FpPolynomialRightDivides(p,db,dc,D,ab,ac,L)

((forall fom_index_pfp_working_right_divides_definition_canonical. (exists fom_gap_pfp_working_right_divides_definition_canonical_index_bound. fom_gap_pfp_working_right_divides_definition_canonical_index_bound + S (fom_index_pfp_working_right_divides_definition_canonical) = (L)) -> exists fom_value_pfp_working_right_divides_definition_canonical. ((((exists fom_beta_height_pfp_working_right_divides_definition_canonical_entry. fom_beta_height_pfp_working_right_divides_definition_canonical_entry + S (fom_value_pfp_working_right_divides_definition_canonical) = S ((S (fom_index_pfp_working_right_divides_definition_canonical)) * (ac))) /\ exists fom_beta_quotient_pfp_working_right_divides_definition_canonical_entry. (ab) = fom_beta_quotient_pfp_working_right_divides_definition_canonical_entry * S ((S (fom_index_pfp_working_right_divides_definition_canonical)) * (ac)) + (fom_value_pfp_working_right_divides_definition_canonical))) /\ (exists fom_gap_pfp_working_right_divides_definition_canonical_value_bound. fom_gap_pfp_working_right_divides_definition_canonical_value_bound + S (fom_value_pfp_working_right_divides_definition_canonical) = (p)))) /\ ((exists pfrd_qb_working_right_divides_definition pfrd_qc_working_right_divides_definition pfrd_qlen_working_right_divides_definition pfrd_pb_working_right_divides_definition pfrd_pc_working_right_divides_definition pfrd_plen_working_right_divides_definition. ((((forall fom_index_pfp_working_right_divides_definition_productleft. (exists fom_gap_pfp_working_right_divides_definition_productleft_index_bound. fom_gap_pfp_working_right_divides_definition_productleft_index_bound + S (fom_index_pfp_working_right_divides_definition_productleft) = pfrd_qlen_working_right_divides_definition) -> exists fom_value_pfp_working_right_divides_definition_productleft. ((((exists fom_beta_height_pfp_working_right_divides_definition_productleft_entry. fom_beta_height_pfp_working_right_divides_definition_productleft_entry + S (fom_value_pfp_working_right_divides_definition_productleft) = S ((S (fom_index_pfp_working_right_divides_definition_productleft)) * pfrd_qc_working_right_divides_definition)) /\ exists fom_beta_quotient_pfp_working_right_divides_definition_productleft_entry. pfrd_qb_working_right_divides_definition = fom_beta_quotient_pfp_working_right_divides_definition_productleft_entry * S ((S (fom_index_pfp_working_right_divides_definition_productleft)) * pfrd_qc_working_right_divides_definition) + (fom_value_pfp_working_right_divides_definition_productleft))) /\ (exists fom_gap_pfp_working_right_divides_definition_productleft_value_bound. fom_gap_pfp_working_right_divides_definition_productleft_value_bound + S (fom_value_pfp_working_right_divides_definition_productleft) = (p)))) /\ (((forall fom_index_pfp_working_right_divides_definition_productright. (exists fom_gap_pfp_working_right_divides_definition_productright_index_bound. fom_gap_pfp_working_right_divides_definition_productright_index_bound + S (fom_index_pfp_working_right_divides_definition_productright) = (D)) -> exists fom_value_pfp_working_right_divides_definition_productright. ((((exists fom_beta_height_pfp_working_right_divides_definition_productright_entry. fom_beta_height_pfp_working_right_divides_definition_productright_entry + S (fom_value_pfp_working_right_divides_definition_productright) = S ((S (fom_index_pfp_working_right_divides_definition_productright)) * (dc))) /\ exists fom_beta_quotient_pfp_working_right_divides_definition_productright_entry. (db) = fom_beta_quotient_pfp_working_right_divides_definition_productright_entry * S ((S (fom_index_pfp_working_right_divides_definition_productright)) * (dc)) + (fom_value_pfp_working_right_divides_definition_productright))) /\ (exists fom_gap_pfp_working_right_divides_definition_productright_value_bound. fom_gap_pfp_working_right_divides_definition_productright_value_bound + S (fom_value_pfp_working_right_divides_definition_productright) = (p)))) /\ (((((((pfrd_qlen_working_right_divides_definition)=0 \/ ((D))=0) /\ (((pfrd_plen_working_right_divides_definition)=0)))) \/ (((~((pfrd_qlen_working_right_divides_definition)=0)) /\ (((~(((D))=0)) /\ (((pfrd_qlen_working_right_divides_definition)+((D))=S (pfrd_plen_working_right_divides_definition)))))))) /\ ((forall pfc_index_working_right_divides_definition_productcoefficients. (exists pfa_gap_working_right_divides_definition_productcoefficientsbound. pfa_gap_working_right_divides_definition_productcoefficientsbound + S (pfc_index_working_right_divides_definition_productcoefficients) = (pfrd_plen_working_right_divides_definition)) -> exists pfc_value_working_right_divides_definition_productcoefficients. ((((exists ff_h_pfp_working_right_divides_definition_productcoefficientsentry. ff_h_pfp_working_right_divides_definition_productcoefficientsentry + S (pfc_value_working_right_divides_definition_productcoefficients) = S ((S (pfc_index_working_right_divides_definition_productcoefficients)) * pfrd_pc_working_right_divides_definition)) /\ exists ff_q_pfp_working_right_divides_definition_productcoefficientsentry. pfrd_pb_working_right_divides_definition = ff_q_pfp_working_right_divides_definition_productcoefficientsentry * S ((S (pfc_index_working_right_divides_definition_productcoefficients)) * pfrd_pc_working_right_divides_definition) + (pfc_value_working_right_divides_definition_productcoefficients))) /\ ((exists pfc_terms_code_working_right_divides_definition_productcoefficientscoefficient pfc_terms_scale_working_right_divides_definition_productcoefficientscoefficient pfc_natural_sum_working_right_divides_definition_productcoefficientscoefficient. ((forall pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal. (exists pfa_gap_working_right_divides_definition_productcoefficientscoefficientdiagonalbound. pfa_gap_working_right_divides_definition_productcoefficientscoefficientdiagonalbound + S (pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal) = (S (pfc_index_working_right_divides_definition_productcoefficients))) -> exists pfc_value_working_right_divides_definition_productcoefficientscoefficientdiagonal. ((((exists ff_h_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonalentry. ff_h_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonalentry + S (pfc_value_working_right_divides_definition_productcoefficientscoefficientdiagonal) = S ((S (pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal)) * pfc_terms_scale_working_right_divides_definition_productcoefficientscoefficient)) /\ exists ff_q_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonalentry. pfc_terms_code_working_right_divides_definition_productcoefficientscoefficient = ff_q_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonalentry * S ((S (pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal)) * pfc_terms_scale_working_right_divides_definition_productcoefficientscoefficient) + (pfc_value_working_right_divides_definition_productcoefficientscoefficientdiagonal))) /\ ((exists pfc_complement_working_right_divides_definition_productcoefficientscoefficientdiagonalterm pfc_left_working_right_divides_definition_productcoefficientscoefficientdiagonalterm pfc_right_working_right_divides_definition_productcoefficientscoefficientdiagonalterm. (((pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal)+pfc_complement_working_right_divides_definition_productcoefficientscoefficientdiagonalterm=(pfc_index_working_right_divides_definition_productcoefficients)) /\ ((((((exists pfa_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftinside. pfa_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftinside + S (pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal) = (pfrd_qlen_working_right_divides_definition)) /\ ((((exists ff_h_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftentry. ff_h_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftentry + S (pfc_left_working_right_divides_definition_productcoefficientscoefficientdiagonalterm) = S ((S (pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal)) * pfrd_qc_working_right_divides_definition)) /\ exists ff_q_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftentry. pfrd_qb_working_right_divides_definition = ff_q_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftentry * S ((S (pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal)) * pfrd_qc_working_right_divides_definition) + (pfc_left_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)))))) \/ (((exists pfc_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftoutside. pfc_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermleftoutside+(pfrd_qlen_working_right_divides_definition)=(pfc_index_working_right_divides_definition_productcoefficientscoefficientdiagonal)) /\ (((pfc_left_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)=0))))) /\ ((((((exists pfa_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightinside. pfa_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightinside + S (pfc_complement_working_right_divides_definition_productcoefficientscoefficientdiagonalterm) = ((D))) /\ ((((exists ff_h_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightentry. ff_h_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightentry + S (pfc_right_working_right_divides_definition_productcoefficientscoefficientdiagonalterm) = S ((S (pfc_complement_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)) * (dc))) /\ exists ff_q_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightentry. (db) = ff_q_pfp_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightentry * S ((S (pfc_complement_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)) * (dc)) + (pfc_right_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)))))) \/ (((exists pfc_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightoutside. pfc_gap_working_right_divides_definition_productcoefficientscoefficientdiagonaltermrightoutside+((D))=(pfc_complement_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)) /\ (((pfc_right_working_right_divides_definition_productcoefficientscoefficientdiagonalterm)=0))))) /\ (((pfc_value_working_right_divides_definition_productcoefficientscoefficientdiagonal)=pfc_left_working_right_divides_definition_productcoefficientscoefficientdiagonalterm*pfc_right_working_right_divides_definition_productcoefficientscoefficientdiagonalterm))))))))))) /\ (((exists fs_u_pfc_working_right_divides_definition_productcoefficientscoefficientsum fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum. ((((exists fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_start. fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_start + S (0) = S ((S (0)) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum)) /\ exists fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_start. fs_u_pfc_working_right_divides_definition_productcoefficientscoefficientsum = fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_start * S ((S (0)) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum) + (0))) /\ ((((exists fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_terminal. fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_terminal + S (pfc_natural_sum_working_right_divides_definition_productcoefficientscoefficient) = S ((S (S (pfc_index_working_right_divides_definition_productcoefficients))) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum)) /\ exists fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_terminal. fs_u_pfc_working_right_divides_definition_productcoefficientscoefficientsum = fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_terminal * S ((S (S (pfc_index_working_right_divides_definition_productcoefficients))) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum) + (pfc_natural_sum_working_right_divides_definition_productcoefficientscoefficient))) /\ forall fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps. (exists fs_lt_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_bound. fs_lt_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_bound + S fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps = S (pfc_index_working_right_divides_definition_productcoefficients)) -> exists fs_a_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps fs_r_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps fs_s_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps. ((((exists fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_summand. fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_summand + S (fs_a_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps) = S ((S (fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)) * pfc_terms_scale_working_right_divides_definition_productcoefficientscoefficient)) /\ exists fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_summand. pfc_terms_code_working_right_divides_definition_productcoefficientscoefficient = fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_summand * S ((S (fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)) * pfc_terms_scale_working_right_divides_definition_productcoefficientscoefficient) + (fs_a_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_partial. fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_partial + S (fs_r_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps) = S ((S (fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum)) /\ exists fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_partial. fs_u_pfc_working_right_divides_definition_productcoefficientscoefficientsum = fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_partial * S ((S (fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum) + (fs_r_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps))) /\ ((((exists fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_successor. fs_h_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_successor + S (fs_s_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps) = S ((S (S fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum)) /\ exists fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_successor. fs_u_pfc_working_right_divides_definition_productcoefficientscoefficientsum = fs_q_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps_successor * S ((S (S fs_i_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)) * fs_v_pfc_working_right_divides_definition_productcoefficientscoefficientsum) + (fs_s_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps))) /\ fs_s_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps = fs_r_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps + fs_a_pfc_working_right_divides_definition_productcoefficientscoefficientsum_body_steps)))))) /\ ((((exists pfa_gap_working_right_divides_definition_productcoefficientscoefficientresiduebound. pfa_gap_working_right_divides_definition_productcoefficientscoefficientresiduebound + S (pfc_value_working_right_divides_definition_productcoefficients) = ((p))) /\ ((exists pfa_offset_left_working_right_divides_definition_productcoefficientscoefficientresiduecongruence pfa_offset_right_working_right_divides_definition_productcoefficientscoefficientresiduecongruence. (pfc_natural_sum_working_right_divides_definition_productcoefficientscoefficient) + ((p)) * pfa_offset_left_working_right_divides_definition_productcoefficientscoefficientresiduecongruence = (pfc_value_working_right_divides_definition_productcoefficients) + ((p)) * pfa_offset_right_working_right_divides_definition_productcoefficientscoefficientresiduecongruence))))))))))))))))))) /\ ((forall pfrep_power_working_right_divides_definition_target pfrep_left_working_right_divides_definition_target pfrep_right_working_right_divides_definition_target. ((exists pfrep_position_working_right_divides_definition_targetfirst. ((pfrep_position_working_right_divides_definition_targetfirst+S (pfrep_power_working_right_divides_definition_target)=(pfrd_plen_working_right_divides_definition)) /\ ((((exists ff_h_pfp_working_right_divides_definition_targetfirstentry. ff_h_pfp_working_right_divides_definition_targetfirstentry + S (pfrep_left_working_right_divides_definition_target) = S ((S (pfrep_position_working_right_divides_definition_targetfirst)) * pfrd_pc_working_right_divides_definition)) /\ exists ff_q_pfp_working_right_divides_definition_targetfirstentry. pfrd_pb_working_right_divides_definition = ff_q_pfp_working_right_divides_definition_targetfirstentry * S ((S (pfrep_position_working_right_divides_definition_targetfirst)) * pfrd_pc_working_right_divides_definition) + (pfrep_left_working_right_divides_definition_target)))))) \/ (((exists pfrep_gap_working_right_divides_definition_targetfirstoutside. pfrep_gap_working_right_divides_definition_targetfirstoutside+(pfrd_plen_working_right_divides_definition)=(pfrep_power_working_right_divides_definition_target)) /\ (((pfrep_left_working_right_divides_definition_target)=0))))) -> ((exists pfrep_position_working_right_divides_definition_targetsecond. ((pfrep_position_working_right_divides_definition_targetsecond+S (pfrep_power_working_right_divides_definition_target)=((L))) /\ ((((exists ff_h_pfp_working_right_divides_definition_targetsecondentry. ff_h_pfp_working_right_divides_definition_targetsecondentry + S (pfrep_right_working_right_divides_definition_target) = S ((S (pfrep_position_working_right_divides_definition_targetsecond)) * (ac))) /\ exists ff_q_pfp_working_right_divides_definition_targetsecondentry. (ab) = ff_q_pfp_working_right_divides_definition_targetsecondentry * S ((S (pfrep_position_working_right_divides_definition_targetsecond)) * (ac)) + (pfrep_right_working_right_divides_definition_target)))))) \/ (((exists pfrep_gap_working_right_divides_definition_targetsecondoutside. pfrep_gap_working_right_divides_definition_targetsecondoutside+((L))=(pfrep_power_working_right_divides_definition_target)) /\ (((pfrep_right_working_right_divides_definition_target)=0))))) -> pfrep_left_working_right_divides_definition_target=pfrep_right_working_right_divides_definition_target))))))

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.