prime_field_convolution_coefficient_right_add

Exact expanded first-order arithmetic statement

forall p ab ac bb bc cb cc L db dc M i u v w. (forall pfp_index_coefficient_add_right_source. (exists pfa_gap_coefficient_add_right_sourceindex. pfa_gap_coefficient_add_right_sourceindex + S (pfp_index_coefficient_add_right_source) = (L)) -> exists pfp_left_coefficient_add_right_source pfp_right_coefficient_add_right_source pfp_value_coefficient_add_right_source. ((((exists ff_h_pfp_coefficient_add_right_sourceleft. ff_h_pfp_coefficient_add_right_sourceleft + S (pfp_left_coefficient_add_right_source) = S ((S (pfp_index_coefficient_add_right_source)) * ac)) /\ exists ff_q_pfp_coefficient_add_right_sourceleft. ab = ff_q_pfp_coefficient_add_right_sourceleft * S ((S (pfp_index_coefficient_add_right_source)) * ac) + (pfp_left_coefficient_add_right_source))) /\ (((((exists ff_h_pfp_coefficient_add_right_sourceright. ff_h_pfp_coefficient_add_right_sourceright + S (pfp_right_coefficient_add_right_source) = S ((S (pfp_index_coefficient_add_right_source)) * bc)) /\ exists ff_q_pfp_coefficient_add_right_sourceright. bb = ff_q_pfp_coefficient_add_right_sourceright * S ((S (pfp_index_coefficient_add_right_source)) * bc) + (pfp_right_coefficient_add_right_source))) /\ (((((exists ff_h_pfp_coefficient_add_right_sourcetarget. ff_h_pfp_coefficient_add_right_sourcetarget + S (pfp_value_coefficient_add_right_source) = S ((S (pfp_index_coefficient_add_right_source)) * cc)) /\ exists ff_q_pfp_coefficient_add_right_sourcetarget. cb = ff_q_pfp_coefficient_add_right_sourcetarget * S ((S (pfp_index_coefficient_add_right_source)) * cc) + (pfp_value_coefficient_add_right_source))) /\ ((((exists pfa_gap_coefficient_add_right_sourceoperationleft. pfa_gap_coefficient_add_right_sourceoperationleft + S (pfp_left_coefficient_add_right_source) = (p)) /\ (((exists pfa_gap_coefficient_add_right_sourceoperationright. pfa_gap_coefficient_add_right_sourceoperationright + S (pfp_right_coefficient_add_right_source) = (p)) /\ ((((exists pfa_gap_coefficient_add_right_sourceoperationresultbound. pfa_gap_coefficient_add_right_sourceoperationresultbound + S (pfp_value_coefficient_add_right_source) = (p)) /\ ((exists pfa_offset_left_coefficient_add_right_sourceoperationresultcongruence pfa_offset_right_coefficient_add_right_sourceoperationresultcongruence. ((pfp_left_coefficient_add_right_source) + (pfp_right_coefficient_add_right_source)) + (p) * pfa_offset_left_coefficient_add_right_sourceoperationresultcongruence = (pfp_value_coefficient_add_right_source) + (p) * pfa_offset_right_coefficient_add_right_sourceoperationresultcongruence)))))))))))))))) -> (exists pfc_terms_code_coefficient_add_right_u pfc_terms_scale_coefficient_add_right_u pfc_natural_sum_coefficient_add_right_u. ((forall pfc_index_coefficient_add_right_udiagonal. (exists pfa_gap_coefficient_add_right_udiagonalbound. pfa_gap_coefficient_add_right_udiagonalbound + S (pfc_index_coefficient_add_right_udiagonal) = (S (i))) -> exists pfc_value_coefficient_add_right_udiagonal. ((((exists ff_h_pfp_coefficient_add_right_udiagonalentry. ff_h_pfp_coefficient_add_right_udiagonalentry + S (pfc_value_coefficient_add_right_udiagonal) = S ((S (pfc_index_coefficient_add_right_udiagonal)) * pfc_terms_scale_coefficient_add_right_u)) /\ exists ff_q_pfp_coefficient_add_right_udiagonalentry. pfc_terms_code_coefficient_add_right_u = ff_q_pfp_coefficient_add_right_udiagonalentry * S ((S (pfc_index_coefficient_add_right_udiagonal)) * pfc_terms_scale_coefficient_add_right_u) + (pfc_value_coefficient_add_right_udiagonal))) /\ ((exists pfc_complement_coefficient_add_right_udiagonalterm pfc_left_coefficient_add_right_udiagonalterm pfc_right_coefficient_add_right_udiagonalterm. (((pfc_index_coefficient_add_right_udiagonal)+pfc_complement_coefficient_add_right_udiagonalterm=(i)) /\ ((((((exists pfa_gap_coefficient_add_right_udiagonaltermleftinside. pfa_gap_coefficient_add_right_udiagonaltermleftinside + S (pfc_index_coefficient_add_right_udiagonal) = (L)) /\ ((((exists ff_h_pfp_coefficient_add_right_udiagonaltermleftentry. ff_h_pfp_coefficient_add_right_udiagonaltermleftentry + S (pfc_left_coefficient_add_right_udiagonalterm) = S ((S (pfc_index_coefficient_add_right_udiagonal)) * ac)) /\ exists ff_q_pfp_coefficient_add_right_udiagonaltermleftentry. ab = ff_q_pfp_coefficient_add_right_udiagonaltermleftentry * S ((S (pfc_index_coefficient_add_right_udiagonal)) * ac) + (pfc_left_coefficient_add_right_udiagonalterm)))))) \/ (((exists pfc_gap_coefficient_add_right_udiagonaltermleftoutside. pfc_gap_coefficient_add_right_udiagonaltermleftoutside+(L)=(pfc_index_coefficient_add_right_udiagonal)) /\ (((pfc_left_coefficient_add_right_udiagonalterm)=0))))) /\ ((((((exists pfa_gap_coefficient_add_right_udiagonaltermrightinside. pfa_gap_coefficient_add_right_udiagonaltermrightinside + S (pfc_complement_coefficient_add_right_udiagonalterm) = (M)) /\ ((((exists ff_h_pfp_coefficient_add_right_udiagonaltermrightentry. ff_h_pfp_coefficient_add_right_udiagonaltermrightentry + S (pfc_right_coefficient_add_right_udiagonalterm) = S ((S (pfc_complement_coefficient_add_right_udiagonalterm)) * dc)) /\ exists ff_q_pfp_coefficient_add_right_udiagonaltermrightentry. db = ff_q_pfp_coefficient_add_right_udiagonaltermrightentry * S ((S (pfc_complement_coefficient_add_right_udiagonalterm)) * dc) + (pfc_right_coefficient_add_right_udiagonalterm)))))) \/ (((exists pfc_gap_coefficient_add_right_udiagonaltermrightoutside. pfc_gap_coefficient_add_right_udiagonaltermrightoutside+(M)=(pfc_complement_coefficient_add_right_udiagonalterm)) /\ (((pfc_right_coefficient_add_right_udiagonalterm)=0))))) /\ (((pfc_value_coefficient_add_right_udiagonal)=pfc_left_coefficient_add_right_udiagonalterm*pfc_right_coefficient_add_right_udiagonalterm))))))))))) /\ (((exists fs_u_pfc_coefficient_add_right_usum fs_v_pfc_coefficient_add_right_usum. ((((exists fs_h_pfc_coefficient_add_right_usum_body_start. fs_h_pfc_coefficient_add_right_usum_body_start + S (0) = S ((S (0)) * fs_v_pfc_coefficient_add_right_usum)) /\ exists fs_q_pfc_coefficient_add_right_usum_body_start. fs_u_pfc_coefficient_add_right_usum = fs_q_pfc_coefficient_add_right_usum_body_start * S ((S (0)) * fs_v_pfc_coefficient_add_right_usum) + (0))) /\ ((((exists fs_h_pfc_coefficient_add_right_usum_body_terminal. fs_h_pfc_coefficient_add_right_usum_body_terminal + S (pfc_natural_sum_coefficient_add_right_u) = S ((S (S (i))) * fs_v_pfc_coefficient_add_right_usum)) /\ exists fs_q_pfc_coefficient_add_right_usum_body_terminal. fs_u_pfc_coefficient_add_right_usum = fs_q_pfc_coefficient_add_right_usum_body_terminal * S ((S (S (i))) * fs_v_pfc_coefficient_add_right_usum) + (pfc_natural_sum_coefficient_add_right_u))) /\ forall fs_i_pfc_coefficient_add_right_usum_body_steps. (exists fs_lt_pfc_coefficient_add_right_usum_body_steps_bound. fs_lt_pfc_coefficient_add_right_usum_body_steps_bound + S fs_i_pfc_coefficient_add_right_usum_body_steps = S (i)) -> exists fs_a_pfc_coefficient_add_right_usum_body_steps fs_r_pfc_coefficient_add_right_usum_body_steps fs_s_pfc_coefficient_add_right_usum_body_steps. ((((exists fs_h_pfc_coefficient_add_right_usum_body_steps_summand. fs_h_pfc_coefficient_add_right_usum_body_steps_summand + S (fs_a_pfc_coefficient_add_right_usum_body_steps) = S ((S (fs_i_pfc_coefficient_add_right_usum_body_steps)) * pfc_terms_scale_coefficient_add_right_u)) /\ exists fs_q_pfc_coefficient_add_right_usum_body_steps_summand. pfc_terms_code_coefficient_add_right_u = fs_q_pfc_coefficient_add_right_usum_body_steps_summand * S ((S (fs_i_pfc_coefficient_add_right_usum_body_steps)) * pfc_terms_scale_coefficient_add_right_u) + (fs_a_pfc_coefficient_add_right_usum_body_steps))) /\ ((((exists fs_h_pfc_coefficient_add_right_usum_body_steps_partial. fs_h_pfc_coefficient_add_right_usum_body_steps_partial + S (fs_r_pfc_coefficient_add_right_usum_body_steps) = S ((S (fs_i_pfc_coefficient_add_right_usum_body_steps)) * fs_v_pfc_coefficient_add_right_usum)) /\ exists fs_q_pfc_coefficient_add_right_usum_body_steps_partial. fs_u_pfc_coefficient_add_right_usum = fs_q_pfc_coefficient_add_right_usum_body_steps_partial * S ((S (fs_i_pfc_coefficient_add_right_usum_body_steps)) * fs_v_pfc_coefficient_add_right_usum) + (fs_r_pfc_coefficient_add_right_usum_body_steps))) /\ ((((exists fs_h_pfc_coefficient_add_right_usum_body_steps_successor. fs_h_pfc_coefficient_add_right_usum_body_steps_successor + S (fs_s_pfc_coefficient_add_right_usum_body_steps) = S ((S (S fs_i_pfc_coefficient_add_right_usum_body_steps)) * fs_v_pfc_coefficient_add_right_usum)) /\ exists fs_q_pfc_coefficient_add_right_usum_body_steps_successor. fs_u_pfc_coefficient_add_right_usum = fs_q_pfc_coefficient_add_right_usum_body_steps_successor * S ((S (S fs_i_pfc_coefficient_add_right_usum_body_steps)) * fs_v_pfc_coefficient_add_right_usum) + (fs_s_pfc_coefficient_add_right_usum_body_steps))) /\ fs_s_pfc_coefficient_add_right_usum_body_steps = fs_r_pfc_coefficient_add_right_usum_body_steps + fs_a_pfc_coefficient_add_right_usum_body_steps)))))) /\ ((((exists pfa_gap_coefficient_add_right_uresiduebound. pfa_gap_coefficient_add_right_uresiduebound + S (u) = (p)) /\ ((exists pfa_offset_left_coefficient_add_right_uresiduecongruence pfa_offset_right_coefficient_add_right_uresiduecongruence. (pfc_natural_sum_coefficient_add_right_u) + (p) * pfa_offset_left_coefficient_add_right_uresiduecongruence = (u) + (p) * pfa_offset_right_coefficient_add_right_uresiduecongruence))))))))) -> (exists pfc_terms_code_coefficient_add_right_v pfc_terms_scale_coefficient_add_right_v pfc_natural_sum_coefficient_add_right_v. ((forall pfc_index_coefficient_add_right_vdiagonal. (exists pfa_gap_coefficient_add_right_vdiagonalbound. pfa_gap_coefficient_add_right_vdiagonalbound + S (pfc_index_coefficient_add_right_vdiagonal) = (S (i))) -> exists pfc_value_coefficient_add_right_vdiagonal. ((((exists ff_h_pfp_coefficient_add_right_vdiagonalentry. ff_h_pfp_coefficient_add_right_vdiagonalentry + S (pfc_value_coefficient_add_right_vdiagonal) = S ((S (pfc_index_coefficient_add_right_vdiagonal)) * pfc_terms_scale_coefficient_add_right_v)) /\ exists ff_q_pfp_coefficient_add_right_vdiagonalentry. pfc_terms_code_coefficient_add_right_v = ff_q_pfp_coefficient_add_right_vdiagonalentry * S ((S (pfc_index_coefficient_add_right_vdiagonal)) * pfc_terms_scale_coefficient_add_right_v) + (pfc_value_coefficient_add_right_vdiagonal))) /\ ((exists pfc_complement_coefficient_add_right_vdiagonalterm pfc_left_coefficient_add_right_vdiagonalterm pfc_right_coefficient_add_right_vdiagonalterm. (((pfc_index_coefficient_add_right_vdiagonal)+pfc_complement_coefficient_add_right_vdiagonalterm=(i)) /\ ((((((exists pfa_gap_coefficient_add_right_vdiagonaltermleftinside. pfa_gap_coefficient_add_right_vdiagonaltermleftinside + S (pfc_index_coefficient_add_right_vdiagonal) = (L)) /\ ((((exists ff_h_pfp_coefficient_add_right_vdiagonaltermleftentry. ff_h_pfp_coefficient_add_right_vdiagonaltermleftentry + S (pfc_left_coefficient_add_right_vdiagonalterm) = S ((S (pfc_index_coefficient_add_right_vdiagonal)) * bc)) /\ exists ff_q_pfp_coefficient_add_right_vdiagonaltermleftentry. bb = ff_q_pfp_coefficient_add_right_vdiagonaltermleftentry * S ((S (pfc_index_coefficient_add_right_vdiagonal)) * bc) + (pfc_left_coefficient_add_right_vdiagonalterm)))))) \/ (((exists pfc_gap_coefficient_add_right_vdiagonaltermleftoutside. pfc_gap_coefficient_add_right_vdiagonaltermleftoutside+(L)=(pfc_index_coefficient_add_right_vdiagonal)) /\ (((pfc_left_coefficient_add_right_vdiagonalterm)=0))))) /\ ((((((exists pfa_gap_coefficient_add_right_vdiagonaltermrightinside. pfa_gap_coefficient_add_right_vdiagonaltermrightinside + S (pfc_complement_coefficient_add_right_vdiagonalterm) = (M)) /\ ((((exists ff_h_pfp_coefficient_add_right_vdiagonaltermrightentry. ff_h_pfp_coefficient_add_right_vdiagonaltermrightentry + S (pfc_right_coefficient_add_right_vdiagonalterm) = S ((S (pfc_complement_coefficient_add_right_vdiagonalterm)) * dc)) /\ exists ff_q_pfp_coefficient_add_right_vdiagonaltermrightentry. db = ff_q_pfp_coefficient_add_right_vdiagonaltermrightentry * S ((S (pfc_complement_coefficient_add_right_vdiagonalterm)) * dc) + (pfc_right_coefficient_add_right_vdiagonalterm)))))) \/ (((exists pfc_gap_coefficient_add_right_vdiagonaltermrightoutside. pfc_gap_coefficient_add_right_vdiagonaltermrightoutside+(M)=(pfc_complement_coefficient_add_right_vdiagonalterm)) /\ (((pfc_right_coefficient_add_right_vdiagonalterm)=0))))) /\ (((pfc_value_coefficient_add_right_vdiagonal)=pfc_left_coefficient_add_right_vdiagonalterm*pfc_right_coefficient_add_right_vdiagonalterm))))))))))) /\ (((exists fs_u_pfc_coefficient_add_right_vsum fs_v_pfc_coefficient_add_right_vsum. ((((exists fs_h_pfc_coefficient_add_right_vsum_body_start. fs_h_pfc_coefficient_add_right_vsum_body_start + S (0) = S ((S (0)) * fs_v_pfc_coefficient_add_right_vsum)) /\ exists fs_q_pfc_coefficient_add_right_vsum_body_start. fs_u_pfc_coefficient_add_right_vsum = fs_q_pfc_coefficient_add_right_vsum_body_start * S ((S (0)) * fs_v_pfc_coefficient_add_right_vsum) + (0))) /\ ((((exists fs_h_pfc_coefficient_add_right_vsum_body_terminal. fs_h_pfc_coefficient_add_right_vsum_body_terminal + S (pfc_natural_sum_coefficient_add_right_v) = S ((S (S (i))) * fs_v_pfc_coefficient_add_right_vsum)) /\ exists fs_q_pfc_coefficient_add_right_vsum_body_terminal. fs_u_pfc_coefficient_add_right_vsum = fs_q_pfc_coefficient_add_right_vsum_body_terminal * S ((S (S (i))) * fs_v_pfc_coefficient_add_right_vsum) + (pfc_natural_sum_coefficient_add_right_v))) /\ forall fs_i_pfc_coefficient_add_right_vsum_body_steps. (exists fs_lt_pfc_coefficient_add_right_vsum_body_steps_bound. fs_lt_pfc_coefficient_add_right_vsum_body_steps_bound + S fs_i_pfc_coefficient_add_right_vsum_body_steps = S (i)) -> exists fs_a_pfc_coefficient_add_right_vsum_body_steps fs_r_pfc_coefficient_add_right_vsum_body_steps fs_s_pfc_coefficient_add_right_vsum_body_steps. ((((exists fs_h_pfc_coefficient_add_right_vsum_body_steps_summand. fs_h_pfc_coefficient_add_right_vsum_body_steps_summand + S (fs_a_pfc_coefficient_add_right_vsum_body_steps) = S ((S (fs_i_pfc_coefficient_add_right_vsum_body_steps)) * pfc_terms_scale_coefficient_add_right_v)) /\ exists fs_q_pfc_coefficient_add_right_vsum_body_steps_summand. pfc_terms_code_coefficient_add_right_v = fs_q_pfc_coefficient_add_right_vsum_body_steps_summand * S ((S (fs_i_pfc_coefficient_add_right_vsum_body_steps)) * pfc_terms_scale_coefficient_add_right_v) + (fs_a_pfc_coefficient_add_right_vsum_body_steps))) /\ ((((exists fs_h_pfc_coefficient_add_right_vsum_body_steps_partial. fs_h_pfc_coefficient_add_right_vsum_body_steps_partial + S (fs_r_pfc_coefficient_add_right_vsum_body_steps) = S ((S (fs_i_pfc_coefficient_add_right_vsum_body_steps)) * fs_v_pfc_coefficient_add_right_vsum)) /\ exists fs_q_pfc_coefficient_add_right_vsum_body_steps_partial. fs_u_pfc_coefficient_add_right_vsum = fs_q_pfc_coefficient_add_right_vsum_body_steps_partial * S ((S (fs_i_pfc_coefficient_add_right_vsum_body_steps)) * fs_v_pfc_coefficient_add_right_vsum) + (fs_r_pfc_coefficient_add_right_vsum_body_steps))) /\ ((((exists fs_h_pfc_coefficient_add_right_vsum_body_steps_successor. fs_h_pfc_coefficient_add_right_vsum_body_steps_successor + S (fs_s_pfc_coefficient_add_right_vsum_body_steps) = S ((S (S fs_i_pfc_coefficient_add_right_vsum_body_steps)) * fs_v_pfc_coefficient_add_right_vsum)) /\ exists fs_q_pfc_coefficient_add_right_vsum_body_steps_successor. fs_u_pfc_coefficient_add_right_vsum = fs_q_pfc_coefficient_add_right_vsum_body_steps_successor * S ((S (S fs_i_pfc_coefficient_add_right_vsum_body_steps)) * fs_v_pfc_coefficient_add_right_vsum) + (fs_s_pfc_coefficient_add_right_vsum_body_steps))) /\ fs_s_pfc_coefficient_add_right_vsum_body_steps = fs_r_pfc_coefficient_add_right_vsum_body_steps + fs_a_pfc_coefficient_add_right_vsum_body_steps)))))) /\ ((((exists pfa_gap_coefficient_add_right_vresiduebound. pfa_gap_coefficient_add_right_vresiduebound + S (v) = (p)) /\ ((exists pfa_offset_left_coefficient_add_right_vresiduecongruence pfa_offset_right_coefficient_add_right_vresiduecongruence. (pfc_natural_sum_coefficient_add_right_v) + (p) * pfa_offset_left_coefficient_add_right_vresiduecongruence = (v) + (p) * pfa_offset_right_coefficient_add_right_vresiduecongruence))))))))) -> (exists pfc_terms_code_coefficient_add_right_w pfc_terms_scale_coefficient_add_right_w pfc_natural_sum_coefficient_add_right_w. ((forall pfc_index_coefficient_add_right_wdiagonal. (exists pfa_gap_coefficient_add_right_wdiagonalbound. pfa_gap_coefficient_add_right_wdiagonalbound + S (pfc_index_coefficient_add_right_wdiagonal) = (S (i))) -> exists pfc_value_coefficient_add_right_wdiagonal. ((((exists ff_h_pfp_coefficient_add_right_wdiagonalentry. ff_h_pfp_coefficient_add_right_wdiagonalentry + S (pfc_value_coefficient_add_right_wdiagonal) = S ((S (pfc_index_coefficient_add_right_wdiagonal)) * pfc_terms_scale_coefficient_add_right_w)) /\ exists ff_q_pfp_coefficient_add_right_wdiagonalentry. pfc_terms_code_coefficient_add_right_w = ff_q_pfp_coefficient_add_right_wdiagonalentry * S ((S (pfc_index_coefficient_add_right_wdiagonal)) * pfc_terms_scale_coefficient_add_right_w) + (pfc_value_coefficient_add_right_wdiagonal))) /\ ((exists pfc_complement_coefficient_add_right_wdiagonalterm pfc_left_coefficient_add_right_wdiagonalterm pfc_right_coefficient_add_right_wdiagonalterm. (((pfc_index_coefficient_add_right_wdiagonal)+pfc_complement_coefficient_add_right_wdiagonalterm=(i)) /\ ((((((exists pfa_gap_coefficient_add_right_wdiagonaltermleftinside. pfa_gap_coefficient_add_right_wdiagonaltermleftinside + S (pfc_index_coefficient_add_right_wdiagonal) = (L)) /\ ((((exists ff_h_pfp_coefficient_add_right_wdiagonaltermleftentry. ff_h_pfp_coefficient_add_right_wdiagonaltermleftentry + S (pfc_left_coefficient_add_right_wdiagonalterm) = S ((S (pfc_index_coefficient_add_right_wdiagonal)) * cc)) /\ exists ff_q_pfp_coefficient_add_right_wdiagonaltermleftentry. cb = ff_q_pfp_coefficient_add_right_wdiagonaltermleftentry * S ((S (pfc_index_coefficient_add_right_wdiagonal)) * cc) + (pfc_left_coefficient_add_right_wdiagonalterm)))))) \/ (((exists pfc_gap_coefficient_add_right_wdiagonaltermleftoutside. pfc_gap_coefficient_add_right_wdiagonaltermleftoutside+(L)=(pfc_index_coefficient_add_right_wdiagonal)) /\ (((pfc_left_coefficient_add_right_wdiagonalterm)=0))))) /\ ((((((exists pfa_gap_coefficient_add_right_wdiagonaltermrightinside. pfa_gap_coefficient_add_right_wdiagonaltermrightinside + S (pfc_complement_coefficient_add_right_wdiagonalterm) = (M)) /\ ((((exists ff_h_pfp_coefficient_add_right_wdiagonaltermrightentry. ff_h_pfp_coefficient_add_right_wdiagonaltermrightentry + S (pfc_right_coefficient_add_right_wdiagonalterm) = S ((S (pfc_complement_coefficient_add_right_wdiagonalterm)) * dc)) /\ exists ff_q_pfp_coefficient_add_right_wdiagonaltermrightentry. db = ff_q_pfp_coefficient_add_right_wdiagonaltermrightentry * S ((S (pfc_complement_coefficient_add_right_wdiagonalterm)) * dc) + (pfc_right_coefficient_add_right_wdiagonalterm)))))) \/ (((exists pfc_gap_coefficient_add_right_wdiagonaltermrightoutside. pfc_gap_coefficient_add_right_wdiagonaltermrightoutside+(M)=(pfc_complement_coefficient_add_right_wdiagonalterm)) /\ (((pfc_right_coefficient_add_right_wdiagonalterm)=0))))) /\ (((pfc_value_coefficient_add_right_wdiagonal)=pfc_left_coefficient_add_right_wdiagonalterm*pfc_right_coefficient_add_right_wdiagonalterm))))))))))) /\ (((exists fs_u_pfc_coefficient_add_right_wsum fs_v_pfc_coefficient_add_right_wsum. ((((exists fs_h_pfc_coefficient_add_right_wsum_body_start. fs_h_pfc_coefficient_add_right_wsum_body_start + S (0) = S ((S (0)) * fs_v_pfc_coefficient_add_right_wsum)) /\ exists fs_q_pfc_coefficient_add_right_wsum_body_start. fs_u_pfc_coefficient_add_right_wsum = fs_q_pfc_coefficient_add_right_wsum_body_start * S ((S (0)) * fs_v_pfc_coefficient_add_right_wsum) + (0))) /\ ((((exists fs_h_pfc_coefficient_add_right_wsum_body_terminal. fs_h_pfc_coefficient_add_right_wsum_body_terminal + S (pfc_natural_sum_coefficient_add_right_w) = S ((S (S (i))) * fs_v_pfc_coefficient_add_right_wsum)) /\ exists fs_q_pfc_coefficient_add_right_wsum_body_terminal. fs_u_pfc_coefficient_add_right_wsum = fs_q_pfc_coefficient_add_right_wsum_body_terminal * S ((S (S (i))) * fs_v_pfc_coefficient_add_right_wsum) + (pfc_natural_sum_coefficient_add_right_w))) /\ forall fs_i_pfc_coefficient_add_right_wsum_body_steps. (exists fs_lt_pfc_coefficient_add_right_wsum_body_steps_bound. fs_lt_pfc_coefficient_add_right_wsum_body_steps_bound + S fs_i_pfc_coefficient_add_right_wsum_body_steps = S (i)) -> exists fs_a_pfc_coefficient_add_right_wsum_body_steps fs_r_pfc_coefficient_add_right_wsum_body_steps fs_s_pfc_coefficient_add_right_wsum_body_steps. ((((exists fs_h_pfc_coefficient_add_right_wsum_body_steps_summand. fs_h_pfc_coefficient_add_right_wsum_body_steps_summand + S (fs_a_pfc_coefficient_add_right_wsum_body_steps) = S ((S (fs_i_pfc_coefficient_add_right_wsum_body_steps)) * pfc_terms_scale_coefficient_add_right_w)) /\ exists fs_q_pfc_coefficient_add_right_wsum_body_steps_summand. pfc_terms_code_coefficient_add_right_w = fs_q_pfc_coefficient_add_right_wsum_body_steps_summand * S ((S (fs_i_pfc_coefficient_add_right_wsum_body_steps)) * pfc_terms_scale_coefficient_add_right_w) + (fs_a_pfc_coefficient_add_right_wsum_body_steps))) /\ ((((exists fs_h_pfc_coefficient_add_right_wsum_body_steps_partial. fs_h_pfc_coefficient_add_right_wsum_body_steps_partial + S (fs_r_pfc_coefficient_add_right_wsum_body_steps) = S ((S (fs_i_pfc_coefficient_add_right_wsum_body_steps)) * fs_v_pfc_coefficient_add_right_wsum)) /\ exists fs_q_pfc_coefficient_add_right_wsum_body_steps_partial. fs_u_pfc_coefficient_add_right_wsum = fs_q_pfc_coefficient_add_right_wsum_body_steps_partial * S ((S (fs_i_pfc_coefficient_add_right_wsum_body_steps)) * fs_v_pfc_coefficient_add_right_wsum) + (fs_r_pfc_coefficient_add_right_wsum_body_steps))) /\ ((((exists fs_h_pfc_coefficient_add_right_wsum_body_steps_successor. fs_h_pfc_coefficient_add_right_wsum_body_steps_successor + S (fs_s_pfc_coefficient_add_right_wsum_body_steps) = S ((S (S fs_i_pfc_coefficient_add_right_wsum_body_steps)) * fs_v_pfc_coefficient_add_right_wsum)) /\ exists fs_q_pfc_coefficient_add_right_wsum_body_steps_successor. fs_u_pfc_coefficient_add_right_wsum = fs_q_pfc_coefficient_add_right_wsum_body_steps_successor * S ((S (S fs_i_pfc_coefficient_add_right_wsum_body_steps)) * fs_v_pfc_coefficient_add_right_wsum) + (fs_s_pfc_coefficient_add_right_wsum_body_steps))) /\ fs_s_pfc_coefficient_add_right_wsum_body_steps = fs_r_pfc_coefficient_add_right_wsum_body_steps + fs_a_pfc_coefficient_add_right_wsum_body_steps)))))) /\ ((((exists pfa_gap_coefficient_add_right_wresiduebound. pfa_gap_coefficient_add_right_wresiduebound + S (w) = (p)) /\ ((exists pfa_offset_left_coefficient_add_right_wresiduecongruence pfa_offset_right_coefficient_add_right_wresiduecongruence. (pfc_natural_sum_coefficient_add_right_w) + (p) * pfa_offset_left_coefficient_add_right_wresiduecongruence = (w) + (p) * pfa_offset_right_coefficient_add_right_wresiduecongruence))))))))) -> (((exists pfa_gap_coefficient_add_right_resultleft. pfa_gap_coefficient_add_right_resultleft + S (u) = (p)) /\ (((exists pfa_gap_coefficient_add_right_resultright. pfa_gap_coefficient_add_right_resultright + S (v) = (p)) /\ ((((exists pfa_gap_coefficient_add_right_resultresultbound. pfa_gap_coefficient_add_right_resultresultbound + S (w) = (p)) /\ ((exists pfa_offset_left_coefficient_add_right_resultresultcongruence pfa_offset_right_coefficient_add_right_resultresultcongruence. ((u) + (v)) + (p) * pfa_offset_left_coefficient_add_right_resultresultcongruence = (w) + (p) * pfa_offset_right_coefficient_add_right_resultresultcongruence)))))))))