prime_field_polynomial_aligned_add_from_common

forall p ab ac L bb bc M rb rc N ub uc vb vc tb tc K. (forall fom_index_pfp_from_common_0. (exists fom_gap_pfp_from_common_0_index_bound. fom_gap_pfp_from_common_0_index_bound + S (fom_index_pfp_from_common_0) = L) -> exists fom_value_pfp_from_common_0. ((((exists fom_beta_height_pfp_from_common_0_entry. fom_beta_height_pfp_from_common_0_entry + S (fom_value_pfp_from_common_0) = S ((S (fom_index_pfp_from_common_0)) * ac)) /\ exists fom_beta_quotient_pfp_from_common_0_entry. ab = fom_beta_quotient_pfp_from_common_0_entry * S ((S (fom_index_pfp_from_common_0)) * ac) + (fom_value_pfp_from_common_0))) /\ (exists fom_gap_pfp_from_common_0_value_bound. fom_gap_pfp_from_common_0_value_bound + S (fom_value_pfp_from_common_0) = p))) -> (forall fom_index_pfp_from_common_1. (exists fom_gap_pfp_from_common_1_index_bound. fom_gap_pfp_from_common_1_index_bound + S (fom_index_pfp_from_common_1) = M) -> exists fom_value_pfp_from_common_1. ((((exists fom_beta_height_pfp_from_common_1_entry. fom_beta_height_pfp_from_common_1_entry + S (fom_value_pfp_from_common_1) = S ((S (fom_index_pfp_from_common_1)) * bc)) /\ exists fom_beta_quotient_pfp_from_common_1_entry. bb = fom_beta_quotient_pfp_from_common_1_entry * S ((S (fom_index_pfp_from_common_1)) * bc) + (fom_value_pfp_from_common_1))) /\ (exists fom_gap_pfp_from_common_1_value_bound. fom_gap_pfp_from_common_1_value_bound + S (fom_value_pfp_from_common_1) = p))) -> (forall fom_index_pfp_from_common_2. (exists fom_gap_pfp_from_common_2_index_bound. fom_gap_pfp_from_common_2_index_bound + S (fom_index_pfp_from_common_2) = N) -> exists fom_value_pfp_from_common_2. ((((exists fom_beta_height_pfp_from_common_2_entry. fom_beta_height_pfp_from_common_2_entry + S (fom_value_pfp_from_common_2) = S ((S (fom_index_pfp_from_common_2)) * rc)) /\ exists fom_beta_quotient_pfp_from_common_2_entry. rb = fom_beta_quotient_pfp_from_common_2_entry * S ((S (fom_index_pfp_from_common_2)) * rc) + (fom_value_pfp_from_common_2))) /\ (exists fom_gap_pfp_from_common_2_value_bound. fom_gap_pfp_from_common_2_value_bound + S (fom_value_pfp_from_common_2) = p))) -> (((forall pfrep_power_from_common_reps_left pfrep_left_from_common_reps_left pfrep_right_from_common_reps_left. ((exists pfrep_position_from_common_reps_leftfirst. ((pfrep_position_from_common_reps_leftfirst+S (pfrep_power_from_common_reps_left)=(L)) /\ ((((exists ff_h_pfp_from_common_reps_leftfirstentry. ff_h_pfp_from_common_reps_leftfirstentry + S (pfrep_left_from_common_reps_left) = S ((S (pfrep_position_from_common_reps_leftfirst)) * ac)) /\ exists ff_q_pfp_from_common_reps_leftfirstentry. ab = ff_q_pfp_from_common_reps_leftfirstentry * S ((S (pfrep_position_from_common_reps_leftfirst)) * ac) + (pfrep_left_from_common_reps_left)))))) \/ (((exists pfrep_gap_from_common_reps_leftfirstoutside. pfrep_gap_from_common_reps_leftfirstoutside+(L)=(pfrep_power_from_common_reps_left)) /\ (((pfrep_left_from_common_reps_left)=0))))) -> ((exists pfrep_position_from_common_reps_leftsecond. ((pfrep_position_from_common_reps_leftsecond+S (pfrep_power_from_common_reps_left)=(K)) /\ ((((exists ff_h_pfp_from_common_reps_leftsecondentry. ff_h_pfp_from_common_reps_leftsecondentry + S (pfrep_right_from_common_reps_left) = S ((S (pfrep_position_from_common_reps_leftsecond)) * uc)) /\ exists ff_q_pfp_from_common_reps_leftsecondentry. ub = ff_q_pfp_from_common_reps_leftsecondentry * S ((S (pfrep_position_from_common_reps_leftsecond)) * uc) + (pfrep_right_from_common_reps_left)))))) \/ (((exists pfrep_gap_from_common_reps_leftsecondoutside. pfrep_gap_from_common_reps_leftsecondoutside+(K)=(pfrep_power_from_common_reps_left)) /\ (((pfrep_right_from_common_reps_left)=0))))) -> pfrep_left_from_common_reps_left=pfrep_right_from_common_reps_left) /\ ((forall pfrep_power_from_common_reps_right pfrep_left_from_common_reps_right pfrep_right_from_common_reps_right. ((exists pfrep_position_from_common_reps_rightfirst. ((pfrep_position_from_common_reps_rightfirst+S (pfrep_power_from_common_reps_right)=(M)) /\ ((((exists ff_h_pfp_from_common_reps_rightfirstentry. ff_h_pfp_from_common_reps_rightfirstentry + S (pfrep_left_from_common_reps_right) = S ((S (pfrep_position_from_common_reps_rightfirst)) * bc)) /\ exists ff_q_pfp_from_common_reps_rightfirstentry. bb = ff_q_pfp_from_common_reps_rightfirstentry * S ((S (pfrep_position_from_common_reps_rightfirst)) * bc) + (pfrep_left_from_common_reps_right)))))) \/ (((exists pfrep_gap_from_common_reps_rightfirstoutside. pfrep_gap_from_common_reps_rightfirstoutside+(M)=(pfrep_power_from_common_reps_right)) /\ (((pfrep_left_from_common_reps_right)=0))))) -> ((exists pfrep_position_from_common_reps_rightsecond. ((pfrep_position_from_common_reps_rightsecond+S (pfrep_power_from_common_reps_right)=(K)) /\ ((((exists ff_h_pfp_from_common_reps_rightsecondentry. ff_h_pfp_from_common_reps_rightsecondentry + S (pfrep_right_from_common_reps_right) = S ((S (pfrep_position_from_common_reps_rightsecond)) * vc)) /\ exists ff_q_pfp_from_common_reps_rightsecondentry. vb = ff_q_pfp_from_common_reps_rightsecondentry * S ((S (pfrep_position_from_common_reps_rightsecond)) * vc) + (pfrep_right_from_common_reps_right)))))) \/ (((exists pfrep_gap_from_common_reps_rightsecondoutside. pfrep_gap_from_common_reps_rightsecondoutside+(K)=(pfrep_power_from_common_reps_right)) /\ (((pfrep_right_from_common_reps_right)=0))))) -> pfrep_left_from_common_reps_right=pfrep_right_from_common_reps_right)))) -> (forall pfp_index_from_common_sum. (exists pfa_gap_from_common_sumindex. pfa_gap_from_common_sumindex + S (pfp_index_from_common_sum) = (K)) -> exists pfp_left_from_common_sum pfp_right_from_common_sum pfp_value_from_common_sum. ((((exists ff_h_pfp_from_common_sumleft. ff_h_pfp_from_common_sumleft + S (pfp_left_from_common_sum) = S ((S (pfp_index_from_common_sum)) * uc)) /\ exists ff_q_pfp_from_common_sumleft. ub = ff_q_pfp_from_common_sumleft * S ((S (pfp_index_from_common_sum)) * uc) + (pfp_left_from_common_sum))) /\ (((((exists ff_h_pfp_from_common_sumright. ff_h_pfp_from_common_sumright + S (pfp_right_from_common_sum) = S ((S (pfp_index_from_common_sum)) * vc)) /\ exists ff_q_pfp_from_common_sumright. vb = ff_q_pfp_from_common_sumright * S ((S (pfp_index_from_common_sum)) * vc) + (pfp_right_from_common_sum))) /\ (((((exists ff_h_pfp_from_common_sumtarget. ff_h_pfp_from_common_sumtarget + S (pfp_value_from_common_sum) = S ((S (pfp_index_from_common_sum)) * tc)) /\ exists ff_q_pfp_from_common_sumtarget. tb = ff_q_pfp_from_common_sumtarget * S ((S (pfp_index_from_common_sum)) * tc) + (pfp_value_from_common_sum))) /\ ((((exists pfa_gap_from_common_sumoperationleft. pfa_gap_from_common_sumoperationleft + S (pfp_left_from_common_sum) = (p)) /\ (((exists pfa_gap_from_common_sumoperationright. pfa_gap_from_common_sumoperationright + S (pfp_right_from_common_sum) = (p)) /\ ((((exists pfa_gap_from_common_sumoperationresultbound. pfa_gap_from_common_sumoperationresultbound + S (pfp_value_from_common_sum) = (p)) /\ ((exists pfa_offset_left_from_common_sumoperationresultcongruence pfa_offset_right_from_common_sumoperationresultcongruence. ((pfp_left_from_common_sum) + (pfp_right_from_common_sum)) + (p) * pfa_offset_left_from_common_sumoperationresultcongruence = (pfp_value_from_common_sum) + (p) * pfa_offset_right_from_common_sumoperationresultcongruence)))))))))))))))) -> (forall pfrep_power_from_common_output pfrep_left_from_common_output pfrep_right_from_common_output. ((exists pfrep_position_from_common_outputfirst. ((pfrep_position_from_common_outputfirst+S (pfrep_power_from_common_output)=(K)) /\ ((((exists ff_h_pfp_from_common_outputfirstentry. ff_h_pfp_from_common_outputfirstentry + S (pfrep_left_from_common_output) = S ((S (pfrep_position_from_common_outputfirst)) * tc)) /\ exists ff_q_pfp_from_common_outputfirstentry. tb = ff_q_pfp_from_common_outputfirstentry * S ((S (pfrep_position_from_common_outputfirst)) * tc) + (pfrep_left_from_common_output)))))) \/ (((exists pfrep_gap_from_common_outputfirstoutside. pfrep_gap_from_common_outputfirstoutside+(K)=(pfrep_power_from_common_output)) /\ (((pfrep_left_from_common_output)=0))))) -> ((exists pfrep_position_from_common_outputsecond. ((pfrep_position_from_common_outputsecond+S (pfrep_power_from_common_output)=(N)) /\ ((((exists ff_h_pfp_from_common_outputsecondentry. ff_h_pfp_from_common_outputsecondentry + S (pfrep_right_from_common_output) = S ((S (pfrep_position_from_common_outputsecond)) * rc)) /\ exists ff_q_pfp_from_common_outputsecondentry. rb = ff_q_pfp_from_common_outputsecondentry * S ((S (pfrep_position_from_common_outputsecond)) * rc) + (pfrep_right_from_common_output)))))) \/ (((exists pfrep_gap_from_common_outputsecondoutside. pfrep_gap_from_common_outputsecondoutside+(N)=(pfrep_power_from_common_output)) /\ (((pfrep_right_from_common_output)=0))))) -> pfrep_left_from_common_output=pfrep_right_from_common_output) -> (((forall fom_index_pfp_from_common_result_left_bounded. (exists fom_gap_pfp_from_common_result_left_bounded_index_bound. fom_gap_pfp_from_common_result_left_bounded_index_bound + S (fom_index_pfp_from_common_result_left_bounded) = L) -> exists fom_value_pfp_from_common_result_left_bounded. ((((exists fom_beta_height_pfp_from_common_result_left_bounded_entry. fom_beta_height_pfp_from_common_result_left_bounded_entry + S (fom_value_pfp_from_common_result_left_bounded) = S ((S (fom_index_pfp_from_common_result_left_bounded)) * ac)) /\ exists fom_beta_quotient_pfp_from_common_result_left_bounded_entry. ab = fom_beta_quotient_pfp_from_common_result_left_bounded_entry * S ((S (fom_index_pfp_from_common_result_left_bounded)) * ac) + (fom_value_pfp_from_common_result_left_bounded))) /\ (exists fom_gap_pfp_from_common_result_left_bounded_value_bound. fom_gap_pfp_from_common_result_left_bounded_value_bound + S (fom_value_pfp_from_common_result_left_bounded) = p))) /\ (((forall fom_index_pfp_from_common_result_right_bounded. (exists fom_gap_pfp_from_common_result_right_bounded_index_bound. fom_gap_pfp_from_common_result_right_bounded_index_bound + S (fom_index_pfp_from_common_result_right_bounded) = M) -> exists fom_value_pfp_from_common_result_right_bounded. ((((exists fom_beta_height_pfp_from_common_result_right_bounded_entry. fom_beta_height_pfp_from_common_result_right_bounded_entry + S (fom_value_pfp_from_common_result_right_bounded) = S ((S (fom_index_pfp_from_common_result_right_bounded)) * bc)) /\ exists fom_beta_quotient_pfp_from_common_result_right_bounded_entry. bb = fom_beta_quotient_pfp_from_common_result_right_bounded_entry * S ((S (fom_index_pfp_from_common_result_right_bounded)) * bc) + (fom_value_pfp_from_common_result_right_bounded))) /\ (exists fom_gap_pfp_from_common_result_right_bounded_value_bound. fom_gap_pfp_from_common_result_right_bounded_value_bound + S (fom_value_pfp_from_common_result_right_bounded) = p))) /\ (((forall fom_index_pfp_from_common_result_result_bounded. (exists fom_gap_pfp_from_common_result_result_bounded_index_bound. fom_gap_pfp_from_common_result_result_bounded_index_bound + S (fom_index_pfp_from_common_result_result_bounded) = N) -> exists fom_value_pfp_from_common_result_result_bounded. ((((exists fom_beta_height_pfp_from_common_result_result_bounded_entry. fom_beta_height_pfp_from_common_result_result_bounded_entry + S (fom_value_pfp_from_common_result_result_bounded) = S ((S (fom_index_pfp_from_common_result_result_bounded)) * rc)) /\ exists fom_beta_quotient_pfp_from_common_result_result_bounded_entry. rb = fom_beta_quotient_pfp_from_common_result_result_bounded_entry * S ((S (fom_index_pfp_from_common_result_result_bounded)) * rc) + (fom_value_pfp_from_common_result_result_bounded))) /\ (exists fom_gap_pfp_from_common_result_result_bounded_value_bound. fom_gap_pfp_from_common_result_result_bounded_value_bound + S (fom_value_pfp_from_common_result_result_bounded) = p))) /\ ((exists pfaa_left_b_from_common_result pfaa_left_c_from_common_result pfaa_right_b_from_common_result pfaa_right_c_from_common_result pfaa_sum_b_from_common_result pfaa_sum_c_from_common_result pfaa_length_from_common_result. ((((forall pfrep_power_from_common_result_witness_common_left pfrep_left_from_common_result_witness_common_left pfrep_right_from_common_result_witness_common_left. ((exists pfrep_position_from_common_result_witness_common_leftfirst. ((pfrep_position_from_common_result_witness_common_leftfirst+S (pfrep_power_from_common_result_witness_common_left)=(L)) /\ ((((exists ff_h_pfp_from_common_result_witness_common_leftfirstentry. ff_h_pfp_from_common_result_witness_common_leftfirstentry + S (pfrep_left_from_common_result_witness_common_left) = S ((S (pfrep_position_from_common_result_witness_common_leftfirst)) * ac)) /\ exists ff_q_pfp_from_common_result_witness_common_leftfirstentry. ab = ff_q_pfp_from_common_result_witness_common_leftfirstentry * S ((S (pfrep_position_from_common_result_witness_common_leftfirst)) * ac) + (pfrep_left_from_common_result_witness_common_left)))))) \/ (((exists pfrep_gap_from_common_result_witness_common_leftfirstoutside. pfrep_gap_from_common_result_witness_common_leftfirstoutside+(L)=(pfrep_power_from_common_result_witness_common_left)) /\ (((pfrep_left_from_common_result_witness_common_left)=0))))) -> ((exists pfrep_position_from_common_result_witness_common_leftsecond. ((pfrep_position_from_common_result_witness_common_leftsecond+S (pfrep_power_from_common_result_witness_common_left)=(pfaa_length_from_common_result)) /\ ((((exists ff_h_pfp_from_common_result_witness_common_leftsecondentry. ff_h_pfp_from_common_result_witness_common_leftsecondentry + S (pfrep_right_from_common_result_witness_common_left) = S ((S (pfrep_position_from_common_result_witness_common_leftsecond)) * pfaa_left_c_from_common_result)) /\ exists ff_q_pfp_from_common_result_witness_common_leftsecondentry. pfaa_left_b_from_common_result = ff_q_pfp_from_common_result_witness_common_leftsecondentry * S ((S (pfrep_position_from_common_result_witness_common_leftsecond)) * pfaa_left_c_from_common_result) + (pfrep_right_from_common_result_witness_common_left)))))) \/ (((exists pfrep_gap_from_common_result_witness_common_leftsecondoutside. pfrep_gap_from_common_result_witness_common_leftsecondoutside+(pfaa_length_from_common_result)=(pfrep_power_from_common_result_witness_common_left)) /\ (((pfrep_right_from_common_result_witness_common_left)=0))))) -> pfrep_left_from_common_result_witness_common_left=pfrep_right_from_common_result_witness_common_left) /\ ((forall pfrep_power_from_common_result_witness_common_right pfrep_left_from_common_result_witness_common_right pfrep_right_from_common_result_witness_common_right. ((exists pfrep_position_from_common_result_witness_common_rightfirst. ((pfrep_position_from_common_result_witness_common_rightfirst+S (pfrep_power_from_common_result_witness_common_right)=(M)) /\ ((((exists ff_h_pfp_from_common_result_witness_common_rightfirstentry. ff_h_pfp_from_common_result_witness_common_rightfirstentry + S (pfrep_left_from_common_result_witness_common_right) = S ((S (pfrep_position_from_common_result_witness_common_rightfirst)) * bc)) /\ exists ff_q_pfp_from_common_result_witness_common_rightfirstentry. bb = ff_q_pfp_from_common_result_witness_common_rightfirstentry * S ((S (pfrep_position_from_common_result_witness_common_rightfirst)) * bc) + (pfrep_left_from_common_result_witness_common_right)))))) \/ (((exists pfrep_gap_from_common_result_witness_common_rightfirstoutside. pfrep_gap_from_common_result_witness_common_rightfirstoutside+(M)=(pfrep_power_from_common_result_witness_common_right)) /\ (((pfrep_left_from_common_result_witness_common_right)=0))))) -> ((exists pfrep_position_from_common_result_witness_common_rightsecond. ((pfrep_position_from_common_result_witness_common_rightsecond+S (pfrep_power_from_common_result_witness_common_right)=(pfaa_length_from_common_result)) /\ ((((exists ff_h_pfp_from_common_result_witness_common_rightsecondentry. ff_h_pfp_from_common_result_witness_common_rightsecondentry + S (pfrep_right_from_common_result_witness_common_right) = S ((S (pfrep_position_from_common_result_witness_common_rightsecond)) * pfaa_right_c_from_common_result)) /\ exists ff_q_pfp_from_common_result_witness_common_rightsecondentry. pfaa_right_b_from_common_result = ff_q_pfp_from_common_result_witness_common_rightsecondentry * S ((S (pfrep_position_from_common_result_witness_common_rightsecond)) * pfaa_right_c_from_common_result) + (pfrep_right_from_common_result_witness_common_right)))))) \/ (((exists pfrep_gap_from_common_result_witness_common_rightsecondoutside. pfrep_gap_from_common_result_witness_common_rightsecondoutside+(pfaa_length_from_common_result)=(pfrep_power_from_common_result_witness_common_right)) /\ (((pfrep_right_from_common_result_witness_common_right)=0))))) -> pfrep_left_from_common_result_witness_common_right=pfrep_right_from_common_result_witness_common_right)))) /\ (((forall pfp_index_from_common_result_witness_operation. (exists pfa_gap_from_common_result_witness_operationindex. pfa_gap_from_common_result_witness_operationindex + S (pfp_index_from_common_result_witness_operation) = (pfaa_length_from_common_result)) -> exists pfp_left_from_common_result_witness_operation pfp_right_from_common_result_witness_operation pfp_value_from_common_result_witness_operation. ((((exists ff_h_pfp_from_common_result_witness_operationleft. ff_h_pfp_from_common_result_witness_operationleft + S (pfp_left_from_common_result_witness_operation) = S ((S (pfp_index_from_common_result_witness_operation)) * pfaa_left_c_from_common_result)) /\ exists ff_q_pfp_from_common_result_witness_operationleft. pfaa_left_b_from_common_result = ff_q_pfp_from_common_result_witness_operationleft * S ((S (pfp_index_from_common_result_witness_operation)) * pfaa_left_c_from_common_result) + (pfp_left_from_common_result_witness_operation))) /\ (((((exists ff_h_pfp_from_common_result_witness_operationright. ff_h_pfp_from_common_result_witness_operationright + S (pfp_right_from_common_result_witness_operation) = S ((S (pfp_index_from_common_result_witness_operation)) * pfaa_right_c_from_common_result)) /\ exists ff_q_pfp_from_common_result_witness_operationright. pfaa_right_b_from_common_result = ff_q_pfp_from_common_result_witness_operationright * S ((S (pfp_index_from_common_result_witness_operation)) * pfaa_right_c_from_common_result) + (pfp_right_from_common_result_witness_operation))) /\ (((((exists ff_h_pfp_from_common_result_witness_operationtarget. ff_h_pfp_from_common_result_witness_operationtarget + S (pfp_value_from_common_result_witness_operation) = S ((S (pfp_index_from_common_result_witness_operation)) * pfaa_sum_c_from_common_result)) /\ exists ff_q_pfp_from_common_result_witness_operationtarget. pfaa_sum_b_from_common_result = ff_q_pfp_from_common_result_witness_operationtarget * S ((S (pfp_index_from_common_result_witness_operation)) * pfaa_sum_c_from_common_result) + (pfp_value_from_common_result_witness_operation))) /\ ((((exists pfa_gap_from_common_result_witness_operationoperationleft. pfa_gap_from_common_result_witness_operationoperationleft + S (pfp_left_from_common_result_witness_operation) = (p)) /\ (((exists pfa_gap_from_common_result_witness_operationoperationright. pfa_gap_from_common_result_witness_operationoperationright + S (pfp_right_from_common_result_witness_operation) = (p)) /\ ((((exists pfa_gap_from_common_result_witness_operationoperationresultbound. pfa_gap_from_common_result_witness_operationoperationresultbound + S (pfp_value_from_common_result_witness_operation) = (p)) /\ ((exists pfa_offset_left_from_common_result_witness_operationoperationresultcongruence pfa_offset_right_from_common_result_witness_operationoperationresultcongruence. ((pfp_left_from_common_result_witness_operation) + (pfp_right_from_common_result_witness_operation)) + (p) * pfa_offset_left_from_common_result_witness_operationoperationresultcongruence = (pfp_value_from_common_result_witness_operation) + (p) * pfa_offset_right_from_common_result_witness_operationoperationresultcongruence)))))))))))))))) /\ ((forall pfrep_power_from_common_result_witness_output pfrep_left_from_common_result_witness_output pfrep_right_from_common_result_witness_output. ((exists pfrep_position_from_common_result_witness_outputfirst. ((pfrep_position_from_common_result_witness_outputfirst+S (pfrep_power_from_common_result_witness_output)=(pfaa_length_from_common_result)) /\ ((((exists ff_h_pfp_from_common_result_witness_outputfirstentry. ff_h_pfp_from_common_result_witness_outputfirstentry + S (pfrep_left_from_common_result_witness_output) = S ((S (pfrep_position_from_common_result_witness_outputfirst)) * pfaa_sum_c_from_common_result)) /\ exists ff_q_pfp_from_common_result_witness_outputfirstentry. pfaa_sum_b_from_common_result = ff_q_pfp_from_common_result_witness_outputfirstentry * S ((S (pfrep_position_from_common_result_witness_outputfirst)) * pfaa_sum_c_from_common_result) + (pfrep_left_from_common_result_witness_output)))))) \/ (((exists pfrep_gap_from_common_result_witness_outputfirstoutside. pfrep_gap_from_common_result_witness_outputfirstoutside+(pfaa_length_from_common_result)=(pfrep_power_from_common_result_witness_output)) /\ (((pfrep_left_from_common_result_witness_output)=0))))) -> ((exists pfrep_position_from_common_result_witness_outputsecond. ((pfrep_position_from_common_result_witness_outputsecond+S (pfrep_power_from_common_result_witness_output)=(N)) /\ ((((exists ff_h_pfp_from_common_result_witness_outputsecondentry. ff_h_pfp_from_common_result_witness_outputsecondentry + S (pfrep_right_from_common_result_witness_output) = S ((S (pfrep_position_from_common_result_witness_outputsecond)) * rc)) /\ exists ff_q_pfp_from_common_result_witness_outputsecondentry. rb = ff_q_pfp_from_common_result_witness_outputsecondentry * S ((S (pfrep_position_from_common_result_witness_outputsecond)) * rc) + (pfrep_right_from_common_result_witness_output)))))) \/ (((exists pfrep_gap_from_common_result_witness_outputsecondoutside. pfrep_gap_from_common_result_witness_outputsecondoutside+(N)=(pfrep_power_from_common_result_witness_output)) /\ (((pfrep_right_from_common_result_witness_output)=0))))) -> pfrep_left_from_common_result_witness_output=pfrep_right_from_common_result_witness_output)))))))))))))