polynomial_diagonal_sum_right_add_congruent

Exact expanded first-order arithmetic statement

forall p ab ac bb bc cb cc L db dc M i N ub uc vb vc wb wc u v w. (forall pfp_index_diagonal_add_right_source. (exists pfa_gap_diagonal_add_right_sourceindex. pfa_gap_diagonal_add_right_sourceindex + S (pfp_index_diagonal_add_right_source) = (L)) -> exists pfp_left_diagonal_add_right_source pfp_right_diagonal_add_right_source pfp_value_diagonal_add_right_source. ((((exists ff_h_pfp_diagonal_add_right_sourceleft. ff_h_pfp_diagonal_add_right_sourceleft + S (pfp_left_diagonal_add_right_source) = S ((S (pfp_index_diagonal_add_right_source)) * ac)) /\ exists ff_q_pfp_diagonal_add_right_sourceleft. ab = ff_q_pfp_diagonal_add_right_sourceleft * S ((S (pfp_index_diagonal_add_right_source)) * ac) + (pfp_left_diagonal_add_right_source))) /\ (((((exists ff_h_pfp_diagonal_add_right_sourceright. ff_h_pfp_diagonal_add_right_sourceright + S (pfp_right_diagonal_add_right_source) = S ((S (pfp_index_diagonal_add_right_source)) * bc)) /\ exists ff_q_pfp_diagonal_add_right_sourceright. bb = ff_q_pfp_diagonal_add_right_sourceright * S ((S (pfp_index_diagonal_add_right_source)) * bc) + (pfp_right_diagonal_add_right_source))) /\ (((((exists ff_h_pfp_diagonal_add_right_sourcetarget. ff_h_pfp_diagonal_add_right_sourcetarget + S (pfp_value_diagonal_add_right_source) = S ((S (pfp_index_diagonal_add_right_source)) * cc)) /\ exists ff_q_pfp_diagonal_add_right_sourcetarget. cb = ff_q_pfp_diagonal_add_right_sourcetarget * S ((S (pfp_index_diagonal_add_right_source)) * cc) + (pfp_value_diagonal_add_right_source))) /\ ((((exists pfa_gap_diagonal_add_right_sourceoperationleft. pfa_gap_diagonal_add_right_sourceoperationleft + S (pfp_left_diagonal_add_right_source) = (p)) /\ (((exists pfa_gap_diagonal_add_right_sourceoperationright. pfa_gap_diagonal_add_right_sourceoperationright + S (pfp_right_diagonal_add_right_source) = (p)) /\ ((((exists pfa_gap_diagonal_add_right_sourceoperationresultbound. pfa_gap_diagonal_add_right_sourceoperationresultbound + S (pfp_value_diagonal_add_right_source) = (p)) /\ ((exists pfa_offset_left_diagonal_add_right_sourceoperationresultcongruence pfa_offset_right_diagonal_add_right_sourceoperationresultcongruence. ((pfp_left_diagonal_add_right_source) + (pfp_right_diagonal_add_right_source)) + (p) * pfa_offset_left_diagonal_add_right_sourceoperationresultcongruence = (pfp_value_diagonal_add_right_source) + (p) * pfa_offset_right_diagonal_add_right_sourceoperationresultcongruence)))))))))))))))) -> (forall pfc_index_diagonal_add_right_u. (exists pfa_gap_diagonal_add_right_ubound. pfa_gap_diagonal_add_right_ubound + S (pfc_index_diagonal_add_right_u) = (N)) -> exists pfc_value_diagonal_add_right_u. ((((exists ff_h_pfp_diagonal_add_right_uentry. ff_h_pfp_diagonal_add_right_uentry + S (pfc_value_diagonal_add_right_u) = S ((S (pfc_index_diagonal_add_right_u)) * uc)) /\ exists ff_q_pfp_diagonal_add_right_uentry. ub = ff_q_pfp_diagonal_add_right_uentry * S ((S (pfc_index_diagonal_add_right_u)) * uc) + (pfc_value_diagonal_add_right_u))) /\ ((exists pfc_complement_diagonal_add_right_uterm pfc_left_diagonal_add_right_uterm pfc_right_diagonal_add_right_uterm. (((pfc_index_diagonal_add_right_u)+pfc_complement_diagonal_add_right_uterm=(i)) /\ ((((((exists pfa_gap_diagonal_add_right_utermleftinside. pfa_gap_diagonal_add_right_utermleftinside + S (pfc_index_diagonal_add_right_u) = (L)) /\ ((((exists ff_h_pfp_diagonal_add_right_utermleftentry. ff_h_pfp_diagonal_add_right_utermleftentry + S (pfc_left_diagonal_add_right_uterm) = S ((S (pfc_index_diagonal_add_right_u)) * ac)) /\ exists ff_q_pfp_diagonal_add_right_utermleftentry. ab = ff_q_pfp_diagonal_add_right_utermleftentry * S ((S (pfc_index_diagonal_add_right_u)) * ac) + (pfc_left_diagonal_add_right_uterm)))))) \/ (((exists pfc_gap_diagonal_add_right_utermleftoutside. pfc_gap_diagonal_add_right_utermleftoutside+(L)=(pfc_index_diagonal_add_right_u)) /\ (((pfc_left_diagonal_add_right_uterm)=0))))) /\ ((((((exists pfa_gap_diagonal_add_right_utermrightinside. pfa_gap_diagonal_add_right_utermrightinside + S (pfc_complement_diagonal_add_right_uterm) = (M)) /\ ((((exists ff_h_pfp_diagonal_add_right_utermrightentry. ff_h_pfp_diagonal_add_right_utermrightentry + S (pfc_right_diagonal_add_right_uterm) = S ((S (pfc_complement_diagonal_add_right_uterm)) * dc)) /\ exists ff_q_pfp_diagonal_add_right_utermrightentry. db = ff_q_pfp_diagonal_add_right_utermrightentry * S ((S (pfc_complement_diagonal_add_right_uterm)) * dc) + (pfc_right_diagonal_add_right_uterm)))))) \/ (((exists pfc_gap_diagonal_add_right_utermrightoutside. pfc_gap_diagonal_add_right_utermrightoutside+(M)=(pfc_complement_diagonal_add_right_uterm)) /\ (((pfc_right_diagonal_add_right_uterm)=0))))) /\ (((pfc_value_diagonal_add_right_u)=pfc_left_diagonal_add_right_uterm*pfc_right_diagonal_add_right_uterm))))))))))) -> (exists fs_u_pfc_diagonal_add_right_sum_u fs_v_pfc_diagonal_add_right_sum_u. ((((exists fs_h_pfc_diagonal_add_right_sum_u_body_start. fs_h_pfc_diagonal_add_right_sum_u_body_start + S (0) = S ((S (0)) * fs_v_pfc_diagonal_add_right_sum_u)) /\ exists fs_q_pfc_diagonal_add_right_sum_u_body_start. fs_u_pfc_diagonal_add_right_sum_u = fs_q_pfc_diagonal_add_right_sum_u_body_start * S ((S (0)) * fs_v_pfc_diagonal_add_right_sum_u) + (0))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_u_body_terminal. fs_h_pfc_diagonal_add_right_sum_u_body_terminal + S (u) = S ((S (N)) * fs_v_pfc_diagonal_add_right_sum_u)) /\ exists fs_q_pfc_diagonal_add_right_sum_u_body_terminal. fs_u_pfc_diagonal_add_right_sum_u = fs_q_pfc_diagonal_add_right_sum_u_body_terminal * S ((S (N)) * fs_v_pfc_diagonal_add_right_sum_u) + (u))) /\ forall fs_i_pfc_diagonal_add_right_sum_u_body_steps. (exists fs_lt_pfc_diagonal_add_right_sum_u_body_steps_bound. fs_lt_pfc_diagonal_add_right_sum_u_body_steps_bound + S fs_i_pfc_diagonal_add_right_sum_u_body_steps = N) -> exists fs_a_pfc_diagonal_add_right_sum_u_body_steps fs_r_pfc_diagonal_add_right_sum_u_body_steps fs_s_pfc_diagonal_add_right_sum_u_body_steps. ((((exists fs_h_pfc_diagonal_add_right_sum_u_body_steps_summand. fs_h_pfc_diagonal_add_right_sum_u_body_steps_summand + S (fs_a_pfc_diagonal_add_right_sum_u_body_steps) = S ((S (fs_i_pfc_diagonal_add_right_sum_u_body_steps)) * uc)) /\ exists fs_q_pfc_diagonal_add_right_sum_u_body_steps_summand. ub = fs_q_pfc_diagonal_add_right_sum_u_body_steps_summand * S ((S (fs_i_pfc_diagonal_add_right_sum_u_body_steps)) * uc) + (fs_a_pfc_diagonal_add_right_sum_u_body_steps))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_u_body_steps_partial. fs_h_pfc_diagonal_add_right_sum_u_body_steps_partial + S (fs_r_pfc_diagonal_add_right_sum_u_body_steps) = S ((S (fs_i_pfc_diagonal_add_right_sum_u_body_steps)) * fs_v_pfc_diagonal_add_right_sum_u)) /\ exists fs_q_pfc_diagonal_add_right_sum_u_body_steps_partial. fs_u_pfc_diagonal_add_right_sum_u = fs_q_pfc_diagonal_add_right_sum_u_body_steps_partial * S ((S (fs_i_pfc_diagonal_add_right_sum_u_body_steps)) * fs_v_pfc_diagonal_add_right_sum_u) + (fs_r_pfc_diagonal_add_right_sum_u_body_steps))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_u_body_steps_successor. fs_h_pfc_diagonal_add_right_sum_u_body_steps_successor + S (fs_s_pfc_diagonal_add_right_sum_u_body_steps) = S ((S (S fs_i_pfc_diagonal_add_right_sum_u_body_steps)) * fs_v_pfc_diagonal_add_right_sum_u)) /\ exists fs_q_pfc_diagonal_add_right_sum_u_body_steps_successor. fs_u_pfc_diagonal_add_right_sum_u = fs_q_pfc_diagonal_add_right_sum_u_body_steps_successor * S ((S (S fs_i_pfc_diagonal_add_right_sum_u_body_steps)) * fs_v_pfc_diagonal_add_right_sum_u) + (fs_s_pfc_diagonal_add_right_sum_u_body_steps))) /\ fs_s_pfc_diagonal_add_right_sum_u_body_steps = fs_r_pfc_diagonal_add_right_sum_u_body_steps + fs_a_pfc_diagonal_add_right_sum_u_body_steps)))))) -> (forall pfc_index_diagonal_add_right_v. (exists pfa_gap_diagonal_add_right_vbound. pfa_gap_diagonal_add_right_vbound + S (pfc_index_diagonal_add_right_v) = (N)) -> exists pfc_value_diagonal_add_right_v. ((((exists ff_h_pfp_diagonal_add_right_ventry. ff_h_pfp_diagonal_add_right_ventry + S (pfc_value_diagonal_add_right_v) = S ((S (pfc_index_diagonal_add_right_v)) * vc)) /\ exists ff_q_pfp_diagonal_add_right_ventry. vb = ff_q_pfp_diagonal_add_right_ventry * S ((S (pfc_index_diagonal_add_right_v)) * vc) + (pfc_value_diagonal_add_right_v))) /\ ((exists pfc_complement_diagonal_add_right_vterm pfc_left_diagonal_add_right_vterm pfc_right_diagonal_add_right_vterm. (((pfc_index_diagonal_add_right_v)+pfc_complement_diagonal_add_right_vterm=(i)) /\ ((((((exists pfa_gap_diagonal_add_right_vtermleftinside. pfa_gap_diagonal_add_right_vtermleftinside + S (pfc_index_diagonal_add_right_v) = (L)) /\ ((((exists ff_h_pfp_diagonal_add_right_vtermleftentry. ff_h_pfp_diagonal_add_right_vtermleftentry + S (pfc_left_diagonal_add_right_vterm) = S ((S (pfc_index_diagonal_add_right_v)) * bc)) /\ exists ff_q_pfp_diagonal_add_right_vtermleftentry. bb = ff_q_pfp_diagonal_add_right_vtermleftentry * S ((S (pfc_index_diagonal_add_right_v)) * bc) + (pfc_left_diagonal_add_right_vterm)))))) \/ (((exists pfc_gap_diagonal_add_right_vtermleftoutside. pfc_gap_diagonal_add_right_vtermleftoutside+(L)=(pfc_index_diagonal_add_right_v)) /\ (((pfc_left_diagonal_add_right_vterm)=0))))) /\ ((((((exists pfa_gap_diagonal_add_right_vtermrightinside. pfa_gap_diagonal_add_right_vtermrightinside + S (pfc_complement_diagonal_add_right_vterm) = (M)) /\ ((((exists ff_h_pfp_diagonal_add_right_vtermrightentry. ff_h_pfp_diagonal_add_right_vtermrightentry + S (pfc_right_diagonal_add_right_vterm) = S ((S (pfc_complement_diagonal_add_right_vterm)) * dc)) /\ exists ff_q_pfp_diagonal_add_right_vtermrightentry. db = ff_q_pfp_diagonal_add_right_vtermrightentry * S ((S (pfc_complement_diagonal_add_right_vterm)) * dc) + (pfc_right_diagonal_add_right_vterm)))))) \/ (((exists pfc_gap_diagonal_add_right_vtermrightoutside. pfc_gap_diagonal_add_right_vtermrightoutside+(M)=(pfc_complement_diagonal_add_right_vterm)) /\ (((pfc_right_diagonal_add_right_vterm)=0))))) /\ (((pfc_value_diagonal_add_right_v)=pfc_left_diagonal_add_right_vterm*pfc_right_diagonal_add_right_vterm))))))))))) -> (exists fs_u_pfc_diagonal_add_right_sum_v fs_v_pfc_diagonal_add_right_sum_v. ((((exists fs_h_pfc_diagonal_add_right_sum_v_body_start. fs_h_pfc_diagonal_add_right_sum_v_body_start + S (0) = S ((S (0)) * fs_v_pfc_diagonal_add_right_sum_v)) /\ exists fs_q_pfc_diagonal_add_right_sum_v_body_start. fs_u_pfc_diagonal_add_right_sum_v = fs_q_pfc_diagonal_add_right_sum_v_body_start * S ((S (0)) * fs_v_pfc_diagonal_add_right_sum_v) + (0))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_v_body_terminal. fs_h_pfc_diagonal_add_right_sum_v_body_terminal + S (v) = S ((S (N)) * fs_v_pfc_diagonal_add_right_sum_v)) /\ exists fs_q_pfc_diagonal_add_right_sum_v_body_terminal. fs_u_pfc_diagonal_add_right_sum_v = fs_q_pfc_diagonal_add_right_sum_v_body_terminal * S ((S (N)) * fs_v_pfc_diagonal_add_right_sum_v) + (v))) /\ forall fs_i_pfc_diagonal_add_right_sum_v_body_steps. (exists fs_lt_pfc_diagonal_add_right_sum_v_body_steps_bound. fs_lt_pfc_diagonal_add_right_sum_v_body_steps_bound + S fs_i_pfc_diagonal_add_right_sum_v_body_steps = N) -> exists fs_a_pfc_diagonal_add_right_sum_v_body_steps fs_r_pfc_diagonal_add_right_sum_v_body_steps fs_s_pfc_diagonal_add_right_sum_v_body_steps. ((((exists fs_h_pfc_diagonal_add_right_sum_v_body_steps_summand. fs_h_pfc_diagonal_add_right_sum_v_body_steps_summand + S (fs_a_pfc_diagonal_add_right_sum_v_body_steps) = S ((S (fs_i_pfc_diagonal_add_right_sum_v_body_steps)) * vc)) /\ exists fs_q_pfc_diagonal_add_right_sum_v_body_steps_summand. vb = fs_q_pfc_diagonal_add_right_sum_v_body_steps_summand * S ((S (fs_i_pfc_diagonal_add_right_sum_v_body_steps)) * vc) + (fs_a_pfc_diagonal_add_right_sum_v_body_steps))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_v_body_steps_partial. fs_h_pfc_diagonal_add_right_sum_v_body_steps_partial + S (fs_r_pfc_diagonal_add_right_sum_v_body_steps) = S ((S (fs_i_pfc_diagonal_add_right_sum_v_body_steps)) * fs_v_pfc_diagonal_add_right_sum_v)) /\ exists fs_q_pfc_diagonal_add_right_sum_v_body_steps_partial. fs_u_pfc_diagonal_add_right_sum_v = fs_q_pfc_diagonal_add_right_sum_v_body_steps_partial * S ((S (fs_i_pfc_diagonal_add_right_sum_v_body_steps)) * fs_v_pfc_diagonal_add_right_sum_v) + (fs_r_pfc_diagonal_add_right_sum_v_body_steps))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_v_body_steps_successor. fs_h_pfc_diagonal_add_right_sum_v_body_steps_successor + S (fs_s_pfc_diagonal_add_right_sum_v_body_steps) = S ((S (S fs_i_pfc_diagonal_add_right_sum_v_body_steps)) * fs_v_pfc_diagonal_add_right_sum_v)) /\ exists fs_q_pfc_diagonal_add_right_sum_v_body_steps_successor. fs_u_pfc_diagonal_add_right_sum_v = fs_q_pfc_diagonal_add_right_sum_v_body_steps_successor * S ((S (S fs_i_pfc_diagonal_add_right_sum_v_body_steps)) * fs_v_pfc_diagonal_add_right_sum_v) + (fs_s_pfc_diagonal_add_right_sum_v_body_steps))) /\ fs_s_pfc_diagonal_add_right_sum_v_body_steps = fs_r_pfc_diagonal_add_right_sum_v_body_steps + fs_a_pfc_diagonal_add_right_sum_v_body_steps)))))) -> (forall pfc_index_diagonal_add_right_w. (exists pfa_gap_diagonal_add_right_wbound. pfa_gap_diagonal_add_right_wbound + S (pfc_index_diagonal_add_right_w) = (N)) -> exists pfc_value_diagonal_add_right_w. ((((exists ff_h_pfp_diagonal_add_right_wentry. ff_h_pfp_diagonal_add_right_wentry + S (pfc_value_diagonal_add_right_w) = S ((S (pfc_index_diagonal_add_right_w)) * wc)) /\ exists ff_q_pfp_diagonal_add_right_wentry. wb = ff_q_pfp_diagonal_add_right_wentry * S ((S (pfc_index_diagonal_add_right_w)) * wc) + (pfc_value_diagonal_add_right_w))) /\ ((exists pfc_complement_diagonal_add_right_wterm pfc_left_diagonal_add_right_wterm pfc_right_diagonal_add_right_wterm. (((pfc_index_diagonal_add_right_w)+pfc_complement_diagonal_add_right_wterm=(i)) /\ ((((((exists pfa_gap_diagonal_add_right_wtermleftinside. pfa_gap_diagonal_add_right_wtermleftinside + S (pfc_index_diagonal_add_right_w) = (L)) /\ ((((exists ff_h_pfp_diagonal_add_right_wtermleftentry. ff_h_pfp_diagonal_add_right_wtermleftentry + S (pfc_left_diagonal_add_right_wterm) = S ((S (pfc_index_diagonal_add_right_w)) * cc)) /\ exists ff_q_pfp_diagonal_add_right_wtermleftentry. cb = ff_q_pfp_diagonal_add_right_wtermleftentry * S ((S (pfc_index_diagonal_add_right_w)) * cc) + (pfc_left_diagonal_add_right_wterm)))))) \/ (((exists pfc_gap_diagonal_add_right_wtermleftoutside. pfc_gap_diagonal_add_right_wtermleftoutside+(L)=(pfc_index_diagonal_add_right_w)) /\ (((pfc_left_diagonal_add_right_wterm)=0))))) /\ ((((((exists pfa_gap_diagonal_add_right_wtermrightinside. pfa_gap_diagonal_add_right_wtermrightinside + S (pfc_complement_diagonal_add_right_wterm) = (M)) /\ ((((exists ff_h_pfp_diagonal_add_right_wtermrightentry. ff_h_pfp_diagonal_add_right_wtermrightentry + S (pfc_right_diagonal_add_right_wterm) = S ((S (pfc_complement_diagonal_add_right_wterm)) * dc)) /\ exists ff_q_pfp_diagonal_add_right_wtermrightentry. db = ff_q_pfp_diagonal_add_right_wtermrightentry * S ((S (pfc_complement_diagonal_add_right_wterm)) * dc) + (pfc_right_diagonal_add_right_wterm)))))) \/ (((exists pfc_gap_diagonal_add_right_wtermrightoutside. pfc_gap_diagonal_add_right_wtermrightoutside+(M)=(pfc_complement_diagonal_add_right_wterm)) /\ (((pfc_right_diagonal_add_right_wterm)=0))))) /\ (((pfc_value_diagonal_add_right_w)=pfc_left_diagonal_add_right_wterm*pfc_right_diagonal_add_right_wterm))))))))))) -> (exists fs_u_pfc_diagonal_add_right_sum_w fs_v_pfc_diagonal_add_right_sum_w. ((((exists fs_h_pfc_diagonal_add_right_sum_w_body_start. fs_h_pfc_diagonal_add_right_sum_w_body_start + S (0) = S ((S (0)) * fs_v_pfc_diagonal_add_right_sum_w)) /\ exists fs_q_pfc_diagonal_add_right_sum_w_body_start. fs_u_pfc_diagonal_add_right_sum_w = fs_q_pfc_diagonal_add_right_sum_w_body_start * S ((S (0)) * fs_v_pfc_diagonal_add_right_sum_w) + (0))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_w_body_terminal. fs_h_pfc_diagonal_add_right_sum_w_body_terminal + S (w) = S ((S (N)) * fs_v_pfc_diagonal_add_right_sum_w)) /\ exists fs_q_pfc_diagonal_add_right_sum_w_body_terminal. fs_u_pfc_diagonal_add_right_sum_w = fs_q_pfc_diagonal_add_right_sum_w_body_terminal * S ((S (N)) * fs_v_pfc_diagonal_add_right_sum_w) + (w))) /\ forall fs_i_pfc_diagonal_add_right_sum_w_body_steps. (exists fs_lt_pfc_diagonal_add_right_sum_w_body_steps_bound. fs_lt_pfc_diagonal_add_right_sum_w_body_steps_bound + S fs_i_pfc_diagonal_add_right_sum_w_body_steps = N) -> exists fs_a_pfc_diagonal_add_right_sum_w_body_steps fs_r_pfc_diagonal_add_right_sum_w_body_steps fs_s_pfc_diagonal_add_right_sum_w_body_steps. ((((exists fs_h_pfc_diagonal_add_right_sum_w_body_steps_summand. fs_h_pfc_diagonal_add_right_sum_w_body_steps_summand + S (fs_a_pfc_diagonal_add_right_sum_w_body_steps) = S ((S (fs_i_pfc_diagonal_add_right_sum_w_body_steps)) * wc)) /\ exists fs_q_pfc_diagonal_add_right_sum_w_body_steps_summand. wb = fs_q_pfc_diagonal_add_right_sum_w_body_steps_summand * S ((S (fs_i_pfc_diagonal_add_right_sum_w_body_steps)) * wc) + (fs_a_pfc_diagonal_add_right_sum_w_body_steps))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_w_body_steps_partial. fs_h_pfc_diagonal_add_right_sum_w_body_steps_partial + S (fs_r_pfc_diagonal_add_right_sum_w_body_steps) = S ((S (fs_i_pfc_diagonal_add_right_sum_w_body_steps)) * fs_v_pfc_diagonal_add_right_sum_w)) /\ exists fs_q_pfc_diagonal_add_right_sum_w_body_steps_partial. fs_u_pfc_diagonal_add_right_sum_w = fs_q_pfc_diagonal_add_right_sum_w_body_steps_partial * S ((S (fs_i_pfc_diagonal_add_right_sum_w_body_steps)) * fs_v_pfc_diagonal_add_right_sum_w) + (fs_r_pfc_diagonal_add_right_sum_w_body_steps))) /\ ((((exists fs_h_pfc_diagonal_add_right_sum_w_body_steps_successor. fs_h_pfc_diagonal_add_right_sum_w_body_steps_successor + S (fs_s_pfc_diagonal_add_right_sum_w_body_steps) = S ((S (S fs_i_pfc_diagonal_add_right_sum_w_body_steps)) * fs_v_pfc_diagonal_add_right_sum_w)) /\ exists fs_q_pfc_diagonal_add_right_sum_w_body_steps_successor. fs_u_pfc_diagonal_add_right_sum_w = fs_q_pfc_diagonal_add_right_sum_w_body_steps_successor * S ((S (S fs_i_pfc_diagonal_add_right_sum_w_body_steps)) * fs_v_pfc_diagonal_add_right_sum_w) + (fs_s_pfc_diagonal_add_right_sum_w_body_steps))) /\ fs_s_pfc_diagonal_add_right_sum_w_body_steps = fs_r_pfc_diagonal_add_right_sum_w_body_steps + fs_a_pfc_diagonal_add_right_sum_w_body_steps)))))) -> (exists pfa_offset_left_diagonal_add_right_result pfa_offset_right_diagonal_add_right_result. (u+v) + (p) * pfa_offset_left_diagonal_add_right_result = (w) + (p) * pfa_offset_right_diagonal_add_right_result)