_q_pfp_prefix_subtract_right_sourceright. bb = ff_q_pfp_prefix_subtract_right_sourceright * S ((S (pfs_index_prefix_subtract_right_source)) * bc) + (pfs_right_prefix_subtract_right_source))) /\ (((((exists ff_h_pfp_prefix_subtract_right_sourceresult. ff_h_pfp_prefix_subtract_right_sourceresult + S (pfs_result_prefix_subtract_right_source) = S ((S (pfs_index_prefix_subtract_right_source)) * cc)) /\ exists ff_q_pfp_prefix_subtract_right_sourceresult. cb = ff_q_pfp_prefix_subtract_right_sourceresult * S ((S (pfs_index_prefix_subtract_right_source)) * cc) + (pfs_result_prefix_subtract_right_source))) /\ ((((exists pfa_gap_prefix_subtract_right_sourceoperationleft. pfa_gap_prefix_subtract_right_sourceoperationleft + S (pfs_right_prefix_subtract_right_source) = (p)) /\ (((exists pfa_gap_prefix_subtract_right_sourceoperationright. pfa_gap_prefix_subtract_right_sourceoperationright + S (pfs_result_prefix_subtract_right_source) = (p)) /\ ((((exists pfa_gap_prefix_subtract_right_sourceoperationresultbound. pfa_gap_prefix_subtract_right_sourceoperationresultbound + S (pfs_left_prefix_subtract_right_source) = (p)) /\ ((exists pfa_offset_left_prefix_subtract_right_sourceoperationresultcongruence pfa_offset_right_prefix_subtract_right_sourceoperationresultcongruence. ((pfs_right_prefix_subtract_right_source) + (pfs_result_prefix_subtract_right_source)) + (p) * pfa_offset_left_prefix_subtract_right_sourceoperationresultcongruence = (pfs_left_prefix_subtract_right_source) + (p) * pfa_offset_right_prefix_subtract_right_sourceoperationresultcongruence)))))))))))))))) -> (forall pfc_index_prefix_subtract_right_ub. (exists pfa_gap_prefix_subtract_right_ubbound. pfa_gap_prefix_subtract_right_ubbound + S (pfc_index_prefix_subtract_right_ub) = (N)) -> exists pfc_value_prefix_subtract_right_ub. ((((exists ff_h_pfp_prefix_subtract_right_ubentry. ff_h_pfp_prefix_subtract_right_ubentry + S (pfc_value_prefix_subtract_right_ub) = S ((S (pfc_index_prefix_subtract_right_ub)) * uc)) /\ exists ff_q_pfp_prefix_subtract_right_ubentry. ub = ff_q_pfp_prefix_subtract_right_ubentry * S ((S (pfc_index_prefix_subtract_right_ub)) * uc) + (pfc_value_prefix_subtract_right_ub))) /\ ((exists pfc_terms_code_prefix_subtract_right_ubcoefficient pfc_terms_scale_prefix_subtract_right_ubcoefficient pfc_natural_sum_prefix_subtract_right_ubcoefficient. ((forall pfc_index_prefix_subtract_right_ubcoefficientdiagonal. (exists pfa_gap_prefix_subtract_right_ubcoefficientdiagonalbound. pfa_gap_prefix_subtract_right_ubcoefficientdiagonalbound + S (pfc_index_prefix_subtract_right_ubcoefficientdiagonal) = (S (pfc_index_prefix_subtract_right_ub))) -> exists pfc_value_prefix_subtract_right_ubcoefficientdiagonal. ((((exists ff_h_pfp_prefix_subtract_right_ubcoefficientdiagonalentry. ff_h_pfp_prefix_subtract_right_ubcoefficientdiagonalentry + S (pfc_value_prefix_subtract_right_ubcoefficientdiagonal) = S ((S (pfc_index_prefix_subtract_right_ubcoefficientdiagonal)) * pfc_terms_scale_prefix_subtract_right_ubcoefficient)) /\ exists ff_q_pfp_prefix_subtract_right_ubcoefficientdiagonalentry. pfc_terms_code_prefix_subtract_right_ubcoefficient = ff_q_pfp_prefix_subtract_right_ubcoefficientdiagonalentry * S ((S (pfc_index_prefix_subtract_right_ubcoefficientdiagonal)) * pfc_terms_scale_prefix_subtract_right_ubcoefficient) + (pfc_value_prefix_subtract_right_ubcoefficientdiagonal))) /\ ((exists pfc_complement_prefix_subtract_right_ubcoefficientdiagonalterm pfc_left_prefix_subtract_right_ubcoefficientdiagonalterm pfc_right_prefix_subtract_right_ubcoefficientdiagonalterm. (((pfc_index_prefix_subtract_right_ubcoefficientdiagonal)+pfc_complement_prefix_subtract_right_ubcoefficientdiagonalterm=(pfc_index_prefix_subtract_right_ub)) /\ ((((((exists pfa_gap_prefix_subtract_right_ubcoefficientdiagonaltermleftinside. pfa_gap_prefix_subtract_right_ubcoefficientdiagonaltermleftinside + S (pfc_index_prefix_subtract_right_ubcoefficientdiagonal) = (L)) /\ ((((exists ff_h_pfp_prefix_subtract_right_ubcoefficientdiagonaltermleftentry. ff_h_pfp_prefix_subtract_right_ubcoefficientdiagonaltermleftentry + S (pfc_left_prefix_subtract_right_ubcoefficientdiagonalterm) = S ((S (pfc_index_prefix_subtract_right_ubcoefficientdiagonal)) * ac)) /\ exists ff_q_pfp_prefix_subtract_right_ubcoefficientdiagonaltermleftentry. ab = ff_q_pfp_prefix_subtract_right_ubcoefficientdiagonaltermleftentry * S ((S (pfc_index_prefix_subtract_right_ubcoefficientdiagonal)) * ac) + (pfc_left_prefix_subtract_right_ubcoefficientdiagonalterm)))))) \/ (((exists pfc_gap_prefix_subtract_right_ubcoefficientdiagonaltermleftoutside. pfc_gap_prefix_subtract_right_ubcoefficientdiagonaltermleftoutside+(L)=(pfc_index_prefix_subtract_right_ubcoefficientdiagonal)) /\ (((pfc_left_prefix_subtract_right_ubcoefficientdiagonalterm)=0))))) /\ ((((((exists pfa_gap_prefix_subtract_right_ubcoefficientdiagonaltermrightinside. pfa_gap_prefix_subtract_right_ubcoefficientdiagonaltermrightinside + S (pfc_complement_prefix_subtract_right_ubcoefficientdiagonalterm) = (M)) /\ ((((exists ff_h_pfp_prefix_subtract_right_ubcoefficientdiagonaltermrightentry. ff_h_pfp_prefix_subtract_right_ubcoefficientdiagonaltermrightentry + S (pfc_right_prefix_subtract_right_ubcoefficientdiagonalterm) = S ((S (pfc_complement_prefix_subtract_right_ubcoefficientdiagonalterm)) * dc)) /\ exists ff_q_pfp_prefix_subtract_right_ubcoefficientdiagonaltermrightentry. db = ff_q_pfp_prefix_subtract_right_ubcoefficientdiagonaltermrightentry * S ((S (pfc_complement_prefix_subtract_right_ubcoefficientdiagonalterm)) * dc) + (pfc_right_prefix_subtract_right_ubcoefficientdiagonalterm)))))) \/ (((exists pfc_gap_prefix_subtract_right_ubcoefficientdiagonaltermrightoutside. pfc_gap_prefix_subtract_right_ubcoefficientdiagonaltermrightoutside+(M)=(pfc_complement_prefix_subtract_right_ubcoefficientdiagonalterm)) /\ (((pfc_right_prefix_subtract_right_ubcoefficientdiagonalterm)=0))))) /\ (((pfc_value_prefix_subtract_right_ubcoefficientdiagonal)=pfc_left_prefix_subtract_right_ubcoefficientdiagonalterm*pfc_right_prefix_subtract_right_ubcoefficientdiagonalterm))))))))))) /\ (((exists fs_u_pfc_prefix_subtract_right_ubcoefficientsum fs_v_pfc_prefix_subtract_right_ubcoefficientsum. ((((exists fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_start. fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_start + S (0) = S ((S (0)) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_start. fs_u_pfc_prefix_subtract_right_ubcoefficientsum = fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_start * S ((S (0)) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum) + (0))) /\ ((((exists fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_terminal. fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_terminal + S (pfc_natural_sum_prefix_subtract_right_ubcoefficient) = S ((S (S (pfc_index_prefix_subtract_right_ub))) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_terminal. fs_u_pfc_prefix_subtract_right_ubcoefficientsum = fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_terminal * S ((S (S (pfc_index_prefix_subtract_right_ub))) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum) + (pfc_natural_sum_prefix_subtract_right_ubcoefficient))) /\ forall fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps. (exists fs_lt_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_bound. fs_lt_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_bound + S fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps = S (pfc_index_prefix_subtract_right_ub)) -> exists fs_a_pfc_prefix_subtract_right_ubcoefficientsum_body_steps fs_r_pfc_prefix_subtract_right_ubcoefficientsum_body_steps fs_s_pfc_prefix_subtract_right_ubcoefficientsum_body_steps. ((((exists fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_summand. fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_summand + S (fs_a_pfc_prefix_subtract_right_ubcoefficientsum_body_steps) = S ((S (fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)) * pfc_terms_scale_prefix_subtract_right_ubcoefficient)) /\ exists fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_summand. pfc_terms_code_prefix_subtract_right_ubcoefficient = fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_summand * S ((S (fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)) * pfc_terms_scale_prefix_subtract_right_ubcoefficient) + (fs_a_pfc_prefix_subtract_right_ubcoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_partial. fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_partial + S (fs_r_pfc_prefix_subtract_right_ubcoefficientsum_body_steps) = S ((S (fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_partial. fs_u_pfc_prefix_subtract_right_ubcoefficientsum = fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_partial * S ((S (fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum) + (fs_r_pfc_prefix_subtract_right_ubcoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_successor. fs_h_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_successor + S (fs_s_pfc_prefix_subtract_right_ubcoefficientsum_body_steps) = S ((S (S fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_successor. fs_u_pfc_prefix_subtract_right_ubcoefficientsum = fs_q_pfc_prefix_subtract_right_ubcoefficientsum_body_steps_successor * S ((S (S fs_i_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_ubcoefficientsum) + (fs_s_pfc_prefix_subtract_right_ubcoefficientsum_body_steps))) /\ fs_s_pfc_prefix_subtract_right_ubcoefficientsum_body_steps = fs_r_pfc_prefix_subtract_right_ubcoefficientsum_body_steps + fs_a_pfc_prefix_subtract_right_ubcoefficientsum_body_steps)))))) /\ ((((exists pfa_gap_prefix_subtract_right_ubcoefficientresiduebound. pfa_gap_prefix_subtract_right_ubcoefficientresiduebound + S (pfc_value_prefix_subtract_right_ub) = (p)) /\ ((exists pfa_offset_left_prefix_subtract_right_ubcoefficientresiduecongruence pfa_offset_right_prefix_subtract_right_ubcoefficientresiduecongruence. (pfc_natural_sum_prefix_subtract_right_ubcoefficient) + (p) * pfa_offset_left_prefix_subtract_right_ubcoefficientresiduecongruence = (pfc_value_prefix_subtract_right_ub) + (p) * pfa_offset_right_prefix_subtract_right_ubcoefficientresiduecongruence)))))))))))) -> (forall pfc_index_prefix_subtract_right_vb. (exists pfa_gap_prefix_subtract_right_vbbound. pfa_gap_prefix_subtract_right_vbbound + S (pfc_index_prefix_subtract_right_vb) = (N)) -> exists pfc_value_prefix_subtract_right_vb. ((((exists ff_h_pfp_prefix_subtract_right_vbentry. ff_h_pfp_prefix_subtract_right_vbentry + S (pfc_value_prefix_subtract_right_vb) = S ((S (pfc_index_prefix_subtract_right_vb)) * vc)) /\ exists ff_q_pfp_prefix_subtract_right_vbentry. vb = ff_q_pfp_prefix_subtract_right_vbentry * S ((S (pfc_index_prefix_subtract_right_vb)) * vc) + (pfc_value_prefix_subtract_right_vb))) /\ ((exists pfc_terms_code_prefix_subtract_right_vbcoefficient pfc_terms_scale_prefix_subtract_right_vbcoefficient pfc_natural_sum_prefix_subtract_right_vbcoefficient. ((forall pfc_index_prefix_subtract_right_vbcoefficientdiagonal. (exists pfa_gap_prefix_subtract_right_vbcoefficientdiagonalbound. pfa_gap_prefix_subtract_right_vbcoefficientdiagonalbound + S (pfc_index_prefix_subtract_right_vbcoefficientdiagonal) = (S (pfc_index_prefix_subtract_right_vb))) -> exists pfc_value_prefix_subtract_right_vbcoefficientdiagonal. ((((exists ff_h_pfp_prefix_subtract_right_vbcoefficientdiagonalentry. ff_h_pfp_prefix_subtract_right_vbcoefficientdiagonalentry + S (pfc_value_prefix_subtract_right_vbcoefficientdiagonal) = S ((S (pfc_index_prefix_subtract_right_vbcoefficientdiagonal)) * pfc_terms_scale_prefix_subtract_right_vbcoefficient)) /\ exists ff_q_pfp_prefix_subtract_right_vbcoefficientdiagonalentry. pfc_terms_code_prefix_subtract_right_vbcoefficient = ff_q_pfp_prefix_subtract_right_vbcoefficientdiagonalentry * S ((S (pfc_index_prefix_subtract_right_vbcoefficientdiagonal)) * pfc_terms_scale_prefix_subtract_right_vbcoefficient) + (pfc_value_prefix_subtract_right_vbcoefficientdiagonal))) /\ ((exists pfc_complement_prefix_subtract_right_vbcoefficientdiagonalterm pfc_left_prefix_subtract_right_vbcoefficientdiagonalterm pfc_right_prefix_subtract_right_vbcoefficientdiagonalterm. (((pfc_index_prefix_subtract_right_vbcoefficientdiagonal)+pfc_complement_prefix_subtract_right_vbcoefficientdiagonalterm=(pfc_index_prefix_subtract_right_vb)) /\ ((((((exists pfa_gap_prefix_subtract_right_vbcoefficientdiagonaltermleftinside. pfa_gap_prefix_subtract_right_vbcoefficientdiagonaltermleftinside + S (pfc_index_prefix_subtract_right_vbcoefficientdiagonal) = (L)) /\ ((((exists ff_h_pfp_prefix_subtract_right_vbcoefficientdiagonaltermleftentry. ff_h_pfp_prefix_subtract_right_vbcoefficientdiagonaltermleftentry + S (pfc_left_prefix_subtract_right_vbcoefficientdiagonalterm) = S ((S (pfc_index_prefix_subtract_right_vbcoefficientdiagonal)) * bc)) /\ exists ff_q_pfp_prefix_subtract_right_vbcoefficientdiagonaltermleftentry. bb = ff_q_pfp_prefix_subtract_right_vbcoefficientdiagonaltermleftentry * S ((S (pfc_index_prefix_subtract_right_vbcoefficientdiagonal)) * bc) + (pfc_left_prefix_subtract_right_vbcoefficientdiagonalterm)))))) \/ (((exists pfc_gap_prefix_subtract_right_vbcoefficientdiagonaltermleftoutside. pfc_gap_prefix_subtract_right_vbcoefficientdiagonaltermleftoutside+(L)=(pfc_index_prefix_subtract_right_vbcoefficientdiagonal)) /\ (((pfc_left_prefix_subtract_right_vbcoefficientdiagonalterm)=0))))) /\ ((((((exists pfa_gap_prefix_subtract_right_vbcoefficientdiagonaltermrightinside. pfa_gap_prefix_subtract_right_vbcoefficientdiagonaltermrightinside + S (pfc_complement_prefix_subtract_right_vbcoefficientdiagonalterm) = (M)) /\ ((((exists ff_h_pfp_prefix_subtract_right_vbcoefficientdiagonaltermrightentry. ff_h_pfp_prefix_subtract_right_vbcoefficientdiagonaltermrightentry + S (pfc_right_prefix_subtract_right_vbcoefficientdiagonalterm) = S ((S (pfc_complement_prefix_subtract_right_vbcoefficientdiagonalterm)) * dc)) /\ exists ff_q_pfp_prefix_subtract_right_vbcoefficientdiagonaltermrightentry. db = ff_q_pfp_prefix_subtract_right_vbcoefficientdiagonaltermrightentry * S ((S (pfc_complement_prefix_subtract_right_vbcoefficientdiagonalterm)) * dc) + (pfc_right_prefix_subtract_right_vbcoefficientdiagonalterm)))))) \/ (((exists pfc_gap_prefix_subtract_right_vbcoefficientdiagonaltermrightoutside. pfc_gap_prefix_subtract_right_vbcoefficientdiagonaltermrightoutside+(M)=(pfc_complement_prefix_subtract_right_vbcoefficientdiagonalterm)) /\ (((pfc_right_prefix_subtract_right_vbcoefficientdiagonalterm)=0))))) /\ (((pfc_value_prefix_subtract_right_vbcoefficientdiagonal)=pfc_left_prefix_subtract_right_vbcoefficientdiagonalterm*pfc_right_prefix_subtract_right_vbcoefficientdiagonalterm))))))))))) /\ (((exists fs_u_pfc_prefix_subtract_right_vbcoefficientsum fs_v_pfc_prefix_subtract_right_vbcoefficientsum. ((((exists fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_start. fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_start + S (0) = S ((S (0)) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_start. fs_u_pfc_prefix_subtract_right_vbcoefficientsum = fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_start * S ((S (0)) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum) + (0))) /\ ((((exists fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_terminal. fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_terminal + S (pfc_natural_sum_prefix_subtract_right_vbcoefficient) = S ((S (S (pfc_index_prefix_subtract_right_vb))) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_terminal. fs_u_pfc_prefix_subtract_right_vbcoefficientsum = fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_terminal * S ((S (S (pfc_index_prefix_subtract_right_vb))) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum) + (pfc_natural_sum_prefix_subtract_right_vbcoefficient))) /\ forall fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps. (exists fs_lt_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_bound. fs_lt_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_bound + S fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps = S (pfc_index_prefix_subtract_right_vb)) -> exists fs_a_pfc_prefix_subtract_right_vbcoefficientsum_body_steps fs_r_pfc_prefix_subtract_right_vbcoefficientsum_body_steps fs_s_pfc_prefix_subtract_right_vbcoefficientsum_body_steps. ((((exists fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_summand. fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_summand + S (fs_a_pfc_prefix_subtract_right_vbcoefficientsum_body_steps) = S ((S (fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)) * pfc_terms_scale_prefix_subtract_right_vbcoefficient)) /\ exists fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_summand. pfc_terms_code_prefix_subtract_right_vbcoefficient = fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_summand * S ((S (fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)) * pfc_terms_scale_prefix_subtract_right_vbcoefficient) + (fs_a_pfc_prefix_subtract_right_vbcoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_partial. fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_partial + S (fs_r_pfc_prefix_subtract_right_vbcoefficientsum_body_steps) = S ((S (fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_partial. fs_u_pfc_prefix_subtract_right_vbcoefficientsum = fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_partial * S ((S (fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum) + (fs_r_pfc_prefix_subtract_right_vbcoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_successor. fs_h_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_successor + S (fs_s_pfc_prefix_subtract_right_vbcoefficientsum_body_steps) = S ((S (S fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_successor. fs_u_pfc_prefix_subtract_right_vbcoefficientsum = fs_q_pfc_prefix_subtract_right_vbcoefficientsum_body_steps_successor * S ((S (S fs_i_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_vbcoefficientsum) + (fs_s_pfc_prefix_subtract_right_vbcoefficientsum_body_steps))) /\ fs_s_pfc_prefix_subtract_right_vbcoefficientsum_body_steps = fs_r_pfc_prefix_subtract_right_vbcoefficientsum_body_steps + fs_a_pfc_prefix_subtract_right_vbcoefficientsum_body_steps)))))) /\ ((((exists pfa_gap_prefix_subtract_right_vbcoefficientresiduebound. pfa_gap_prefix_subtract_right_vbcoefficientresiduebound + S (pfc_value_prefix_subtract_right_vb) = (p)) /\ ((exists pfa_offset_left_prefix_subtract_right_vbcoefficientresiduecongruence pfa_offset_right_prefix_subtract_right_vbcoefficientresiduecongruence. (pfc_natural_sum_prefix_subtract_right_vbcoefficient) + (p) * pfa_offset_left_prefix_subtract_right_vbcoefficientresiduecongruence = (pfc_value_prefix_subtract_right_vb) + (p) * pfa_offset_right_prefix_subtract_right_vbcoefficientresiduecongruence)))))))))))) -> (forall pfc_index_prefix_subtract_right_wb. (exists pfa_gap_prefix_subtract_right_wbbound. pfa_gap_prefix_subtract_right_wbbound + S (pfc_index_prefix_subtract_right_wb) = (N)) -> exists pfc_value_prefix_subtract_right_wb. ((((exists ff_h_pfp_prefix_subtract_right_wbentry. ff_h_pfp_prefix_subtract_right_wbentry + S (pfc_value_prefix_subtract_right_wb) = S ((S (pfc_index_prefix_subtract_right_wb)) * wc)) /\ exists ff_q_pfp_prefix_subtract_right_wbentry. wb = ff_q_pfp_prefix_subtract_right_wbentry * S ((S (pfc_index_prefix_subtract_right_wb)) * wc) + (pfc_value_prefix_subtract_right_wb))) /\ ((exists pfc_terms_code_prefix_subtract_right_wbcoefficient pfc_terms_scale_prefix_subtract_right_wbcoefficient pfc_natural_sum_prefix_subtract_right_wbcoefficient. ((forall pfc_index_prefix_subtract_right_wbcoefficientdiagonal. (exists pfa_gap_prefix_subtract_right_wbcoefficientdiagonalbound. pfa_gap_prefix_subtract_right_wbcoefficientdiagonalbound + S (pfc_index_prefix_subtract_right_wbcoefficientdiagonal) = (S (pfc_index_prefix_subtract_right_wb))) -> exists pfc_value_prefix_subtract_right_wbcoefficientdiagonal. ((((exists ff_h_pfp_prefix_subtract_right_wbcoefficientdiagonalentry. ff_h_pfp_prefix_subtract_right_wbcoefficientdiagonalentry + S (pfc_value_prefix_subtract_right_wbcoefficientdiagonal) = S ((S (pfc_index_prefix_subtract_right_wbcoefficientdiagonal)) * pfc_terms_scale_prefix_subtract_right_wbcoefficient)) /\ exists ff_q_pfp_prefix_subtract_right_wbcoefficientdiagonalentry. pfc_terms_code_prefix_subtract_right_wbcoefficient = ff_q_pfp_prefix_subtract_right_wbcoefficientdiagonalentry * S ((S (pfc_index_prefix_subtract_right_wbcoefficientdiagonal)) * pfc_terms_scale_prefix_subtract_right_wbcoefficient) + (pfc_value_prefix_subtract_right_wbcoefficientdiagonal))) /\ ((exists pfc_complement_prefix_subtract_right_wbcoefficientdiagonalterm pfc_left_prefix_subtract_right_wbcoefficientdiagonalterm pfc_right_prefix_subtract_right_wbcoefficientdiagonalterm. (((pfc_index_prefix_subtract_right_wbcoefficientdiagonal)+pfc_complement_prefix_subtract_right_wbcoefficientdiagonalterm=(pfc_index_prefix_subtract_right_wb)) /\ ((((((exists pfa_gap_prefix_subtract_right_wbcoefficientdiagonaltermleftinside. pfa_gap_prefix_subtract_right_wbcoefficientdiagonaltermleftinside + S (pfc_index_prefix_subtract_right_wbcoefficientdiagonal) = (L)) /\ ((((exists ff_h_pfp_prefix_subtract_right_wbcoefficientdiagonaltermleftentry. ff_h_pfp_prefix_subtract_right_wbcoefficientdiagonaltermleftentry + S (pfc_left_prefix_subtract_right_wbcoefficientdiagonalterm) = S ((S (pfc_index_prefix_subtract_right_wbcoefficientdiagonal)) * cc)) /\ exists ff_q_pfp_prefix_subtract_right_wbcoefficientdiagonaltermleftentry. cb = ff_q_pfp_prefix_subtract_right_wbcoefficientdiagonaltermleftentry * S ((S (pfc_index_prefix_subtract_right_wbcoefficientdiagonal)) * cc) + (pfc_left_prefix_subtract_right_wbcoefficientdiagonalterm)))))) \/ (((exists pfc_gap_prefix_subtract_right_wbcoefficientdiagonaltermleftoutside. pfc_gap_prefix_subtract_right_wbcoefficientdiagonaltermleftoutside+(L)=(pfc_index_prefix_subtract_right_wbcoefficientdiagonal)) /\ (((pfc_left_prefix_subtract_right_wbcoefficientdiagonalterm)=0))))) /\ ((((((exists pfa_gap_prefix_subtract_right_wbcoefficientdiagonaltermrightinside. pfa_gap_prefix_subtract_right_wbcoefficientdiagonaltermrightinside + S (pfc_complement_prefix_subtract_right_wbcoefficientdiagonalterm) = (M)) /\ ((((exists ff_h_pfp_prefix_subtract_right_wbcoefficientdiagonaltermrightentry. ff_h_pfp_prefix_subtract_right_wbcoefficientdiagonaltermrightentry + S (pfc_right_prefix_subtract_right_wbcoefficientdiagonalterm) = S ((S (pfc_complement_prefix_subtract_right_wbcoefficientdiagonalterm)) * dc)) /\ exists ff_q_pfp_prefix_subtract_right_wbcoefficientdiagonaltermrightentry. db = ff_q_pfp_prefix_subtract_right_wbcoefficientdiagonaltermrightentry * S ((S (pfc_complement_prefix_subtract_right_wbcoefficientdiagonalterm)) * dc) + (pfc_right_prefix_subtract_right_wbcoefficientdiagonalterm)))))) \/ (((exists pfc_gap_prefix_subtract_right_wbcoefficientdiagonaltermrightoutside. pfc_gap_prefix_subtract_right_wbcoefficientdiagonaltermrightoutside+(M)=(pfc_complement_prefix_subtract_right_wbcoefficientdiagonalterm)) /\ (((pfc_right_prefix_subtract_right_wbcoefficientdiagonalterm)=0))))) /\ (((pfc_value_prefix_subtract_right_wbcoefficientdiagonal)=pfc_left_prefix_subtract_right_wbcoefficientdiagonalterm*pfc_right_prefix_subtract_right_wbcoefficientdiagonalterm))))))))))) /\ (((exists fs_u_pfc_prefix_subtract_right_wbcoefficientsum fs_v_pfc_prefix_subtract_right_wbcoefficientsum. ((((exists fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_start. fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_start + S (0) = S ((S (0)) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_start. fs_u_pfc_prefix_subtract_right_wbcoefficientsum = fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_start * S ((S (0)) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum) + (0))) /\ ((((exists fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_terminal. fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_terminal + S (pfc_natural_sum_prefix_subtract_right_wbcoefficient) = S ((S (S (pfc_index_prefix_subtract_right_wb))) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_terminal. fs_u_pfc_prefix_subtract_right_wbcoefficientsum = fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_terminal * S ((S (S (pfc_index_prefix_subtract_right_wb))) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum) + (pfc_natural_sum_prefix_subtract_right_wbcoefficient))) /\ forall fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps. (exists fs_lt_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_bound. fs_lt_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_bound + S fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps = S (pfc_index_prefix_subtract_right_wb)) -> exists fs_a_pfc_prefix_subtract_right_wbcoefficientsum_body_steps fs_r_pfc_prefix_subtract_right_wbcoefficientsum_body_steps fs_s_pfc_prefix_subtract_right_wbcoefficientsum_body_steps. ((((exists fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_summand. fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_summand + S (fs_a_pfc_prefix_subtract_right_wbcoefficientsum_body_steps) = S ((S (fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)) * pfc_terms_scale_prefix_subtract_right_wbcoefficient)) /\ exists fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_summand. pfc_terms_code_prefix_subtract_right_wbcoefficient = fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_summand * S ((S (fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)) * pfc_terms_scale_prefix_subtract_right_wbcoefficient) + (fs_a_pfc_prefix_subtract_right_wbcoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_partial. fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_partial + S (fs_r_pfc_prefix_subtract_right_wbcoefficientsum_body_steps) = S ((S (fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_partial. fs_u_pfc_prefix_subtract_right_wbcoefficientsum = fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_partial * S ((S (fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum) + (fs_r_pfc_prefix_subtract_right_wbcoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_successor. fs_h_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_successor + S (fs_s_pfc_prefix_subtract_right_wbcoefficientsum_body_steps) = S ((S (S fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum)) /\ exists fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_successor. fs_u_pfc_prefix_subtract_right_wbcoefficientsum = fs_q_pfc_prefix_subtract_right_wbcoefficientsum_body_steps_successor * S ((S (S fs_i_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)) * fs_v_pfc_prefix_subtract_right_wbcoefficientsum) + (fs_s_pfc_prefix_subtract_right_wbcoefficientsum_body_steps))) /\ fs_s_pfc_prefix_subtract_right_wbcoefficientsum_body_steps = fs_r_pfc_prefix_subtract_right_wbcoefficientsum_body_steps + fs_a_pfc_prefix_subtract_right_wbcoefficientsum_body_steps)))))) /\ ((((exists pfa_gap_prefix_subtract_right_wbcoefficientresiduebound. pfa_gap_prefix_subtract_right_wbcoefficientresiduebound + S (pfc_value_prefix_subtract_right_wb) = (p)) /\ ((exists pfa_offset_left_prefix_subtract_right_wbcoefficientresiduecongruence pfa_offset_right_prefix_subtract_right_wbcoefficientresiduecongruence. (pfc_natural_sum_prefix_subtract_right_wbcoefficient) + (p) * pfa_offset_left_prefix_subtract_right_wbcoefficientresiduecongruence = (pfc_value_prefix_subtract_right_wb) + (p) * pfa_offset_right_prefix_subtract_right_wbcoefficientresiduecongruence)))))))))))) -> (forall pfs_index_prefix_subtract_right_result. (exists pfa_gap_prefix_subtract_right_resultindex. pfa_gap_prefix_subtract_right_resultindex + S (pfs_index_prefix_subtract_right_result) = (N)) -> exists pfs_left_prefix_subtract_right_result pfs_right_prefix_subtract_right_result pfs_result_prefix_subtract_right_result. ((((exists ff_h_pfp_prefix_subtract_right_resultleft. ff_h_pfp_prefix_subtract_right_resultleft + S (pfs_left_prefix_subtract_right_result) = S ((S (pfs_index_prefix_subtract_right_result)) * uc)) /\ exists ff_q_pfp_prefix_subtract_right_resultleft. ub = ff_q_pfp_prefix_subtract_right_resultleft * S ((S (pfs_index_prefix_subtract_right_result)) * uc) + (pfs_left_prefix_subtract_right_result))) /\ (((((exists ff_h_pfp_prefix_subtract_right_resultright. ff_h_pfp_prefix_subtract_right_resultright + S (pfs_right_prefix_subtract_right_result) = S ((S (pfs_index_prefix_subtract_right_result)) * vc)) /\ exists ff_q_pfp_prefix_subtract_right_resultright. vb = ff_q_pfp_prefix_subtract_right_resultright * S ((S (pfs_index_prefix_subtract_right_result)) * vc) + (pfs_right_prefix_subtract_right_result))) /\ (((((exists ff_h_pfp_prefix_subtract_right_resultresult. ff_h_pfp_prefix_subtract_right_resultresult + S (pfs_result_prefix_subtract_right_result) = S ((S (pfs_index_prefix_subtract_right_result)) * wc)) /\ exists ff_q_pfp_prefix_subtract_right_resultresult. wb = ff_q_pfp_prefix_subtract_right_resultresult * S ((S (pfs_index_prefix_subtract_right_result)) * wc) + (pfs_result_prefix_subtract_right_result))) /\ ((((exists pfa_gap_prefix_subtract_right_resultoperationleft. pfa_gap_prefix_subtract_right_resultoperationleft + S (pfs_right_prefix_subtract_right_result) = (p)) /\ (((exists pfa_gap_prefix_subtract_right_resultoperationright. pfa_gap_prefix_subtract_right_resultoperationright + S (pfs_result_prefix_subtract_right_result) = (p)) /\ ((((exists pfa_gap_prefix_subtract_right_resultoperationresultbound. pfa_gap_prefix_subtract_right_resultoperationresultbound + S (pfs_left_prefix_subtract_right_result) = (p)) /\ ((exists pfa_offset_left_prefix_subtract_right_resultoperationresultcongruence pfa_offset_right_prefix_subtract_right_resultoperationresultcongruence. ((pfs_right_prefix_subtract_right_result) + (pfs_result_prefix_subtract_right_result)) + (p) * pfa_offset_left_prefix_subtract_right_resultoperationresultcongruence = (pfs_left_prefix_subtract_right_result) + (p) * pfa_offset_right_prefix_subtract_right_resultoperationresultcongruence))))))))))))))))