factorial_legendre_successor_agreement

forall p n a b c d f. ((~(p = 1) /\ forall frm_prime_left_blfg_agreement_prime frm_prime_right_blfg_agreement_prime. p = frm_prime_left_blfg_agreement_prime * frm_prime_right_blfg_agreement_prime -> frm_prime_left_blfg_agreement_prime = 1 \/ frm_prime_right_blfg_agreement_prime = 1)) -> (exists bfv_factorial_blfg_agreement_factorial_old. ((exists ff_b_blfg_agreement_factorial_old_factorial ff_c_blfg_agreement_factorial_old_factorial. ((forall ff_i_blfg_agreement_factorial_old_factorial_range. (exists ff_lt_blfg_agreement_factorial_old_factorial_range_bound. ff_lt_blfg_agreement_factorial_old_factorial_range_bound + S ff_i_blfg_agreement_factorial_old_factorial_range = n) -> (((exists ff_h_blfg_agreement_factorial_old_factorial_range_decoded. ff_h_blfg_agreement_factorial_old_factorial_range_decoded + S (1 + ff_i_blfg_agreement_factorial_old_factorial_range) = S ((S (ff_i_blfg_agreement_factorial_old_factorial_range)) * ff_c_blfg_agreement_factorial_old_factorial)) /\ exists ff_q_blfg_agreement_factorial_old_factorial_range_decoded. ff_b_blfg_agreement_factorial_old_factorial = ff_q_blfg_agreement_factorial_old_factorial_range_decoded * S ((S (ff_i_blfg_agreement_factorial_old_factorial_range)) * ff_c_blfg_agreement_factorial_old_factorial) + (1 + ff_i_blfg_agreement_factorial_old_factorial_range)))) /\ (exists ff_u_blfg_agreement_factorial_old_factorial_product ff_v_blfg_agreement_factorial_old_factorial_product. ((((exists ff_h_blfg_agreement_factorial_old_factorial_product_start. ff_h_blfg_agreement_factorial_old_factorial_product_start + S (1) = S ((S (0)) * ff_v_blfg_agreement_factorial_old_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_old_factorial_product_start. ff_u_blfg_agreement_factorial_old_factorial_product = ff_q_blfg_agreement_factorial_old_factorial_product_start * S ((S (0)) * ff_v_blfg_agreement_factorial_old_factorial_product) + (1))) /\ ((((exists ff_h_blfg_agreement_factorial_old_factorial_product_terminal. ff_h_blfg_agreement_factorial_old_factorial_product_terminal + S (bfv_factorial_blfg_agreement_factorial_old) = S ((S (n)) * ff_v_blfg_agreement_factorial_old_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_old_factorial_product_terminal. ff_u_blfg_agreement_factorial_old_factorial_product = ff_q_blfg_agreement_factorial_old_factorial_product_terminal * S ((S (n)) * ff_v_blfg_agreement_factorial_old_factorial_product) + (bfv_factorial_blfg_agreement_factorial_old))) /\ forall ff_i_blfg_agreement_factorial_old_factorial_product. (exists ff_lt_blfg_agreement_factorial_old_factorial_product_bound. ff_lt_blfg_agreement_factorial_old_factorial_product_bound + S ff_i_blfg_agreement_factorial_old_factorial_product = n) -> exists ff_p_blfg_agreement_factorial_old_factorial_product ff_r_blfg_agreement_factorial_old_factorial_product ff_s_blfg_agreement_factorial_old_factorial_product. ((((exists ff_h_blfg_agreement_factorial_old_factorial_product_factor. ff_h_blfg_agreement_factorial_old_factorial_product_factor + S (ff_p_blfg_agreement_factorial_old_factorial_product) = S ((S (ff_i_blfg_agreement_factorial_old_factorial_product)) * ff_c_blfg_agreement_factorial_old_factorial)) /\ exists ff_q_blfg_agreement_factorial_old_factorial_product_factor. ff_b_blfg_agreement_factorial_old_factorial = ff_q_blfg_agreement_factorial_old_factorial_product_factor * S ((S (ff_i_blfg_agreement_factorial_old_factorial_product)) * ff_c_blfg_agreement_factorial_old_factorial) + (ff_p_blfg_agreement_factorial_old_factorial_product))) /\ ((((exists ff_h_blfg_agreement_factorial_old_factorial_product_partial. ff_h_blfg_agreement_factorial_old_factorial_product_partial + S (ff_r_blfg_agreement_factorial_old_factorial_product) = S ((S (ff_i_blfg_agreement_factorial_old_factorial_product)) * ff_v_blfg_agreement_factorial_old_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_old_factorial_product_partial. ff_u_blfg_agreement_factorial_old_factorial_product = ff_q_blfg_agreement_factorial_old_factorial_product_partial * S ((S (ff_i_blfg_agreement_factorial_old_factorial_product)) * ff_v_blfg_agreement_factorial_old_factorial_product) + (ff_r_blfg_agreement_factorial_old_factorial_product))) /\ ((((exists ff_h_blfg_agreement_factorial_old_factorial_product_successor. ff_h_blfg_agreement_factorial_old_factorial_product_successor + S (ff_s_blfg_agreement_factorial_old_factorial_product) = S ((S (S ff_i_blfg_agreement_factorial_old_factorial_product)) * ff_v_blfg_agreement_factorial_old_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_old_factorial_product_successor. ff_u_blfg_agreement_factorial_old_factorial_product = ff_q_blfg_agreement_factorial_old_factorial_product_successor * S ((S (S ff_i_blfg_agreement_factorial_old_factorial_product)) * ff_v_blfg_agreement_factorial_old_factorial_product) + (ff_s_blfg_agreement_factorial_old_factorial_product))) /\ ff_s_blfg_agreement_factorial_old_factorial_product = ff_r_blfg_agreement_factorial_old_factorial_product * ff_p_blfg_agreement_factorial_old_factorial_product)))))))) /\ (((exists bpv_gap_blfg_agreement_factorial_old_valuation_exponent_bound. bpv_gap_blfg_agreement_factorial_old_valuation_exponent_bound + a = bfv_factorial_blfg_agreement_factorial_old) /\ (exists bpv_result_blfg_agreement_factorial_old_valuation_selected. ((exists ff_b_blfg_agreement_factorial_old_valuation_selected_power ff_c_blfg_agreement_factorial_old_valuation_selected_power. ((forall ff_i_blfg_agreement_factorial_old_valuation_selected_power_repeat. (exists ff_lt_blfg_agreement_factorial_old_valuation_selected_power_repeat_bound. ff_lt_blfg_agreement_factorial_old_valuation_selected_power_repeat_bound + S ff_i_blfg_agreement_factorial_old_valuation_selected_power_repeat = a) -> (((exists ff_h_blfg_agreement_factorial_old_valuation_selected_power_repeat_decoded. ff_h_blfg_agreement_factorial_old_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_blfg_agreement_factorial_old_valuation_selected_power_repeat)) * ff_c_blfg_agreement_factorial_old_valuation_selected_power)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_selected_power_repeat_decoded. ff_b_blfg_agreement_factorial_old_valuation_selected_power = ff_q_blfg_agreement_factorial_old_valuation_selected_power_repeat_decoded * S ((S (ff_i_blfg_agreement_factorial_old_valuation_selected_power_repeat)) * ff_c_blfg_agreement_factorial_old_valuation_selected_power) + (p)))) /\ (exists ff_u_blfg_agreement_factorial_old_valuation_selected_power_product ff_v_blfg_agreement_factorial_old_valuation_selected_power_product. ((((exists ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_start. ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_start. ff_u_blfg_agreement_factorial_old_valuation_selected_power_product = ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_start * S ((S (0)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_terminal. ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_terminal + S (bpv_result_blfg_agreement_factorial_old_valuation_selected) = S ((S (a)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_terminal. ff_u_blfg_agreement_factorial_old_valuation_selected_power_product = ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_terminal * S ((S (a)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product) + (bpv_result_blfg_agreement_factorial_old_valuation_selected))) /\ forall ff_i_blfg_agreement_factorial_old_valuation_selected_power_product. (exists ff_lt_blfg_agreement_factorial_old_valuation_selected_power_product_bound. ff_lt_blfg_agreement_factorial_old_valuation_selected_power_product_bound + S ff_i_blfg_agreement_factorial_old_valuation_selected_power_product = a) -> exists ff_p_blfg_agreement_factorial_old_valuation_selected_power_product ff_r_blfg_agreement_factorial_old_valuation_selected_power_product ff_s_blfg_agreement_factorial_old_valuation_selected_power_product. ((((exists ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_factor. ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_factor + S (ff_p_blfg_agreement_factorial_old_valuation_selected_power_product) = S ((S (ff_i_blfg_agreement_factorial_old_valuation_selected_power_product)) * ff_c_blfg_agreement_factorial_old_valuation_selected_power)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_factor. ff_b_blfg_agreement_factorial_old_valuation_selected_power = ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_factor * S ((S (ff_i_blfg_agreement_factorial_old_valuation_selected_power_product)) * ff_c_blfg_agreement_factorial_old_valuation_selected_power) + (ff_p_blfg_agreement_factorial_old_valuation_selected_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_partial. ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_partial + S (ff_r_blfg_agreement_factorial_old_valuation_selected_power_product) = S ((S (ff_i_blfg_agreement_factorial_old_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_partial. ff_u_blfg_agreement_factorial_old_valuation_selected_power_product = ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_partial * S ((S (ff_i_blfg_agreement_factorial_old_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product) + (ff_r_blfg_agreement_factorial_old_valuation_selected_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_successor. ff_h_blfg_agreement_factorial_old_valuation_selected_power_product_successor + S (ff_s_blfg_agreement_factorial_old_valuation_selected_power_product) = S ((S (S ff_i_blfg_agreement_factorial_old_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_successor. ff_u_blfg_agreement_factorial_old_valuation_selected_power_product = ff_q_blfg_agreement_factorial_old_valuation_selected_power_product_successor * S ((S (S ff_i_blfg_agreement_factorial_old_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_selected_power_product) + (ff_s_blfg_agreement_factorial_old_valuation_selected_power_product))) /\ ff_s_blfg_agreement_factorial_old_valuation_selected_power_product = ff_r_blfg_agreement_factorial_old_valuation_selected_power_product * ff_p_blfg_agreement_factorial_old_valuation_selected_power_product)))))))) /\ (exists bpv_factor_blfg_agreement_factorial_old_valuation_selected_divides. bfv_factorial_blfg_agreement_factorial_old = bpv_result_blfg_agreement_factorial_old_valuation_selected * bpv_factor_blfg_agreement_factorial_old_valuation_selected_divides)))) /\ forall bpv_candidate_blfg_agreement_factorial_old_valuation. (exists bpv_gap_blfg_agreement_factorial_old_valuation_candidate_bound. bpv_gap_blfg_agreement_factorial_old_valuation_candidate_bound + bpv_candidate_blfg_agreement_factorial_old_valuation = bfv_factorial_blfg_agreement_factorial_old) -> (exists bpv_result_blfg_agreement_factorial_old_valuation_candidate. ((exists ff_b_blfg_agreement_factorial_old_valuation_candidate_power ff_c_blfg_agreement_factorial_old_valuation_candidate_power. ((forall ff_i_blfg_agreement_factorial_old_valuation_candidate_power_repeat. (exists ff_lt_blfg_agreement_factorial_old_valuation_candidate_power_repeat_bound. ff_lt_blfg_agreement_factorial_old_valuation_candidate_power_repeat_bound + S ff_i_blfg_agreement_factorial_old_valuation_candidate_power_repeat = bpv_candidate_blfg_agreement_factorial_old_valuation) -> (((exists ff_h_blfg_agreement_factorial_old_valuation_candidate_power_repeat_decoded. ff_h_blfg_agreement_factorial_old_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_blfg_agreement_factorial_old_valuation_candidate_power_repeat)) * ff_c_blfg_agreement_factorial_old_valuation_candidate_power)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_candidate_power_repeat_decoded. ff_b_blfg_agreement_factorial_old_valuation_candidate_power = ff_q_blfg_agreement_factorial_old_valuation_candidate_power_repeat_decoded * S ((S (ff_i_blfg_agreement_factorial_old_valuation_candidate_power_repeat)) * ff_c_blfg_agreement_factorial_old_valuation_candidate_power) + (p)))) /\ (exists ff_u_blfg_agreement_factorial_old_valuation_candidate_power_product ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product. ((((exists ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_start. ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_start. ff_u_blfg_agreement_factorial_old_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_start * S ((S (0)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_terminal. ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_terminal + S (bpv_result_blfg_agreement_factorial_old_valuation_candidate) = S ((S (bpv_candidate_blfg_agreement_factorial_old_valuation)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_terminal. ff_u_blfg_agreement_factorial_old_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_blfg_agreement_factorial_old_valuation)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product) + (bpv_result_blfg_agreement_factorial_old_valuation_candidate))) /\ forall ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product. (exists ff_lt_blfg_agreement_factorial_old_valuation_candidate_power_product_bound. ff_lt_blfg_agreement_factorial_old_valuation_candidate_power_product_bound + S ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product = bpv_candidate_blfg_agreement_factorial_old_valuation) -> exists ff_p_blfg_agreement_factorial_old_valuation_candidate_power_product ff_r_blfg_agreement_factorial_old_valuation_candidate_power_product ff_s_blfg_agreement_factorial_old_valuation_candidate_power_product. ((((exists ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_factor. ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_factor + S (ff_p_blfg_agreement_factorial_old_valuation_candidate_power_product) = S ((S (ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product)) * ff_c_blfg_agreement_factorial_old_valuation_candidate_power)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_factor. ff_b_blfg_agreement_factorial_old_valuation_candidate_power = ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_factor * S ((S (ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product)) * ff_c_blfg_agreement_factorial_old_valuation_candidate_power) + (ff_p_blfg_agreement_factorial_old_valuation_candidate_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_partial. ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_partial + S (ff_r_blfg_agreement_factorial_old_valuation_candidate_power_product) = S ((S (ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_partial. ff_u_blfg_agreement_factorial_old_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_partial * S ((S (ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product) + (ff_r_blfg_agreement_factorial_old_valuation_candidate_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_successor. ff_h_blfg_agreement_factorial_old_valuation_candidate_power_product_successor + S (ff_s_blfg_agreement_factorial_old_valuation_candidate_power_product) = S ((S (S ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_successor. ff_u_blfg_agreement_factorial_old_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_old_valuation_candidate_power_product_successor * S ((S (S ff_i_blfg_agreement_factorial_old_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_old_valuation_candidate_power_product) + (ff_s_blfg_agreement_factorial_old_valuation_candidate_power_product))) /\ ff_s_blfg_agreement_factorial_old_valuation_candidate_power_product = ff_r_blfg_agreement_factorial_old_valuation_candidate_power_product * ff_p_blfg_agreement_factorial_old_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_blfg_agreement_factorial_old_valuation_candidate_divides. bfv_factorial_blfg_agreement_factorial_old = bpv_result_blfg_agreement_factorial_old_valuation_candidate * bpv_factor_blfg_agreement_factorial_old_valuation_candidate_divides))) -> (exists bpv_gap_blfg_agreement_factorial_old_valuation_maximal. bpv_gap_blfg_agreement_factorial_old_valuation_maximal + bpv_candidate_blfg_agreement_factorial_old_valuation = a)))) -> (exists blfg_factorial_blfg_agreement_factorial_new. ((exists ff_b_blfg_agreement_factorial_new_factorial ff_c_blfg_agreement_factorial_new_factorial. ((forall ff_i_blfg_agreement_factorial_new_factorial_range. (exists ff_lt_blfg_agreement_factorial_new_factorial_range_bound. ff_lt_blfg_agreement_factorial_new_factorial_range_bound + S ff_i_blfg_agreement_factorial_new_factorial_range = S n) -> (((exists ff_h_blfg_agreement_factorial_new_factorial_range_decoded. ff_h_blfg_agreement_factorial_new_factorial_range_decoded + S (1 + ff_i_blfg_agreement_factorial_new_factorial_range) = S ((S (ff_i_blfg_agreement_factorial_new_factorial_range)) * ff_c_blfg_agreement_factorial_new_factorial)) /\ exists ff_q_blfg_agreement_factorial_new_factorial_range_decoded. ff_b_blfg_agreement_factorial_new_factorial = ff_q_blfg_agreement_factorial_new_factorial_range_decoded * S ((S (ff_i_blfg_agreement_factorial_new_factorial_range)) * ff_c_blfg_agreement_factorial_new_factorial) + (1 + ff_i_blfg_agreement_factorial_new_factorial_range)))) /\ (exists ff_u_blfg_agreement_factorial_new_factorial_product ff_v_blfg_agreement_factorial_new_factorial_product. ((((exists ff_h_blfg_agreement_factorial_new_factorial_product_start. ff_h_blfg_agreement_factorial_new_factorial_product_start + S (1) = S ((S (0)) * ff_v_blfg_agreement_factorial_new_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_new_factorial_product_start. ff_u_blfg_agreement_factorial_new_factorial_product = ff_q_blfg_agreement_factorial_new_factorial_product_start * S ((S (0)) * ff_v_blfg_agreement_factorial_new_factorial_product) + (1))) /\ ((((exists ff_h_blfg_agreement_factorial_new_factorial_product_terminal. ff_h_blfg_agreement_factorial_new_factorial_product_terminal + S (blfg_factorial_blfg_agreement_factorial_new) = S ((S (S n)) * ff_v_blfg_agreement_factorial_new_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_new_factorial_product_terminal. ff_u_blfg_agreement_factorial_new_factorial_product = ff_q_blfg_agreement_factorial_new_factorial_product_terminal * S ((S (S n)) * ff_v_blfg_agreement_factorial_new_factorial_product) + (blfg_factorial_blfg_agreement_factorial_new))) /\ forall ff_i_blfg_agreement_factorial_new_factorial_product. (exists ff_lt_blfg_agreement_factorial_new_factorial_product_bound. ff_lt_blfg_agreement_factorial_new_factorial_product_bound + S ff_i_blfg_agreement_factorial_new_factorial_product = S n) -> exists ff_p_blfg_agreement_factorial_new_factorial_product ff_r_blfg_agreement_factorial_new_factorial_product ff_s_blfg_agreement_factorial_new_factorial_product. ((((exists ff_h_blfg_agreement_factorial_new_factorial_product_factor. ff_h_blfg_agreement_factorial_new_factorial_product_factor + S (ff_p_blfg_agreement_factorial_new_factorial_product) = S ((S (ff_i_blfg_agreement_factorial_new_factorial_product)) * ff_c_blfg_agreement_factorial_new_factorial)) /\ exists ff_q_blfg_agreement_factorial_new_factorial_product_factor. ff_b_blfg_agreement_factorial_new_factorial = ff_q_blfg_agreement_factorial_new_factorial_product_factor * S ((S (ff_i_blfg_agreement_factorial_new_factorial_product)) * ff_c_blfg_agreement_factorial_new_factorial) + (ff_p_blfg_agreement_factorial_new_factorial_product))) /\ ((((exists ff_h_blfg_agreement_factorial_new_factorial_product_partial. ff_h_blfg_agreement_factorial_new_factorial_product_partial + S (ff_r_blfg_agreement_factorial_new_factorial_product) = S ((S (ff_i_blfg_agreement_factorial_new_factorial_product)) * ff_v_blfg_agreement_factorial_new_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_new_factorial_product_partial. ff_u_blfg_agreement_factorial_new_factorial_product = ff_q_blfg_agreement_factorial_new_factorial_product_partial * S ((S (ff_i_blfg_agreement_factorial_new_factorial_product)) * ff_v_blfg_agreement_factorial_new_factorial_product) + (ff_r_blfg_agreement_factorial_new_factorial_product))) /\ ((((exists ff_h_blfg_agreement_factorial_new_factorial_product_successor. ff_h_blfg_agreement_factorial_new_factorial_product_successor + S (ff_s_blfg_agreement_factorial_new_factorial_product) = S ((S (S ff_i_blfg_agreement_factorial_new_factorial_product)) * ff_v_blfg_agreement_factorial_new_factorial_product)) /\ exists ff_q_blfg_agreement_factorial_new_factorial_product_successor. ff_u_blfg_agreement_factorial_new_factorial_product = ff_q_blfg_agreement_factorial_new_factorial_product_successor * S ((S (S ff_i_blfg_agreement_factorial_new_factorial_product)) * ff_v_blfg_agreement_factorial_new_factorial_product) + (ff_s_blfg_agreement_factorial_new_factorial_product))) /\ ff_s_blfg_agreement_factorial_new_factorial_product = ff_r_blfg_agreement_factorial_new_factorial_product * ff_p_blfg_agreement_factorial_new_factorial_product)))))))) /\ (((exists bpv_gap_blfg_agreement_factorial_new_valuation_exponent_bound. bpv_gap_blfg_agreement_factorial_new_valuation_exponent_bound + b = blfg_factorial_blfg_agreement_factorial_new) /\ (exists bpv_result_blfg_agreement_factorial_new_valuation_selected. ((exists ff_b_blfg_agreement_factorial_new_valuation_selected_power ff_c_blfg_agreement_factorial_new_valuation_selected_power. ((forall ff_i_blfg_agreement_factorial_new_valuation_selected_power_repeat. (exists ff_lt_blfg_agreement_factorial_new_valuation_selected_power_repeat_bound. ff_lt_blfg_agreement_factorial_new_valuation_selected_power_repeat_bound + S ff_i_blfg_agreement_factorial_new_valuation_selected_power_repeat = b) -> (((exists ff_h_blfg_agreement_factorial_new_valuation_selected_power_repeat_decoded. ff_h_blfg_agreement_factorial_new_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_blfg_agreement_factorial_new_valuation_selected_power_repeat)) * ff_c_blfg_agreement_factorial_new_valuation_selected_power)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_selected_power_repeat_decoded. ff_b_blfg_agreement_factorial_new_valuation_selected_power = ff_q_blfg_agreement_factorial_new_valuation_selected_power_repeat_decoded * S ((S (ff_i_blfg_agreement_factorial_new_valuation_selected_power_repeat)) * ff_c_blfg_agreement_factorial_new_valuation_selected_power) + (p)))) /\ (exists ff_u_blfg_agreement_factorial_new_valuation_selected_power_product ff_v_blfg_agreement_factorial_new_valuation_selected_power_product. ((((exists ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_start. ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_start. ff_u_blfg_agreement_factorial_new_valuation_selected_power_product = ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_start * S ((S (0)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_terminal. ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_terminal + S (bpv_result_blfg_agreement_factorial_new_valuation_selected) = S ((S (b)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_terminal. ff_u_blfg_agreement_factorial_new_valuation_selected_power_product = ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_terminal * S ((S (b)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product) + (bpv_result_blfg_agreement_factorial_new_valuation_selected))) /\ forall ff_i_blfg_agreement_factorial_new_valuation_selected_power_product. (exists ff_lt_blfg_agreement_factorial_new_valuation_selected_power_product_bound. ff_lt_blfg_agreement_factorial_new_valuation_selected_power_product_bound + S ff_i_blfg_agreement_factorial_new_valuation_selected_power_product = b) -> exists ff_p_blfg_agreement_factorial_new_valuation_selected_power_product ff_r_blfg_agreement_factorial_new_valuation_selected_power_product ff_s_blfg_agreement_factorial_new_valuation_selected_power_product. ((((exists ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_factor. ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_factor + S (ff_p_blfg_agreement_factorial_new_valuation_selected_power_product) = S ((S (ff_i_blfg_agreement_factorial_new_valuation_selected_power_product)) * ff_c_blfg_agreement_factorial_new_valuation_selected_power)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_factor. ff_b_blfg_agreement_factorial_new_valuation_selected_power = ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_factor * S ((S (ff_i_blfg_agreement_factorial_new_valuation_selected_power_product)) * ff_c_blfg_agreement_factorial_new_valuation_selected_power) + (ff_p_blfg_agreement_factorial_new_valuation_selected_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_partial. ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_partial + S (ff_r_blfg_agreement_factorial_new_valuation_selected_power_product) = S ((S (ff_i_blfg_agreement_factorial_new_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_partial. ff_u_blfg_agreement_factorial_new_valuation_selected_power_product = ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_partial * S ((S (ff_i_blfg_agreement_factorial_new_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product) + (ff_r_blfg_agreement_factorial_new_valuation_selected_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_successor. ff_h_blfg_agreement_factorial_new_valuation_selected_power_product_successor + S (ff_s_blfg_agreement_factorial_new_valuation_selected_power_product) = S ((S (S ff_i_blfg_agreement_factorial_new_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_successor. ff_u_blfg_agreement_factorial_new_valuation_selected_power_product = ff_q_blfg_agreement_factorial_new_valuation_selected_power_product_successor * S ((S (S ff_i_blfg_agreement_factorial_new_valuation_selected_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_selected_power_product) + (ff_s_blfg_agreement_factorial_new_valuation_selected_power_product))) /\ ff_s_blfg_agreement_factorial_new_valuation_selected_power_product = ff_r_blfg_agreement_factorial_new_valuation_selected_power_product * ff_p_blfg_agreement_factorial_new_valuation_selected_power_product)))))))) /\ (exists bpv_factor_blfg_agreement_factorial_new_valuation_selected_divides. blfg_factorial_blfg_agreement_factorial_new = bpv_result_blfg_agreement_factorial_new_valuation_selected * bpv_factor_blfg_agreement_factorial_new_valuation_selected_divides)))) /\ forall bpv_candidate_blfg_agreement_factorial_new_valuation. (exists bpv_gap_blfg_agreement_factorial_new_valuation_candidate_bound. bpv_gap_blfg_agreement_factorial_new_valuation_candidate_bound + bpv_candidate_blfg_agreement_factorial_new_valuation = blfg_factorial_blfg_agreement_factorial_new) -> (exists bpv_result_blfg_agreement_factorial_new_valuation_candidate. ((exists ff_b_blfg_agreement_factorial_new_valuation_candidate_power ff_c_blfg_agreement_factorial_new_valuation_candidate_power. ((forall ff_i_blfg_agreement_factorial_new_valuation_candidate_power_repeat. (exists ff_lt_blfg_agreement_factorial_new_valuation_candidate_power_repeat_bound. ff_lt_blfg_agreement_factorial_new_valuation_candidate_power_repeat_bound + S ff_i_blfg_agreement_factorial_new_valuation_candidate_power_repeat = bpv_candidate_blfg_agreement_factorial_new_valuation) -> (((exists ff_h_blfg_agreement_factorial_new_valuation_candidate_power_repeat_decoded. ff_h_blfg_agreement_factorial_new_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_blfg_agreement_factorial_new_valuation_candidate_power_repeat)) * ff_c_blfg_agreement_factorial_new_valuation_candidate_power)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_candidate_power_repeat_decoded. ff_b_blfg_agreement_factorial_new_valuation_candidate_power = ff_q_blfg_agreement_factorial_new_valuation_candidate_power_repeat_decoded * S ((S (ff_i_blfg_agreement_factorial_new_valuation_candidate_power_repeat)) * ff_c_blfg_agreement_factorial_new_valuation_candidate_power) + (p)))) /\ (exists ff_u_blfg_agreement_factorial_new_valuation_candidate_power_product ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product. ((((exists ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_start. ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_start. ff_u_blfg_agreement_factorial_new_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_start * S ((S (0)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_terminal. ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_terminal + S (bpv_result_blfg_agreement_factorial_new_valuation_candidate) = S ((S (bpv_candidate_blfg_agreement_factorial_new_valuation)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_terminal. ff_u_blfg_agreement_factorial_new_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_blfg_agreement_factorial_new_valuation)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product) + (bpv_result_blfg_agreement_factorial_new_valuation_candidate))) /\ forall ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product. (exists ff_lt_blfg_agreement_factorial_new_valuation_candidate_power_product_bound. ff_lt_blfg_agreement_factorial_new_valuation_candidate_power_product_bound + S ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product = bpv_candidate_blfg_agreement_factorial_new_valuation) -> exists ff_p_blfg_agreement_factorial_new_valuation_candidate_power_product ff_r_blfg_agreement_factorial_new_valuation_candidate_power_product ff_s_blfg_agreement_factorial_new_valuation_candidate_power_product. ((((exists ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_factor. ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_factor + S (ff_p_blfg_agreement_factorial_new_valuation_candidate_power_product) = S ((S (ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product)) * ff_c_blfg_agreement_factorial_new_valuation_candidate_power)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_factor. ff_b_blfg_agreement_factorial_new_valuation_candidate_power = ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_factor * S ((S (ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product)) * ff_c_blfg_agreement_factorial_new_valuation_candidate_power) + (ff_p_blfg_agreement_factorial_new_valuation_candidate_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_partial. ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_partial + S (ff_r_blfg_agreement_factorial_new_valuation_candidate_power_product) = S ((S (ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_partial. ff_u_blfg_agreement_factorial_new_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_partial * S ((S (ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product) + (ff_r_blfg_agreement_factorial_new_valuation_candidate_power_product))) /\ ((((exists ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_successor. ff_h_blfg_agreement_factorial_new_valuation_candidate_power_product_successor + S (ff_s_blfg_agreement_factorial_new_valuation_candidate_power_product) = S ((S (S ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product)) /\ exists ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_successor. ff_u_blfg_agreement_factorial_new_valuation_candidate_power_product = ff_q_blfg_agreement_factorial_new_valuation_candidate_power_product_successor * S ((S (S ff_i_blfg_agreement_factorial_new_valuation_candidate_power_product)) * ff_v_blfg_agreement_factorial_new_valuation_candidate_power_product) + (ff_s_blfg_agreement_factorial_new_valuation_candidate_power_product))) /\ ff_s_blfg_agreement_factorial_new_valuation_candidate_power_product = ff_r_blfg_agreement_factorial_new_valuation_candidate_power_product * ff_p_blfg_agreement_factorial_new_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_blfg_agreement_factorial_new_valuation_candidate_divides. blfg_factorial_blfg_agreement_factorial_new = bpv_result_blfg_agreement_factorial_new_valuation_candidate * bpv_factor_blfg_agreement_factorial_new_valuation_candidate_divides))) -> (exists bpv_gap_blfg_agreement_factorial_new_valuation_maximal. bpv_gap_blfg_agreement_factorial_new_valuation_maximal + bpv_candidate_blfg_agreement_factorial_new_valuation = b)))) -> ((((exists blsr_le_gap_blfg_agreement_contribution_exponent_bound. blsr_le_gap_blfg_agreement_contribution_exponent_bound + (f) = (S n)) /\ (exists bpvi_result_blfg_agreement_contribution_selected. ((exists bpvi_b_blfg_agreement_contribution_selected_power bpvi_c_blfg_agreement_contribution_selected_power. ((forall bpvi_i_blfg_agreement_contribution_selected_power. (exists bpvi_repeat_gap_blfg_agreement_contribution_selected_power. bpvi_repeat_gap_blfg_agreement_contribution_selected_power + S bpvi_i_blfg_agreement_contribution_selected_power = f) -> (((exists bpvi_h_blfg_agreement_contribution_selected_power_repeat. bpvi_h_blfg_agreement_contribution_selected_power_repeat + S (p) = S ((S (bpvi_i_blfg_agreement_contribution_selected_power)) * bpvi_c_blfg_agreement_contribution_selected_power)) /\ exists bpvi_q_blfg_agreement_contribution_selected_power_repeat. bpvi_b_blfg_agreement_contribution_selected_power = bpvi_q_blfg_agreement_contribution_selected_power_repeat * S ((S (bpvi_i_blfg_agreement_contribution_selected_power)) * bpvi_c_blfg_agreement_contribution_selected_power) + (p)))) /\ (exists bpvi_u_blfg_agreement_contribution_selected_power bpvi_v_blfg_agreement_contribution_selected_power. ((((exists bpvi_h_blfg_agreement_contribution_selected_power_start. bpvi_h_blfg_agreement_contribution_selected_power_start + S (1) = S ((S (0)) * bpvi_v_blfg_agreement_contribution_selected_power)) /\ exists bpvi_q_blfg_agreement_contribution_selected_power_start. bpvi_u_blfg_agreement_contribution_selected_power = bpvi_q_blfg_agreement_contribution_selected_power_start * S ((S (0)) * bpvi_v_blfg_agreement_contribution_selected_power) + (1))) /\ ((((exists bpvi_h_blfg_agreement_contribution_selected_power_terminal. bpvi_h_blfg_agreement_contribution_selected_power_terminal + S (bpvi_result_blfg_agreement_contribution_selected) = S ((S (f)) * bpvi_v_blfg_agreement_contribution_selected_power)) /\ exists bpvi_q_blfg_agreement_contribution_selected_power_terminal. bpvi_u_blfg_agreement_contribution_selected_power = bpvi_q_blfg_agreement_contribution_selected_power_terminal * S ((S (f)) * bpvi_v_blfg_agreement_contribution_selected_power) + (bpvi_result_blfg_agreement_contribution_selected))) /\ forall bpvi_j_blfg_agreement_contribution_selected_power. (exists bpvi_product_gap_blfg_agreement_contribution_selected_power. bpvi_product_gap_blfg_agreement_contribution_selected_power + S bpvi_j_blfg_agreement_contribution_selected_power = f) -> exists bpvi_factor_blfg_agreement_contribution_selected_power bpvi_partial_blfg_agreement_contribution_selected_power bpvi_successor_blfg_agreement_contribution_selected_power. ((((exists bpvi_h_blfg_agreement_contribution_selected_power_factor. bpvi_h_blfg_agreement_contribution_selected_power_factor + S (bpvi_factor_blfg_agreement_contribution_selected_power) = S ((S (bpvi_j_blfg_agreement_contribution_selected_power)) * bpvi_c_blfg_agreement_contribution_selected_power)) /\ exists bpvi_q_blfg_agreement_contribution_selected_power_factor. bpvi_b_blfg_agreement_contribution_selected_power = bpvi_q_blfg_agreement_contribution_selected_power_factor * S ((S (bpvi_j_blfg_agreement_contribution_selected_power)) * bpvi_c_blfg_agreement_contribution_selected_power) + (bpvi_factor_blfg_agreement_contribution_selected_power))) /\ ((((exists bpvi_h_blfg_agreement_contribution_selected_power_partial. bpvi_h_blfg_agreement_contribution_selected_power_partial + S (bpvi_partial_blfg_agreement_contribution_selected_power) = S ((S (bpvi_j_blfg_agreement_contribution_selected_power)) * bpvi_v_blfg_agreement_contribution_selected_power)) /\ exists bpvi_q_blfg_agreement_contribution_selected_power_partial. bpvi_u_blfg_agreement_contribution_selected_power = bpvi_q_blfg_agreement_contribution_selected_power_partial * S ((S (bpvi_j_blfg_agreement_contribution_selected_power)) * bpvi_v_blfg_agreement_contribution_selected_power) + (bpvi_partial_blfg_agreement_contribution_selected_power))) /\ ((((exists bpvi_h_blfg_agreement_contribution_selected_power_successor. bpvi_h_blfg_agreement_contribution_selected_power_successor + S (bpvi_successor_blfg_agreement_contribution_selected_power) = S ((S (S bpvi_j_blfg_agreement_contribution_selected_power)) * bpvi_v_blfg_agreement_contribution_selected_power)) /\ exists bpvi_q_blfg_agreement_contribution_selected_power_successor. bpvi_u_blfg_agreement_contribution_selected_power = bpvi_q_blfg_agreement_contribution_selected_power_successor * S ((S (S bpvi_j_blfg_agreement_contribution_selected_power)) * bpvi_v_blfg_agreement_contribution_selected_power) + (bpvi_successor_blfg_agreement_contribution_selected_power))) /\ bpvi_successor_blfg_agreement_contribution_selected_power = bpvi_partial_blfg_agreement_contribution_selected_power * bpvi_factor_blfg_agreement_contribution_selected_power)))))))) /\ exists bpvi_divisor_factor_blfg_agreement_contribution_selected. S n = bpvi_result_blfg_agreement_contribution_selected * bpvi_divisor_factor_blfg_agreement_contribution_selected))) /\ forall blsr_candidate_blfg_agreement_contribution. (exists blsr_le_gap_blfg_agreement_contribution_candidate_bound. blsr_le_gap_blfg_agreement_contribution_candidate_bound + (blsr_candidate_blfg_agreement_contribution) = (S n)) -> (exists bpvi_result_blfg_agreement_contribution_candidate. ((exists bpvi_b_blfg_agreement_contribution_candidate_power bpvi_c_blfg_agreement_contribution_candidate_power. ((forall bpvi_i_blfg_agreement_contribution_candidate_power. (exists bpvi_repeat_gap_blfg_agreement_contribution_candidate_power. bpvi_repeat_gap_blfg_agreement_contribution_candidate_power + S bpvi_i_blfg_agreement_contribution_candidate_power = blsr_candidate_blfg_agreement_contribution) -> (((exists bpvi_h_blfg_agreement_contribution_candidate_power_repeat. bpvi_h_blfg_agreement_contribution_candidate_power_repeat + S (p) = S ((S (bpvi_i_blfg_agreement_contribution_candidate_power)) * bpvi_c_blfg_agreement_contribution_candidate_power)) /\ exists bpvi_q_blfg_agreement_contribution_candidate_power_repeat. bpvi_b_blfg_agreement_contribution_candidate_power = bpvi_q_blfg_agreement_contribution_candidate_power_repeat * S ((S (bpvi_i_blfg_agreement_contribution_candidate_power)) * bpvi_c_blfg_agreement_contribution_candidate_power) + (p)))) /\ (exists bpvi_u_blfg_agreement_contribution_candidate_power bpvi_v_blfg_agreement_contribution_candidate_power. ((((exists bpvi_h_blfg_agreement_contribution_candidate_power_start. bpvi_h_blfg_agreement_contribution_candidate_power_start + S (1) = S ((S (0)) * bpvi_v_blfg_agreement_contribution_candidate_power)) /\ exists bpvi_q_blfg_agreement_contribution_candidate_power_start. bpvi_u_blfg_agreement_contribution_candidate_power = bpvi_q_blfg_agreement_contribution_candidate_power_start * S ((S (0)) * bpvi_v_blfg_agreement_contribution_candidate_power) + (1))) /\ ((((exists bpvi_h_blfg_agreement_contribution_candidate_power_terminal. bpvi_h_blfg_agreement_contribution_candidate_power_terminal + S (bpvi_result_blfg_agreement_contribution_candidate) = S ((S (blsr_candidate_blfg_agreement_contribution)) * bpvi_v_blfg_agreement_contribution_candidate_power)) /\ exists bpvi_q_blfg_agreement_contribution_candidate_power_terminal. bpvi_u_blfg_agreement_contribution_candidate_power = bpvi_q_blfg_agreement_contribution_candidate_power_terminal * S ((S (blsr_candidate_blfg_agreement_contribution)) * bpvi_v_blfg_agreement_contribution_candidate_power) + (bpvi_result_blfg_agreement_contribution_candidate))) /\ forall bpvi_j_blfg_agreement_contribution_candidate_power. (exists bpvi_product_gap_blfg_agreement_contribution_candidate_power. bpvi_product_gap_blfg_agreement_contribution_candidate_power + S bpvi_j_blfg_agreement_contribution_candidate_power = blsr_candidate_blfg_agreement_contribution) -> exists bpvi_factor_blfg_agreement_contribution_candidate_power bpvi_partial_blfg_agreement_contribution_candidate_power bpvi_successor_blfg_agreement_contribution_candidate_power. ((((exists bpvi_h_blfg_agreement_contribution_candidate_power_factor. bpvi_h_blfg_agreement_contribution_candidate_power_factor + S (bpvi_factor_blfg_agreement_contribution_candidate_power) = S ((S (bpvi_j_blfg_agreement_contribution_candidate_power)) * bpvi_c_blfg_agreement_contribution_candidate_power)) /\ exists bpvi_q_blfg_agreement_contribution_candidate_power_factor. bpvi_b_blfg_agreement_contribution_candidate_power = bpvi_q_blfg_agreement_contribution_candidate_power_factor * S ((S (bpvi_j_blfg_agreement_contribution_candidate_power)) * bpvi_c_blfg_agreement_contribution_candidate_power) + (bpvi_factor_blfg_agreement_contribution_candidate_power))) /\ ((((exists bpvi_h_blfg_agreement_contribution_candidate_power_partial. bpvi_h_blfg_agreement_contribution_candidate_power_partial + S (bpvi_partial_blfg_agreement_contribution_candidate_power) = S ((S (bpvi_j_blfg_agreement_contribution_candidate_power)) * bpvi_v_blfg_agreement_contribution_candidate_power)) /\ exists bpvi_q_blfg_agreement_contribution_candidate_power_partial. bpvi_u_blfg_agreement_contribution_candidate_power = bpvi_q_blfg_agreement_contribution_candidate_power_partial * S ((S (bpvi_j_blfg_agreement_contribution_candidate_power)) * bpvi_v_blfg_agreement_contribution_candidate_power) + (bpvi_partial_blfg_agreement_contribution_candidate_power))) /\ ((((exists bpvi_h_blfg_agreement_contribution_candidate_power_successor. bpvi_h_blfg_agreement_contribution_candidate_power_successor + S (bpvi_successor_blfg_agreement_contribution_candidate_power) = S ((S (S bpvi_j_blfg_agreement_contribution_candidate_power)) * bpvi_v_blfg_agreement_contribution_candidate_power)) /\ exists bpvi_q_blfg_agreement_contribution_candidate_power_successor. bpvi_u_blfg_agreement_contribution_candidate_power = bpvi_q_blfg_agreement_contribution_candidate_power_successor * S ((S (S bpvi_j_blfg_agreement_contribution_candidate_power)) * bpvi_v_blfg_agreement_contribution_candidate_power) + (bpvi_successor_blfg_agreement_contribution_candidate_power))) /\ bpvi_successor_blfg_agreement_contribution_candidate_power = bpvi_partial_blfg_agreement_contribution_candidate_power * bpvi_factor_blfg_agreement_contribution_candidate_power)))))))) /\ exists bpvi_divisor_factor_blfg_agreement_contribution_candidate. S n = bpvi_result_blfg_agreement_contribution_candidate * bpvi_divisor_factor_blfg_agreement_contribution_candidate)) -> (exists blsr_le_gap_blfg_agreement_contribution_maximal. blsr_le_gap_blfg_agreement_contribution_maximal + (blsr_candidate_blfg_agreement_contribution) = (f)))) -> (exists bls_code_blfg_agreement_legendre_old bls_scale_blfg_agreement_legendre_old. ((forall bls_index_blfg_agreement_legendre_old_prefix. (exists bls_gap_blfg_agreement_legendre_old_prefix_bound. bls_gap_blfg_agreement_legendre_old_prefix_bound + S (bls_index_blfg_agreement_legendre_old_prefix) = (n)) -> exists bls_power_blfg_agreement_legendre_old_prefix bls_quotient_blfg_agreement_legendre_old_prefix bls_remainder_blfg_agreement_legendre_old_prefix. ((exists bpvi_b_bls_blfg_agreement_legendre_old_prefix_power bpvi_c_bls_blfg_agreement_legendre_old_prefix_power. ((forall bpvi_i_bls_blfg_agreement_legendre_old_prefix_power. (exists bpvi_repeat_gap_bls_blfg_agreement_legendre_old_prefix_power. bpvi_repeat_gap_bls_blfg_agreement_legendre_old_prefix_power + S bpvi_i_bls_blfg_agreement_legendre_old_prefix_power = S bls_index_blfg_agreement_legendre_old_prefix) -> (((exists bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_repeat. bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_repeat + S (p) = S ((S (bpvi_i_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_old_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_repeat. bpvi_b_bls_blfg_agreement_legendre_old_prefix_power = bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_repeat * S ((S (bpvi_i_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_old_prefix_power) + (p)))) /\ (exists bpvi_u_bls_blfg_agreement_legendre_old_prefix_power bpvi_v_bls_blfg_agreement_legendre_old_prefix_power. ((((exists bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_start. bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_start + S (1) = S ((S (0)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_start. bpvi_u_bls_blfg_agreement_legendre_old_prefix_power = bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_start * S ((S (0)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power) + (1))) /\ ((((exists bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_terminal. bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_terminal + S (bls_power_blfg_agreement_legendre_old_prefix) = S ((S (S bls_index_blfg_agreement_legendre_old_prefix)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_terminal. bpvi_u_bls_blfg_agreement_legendre_old_prefix_power = bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_terminal * S ((S (S bls_index_blfg_agreement_legendre_old_prefix)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power) + (bls_power_blfg_agreement_legendre_old_prefix))) /\ forall bpvi_j_bls_blfg_agreement_legendre_old_prefix_power. (exists bpvi_product_gap_bls_blfg_agreement_legendre_old_prefix_power. bpvi_product_gap_bls_blfg_agreement_legendre_old_prefix_power + S bpvi_j_bls_blfg_agreement_legendre_old_prefix_power = S bls_index_blfg_agreement_legendre_old_prefix) -> exists bpvi_factor_bls_blfg_agreement_legendre_old_prefix_power bpvi_partial_bls_blfg_agreement_legendre_old_prefix_power bpvi_successor_bls_blfg_agreement_legendre_old_prefix_power. ((((exists bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_factor. bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_factor + S (bpvi_factor_bls_blfg_agreement_legendre_old_prefix_power) = S ((S (bpvi_j_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_old_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_factor. bpvi_b_bls_blfg_agreement_legendre_old_prefix_power = bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_factor * S ((S (bpvi_j_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_old_prefix_power) + (bpvi_factor_bls_blfg_agreement_legendre_old_prefix_power))) /\ ((((exists bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_partial. bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_partial + S (bpvi_partial_bls_blfg_agreement_legendre_old_prefix_power) = S ((S (bpvi_j_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_partial. bpvi_u_bls_blfg_agreement_legendre_old_prefix_power = bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_partial * S ((S (bpvi_j_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power) + (bpvi_partial_bls_blfg_agreement_legendre_old_prefix_power))) /\ ((((exists bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_successor. bpvi_h_bls_blfg_agreement_legendre_old_prefix_power_successor + S (bpvi_successor_bls_blfg_agreement_legendre_old_prefix_power) = S ((S (S bpvi_j_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_successor. bpvi_u_bls_blfg_agreement_legendre_old_prefix_power = bpvi_q_bls_blfg_agreement_legendre_old_prefix_power_successor * S ((S (S bpvi_j_bls_blfg_agreement_legendre_old_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_old_prefix_power) + (bpvi_successor_bls_blfg_agreement_legendre_old_prefix_power))) /\ bpvi_successor_bls_blfg_agreement_legendre_old_prefix_power = bpvi_partial_bls_blfg_agreement_legendre_old_prefix_power * bpvi_factor_bls_blfg_agreement_legendre_old_prefix_power)))))))) /\ ((((exists ff_h_bls_blfg_agreement_legendre_old_prefix_quotient_entry. ff_h_bls_blfg_agreement_legendre_old_prefix_quotient_entry + S (bls_quotient_blfg_agreement_legendre_old_prefix) = S ((S (bls_index_blfg_agreement_legendre_old_prefix)) * bls_scale_blfg_agreement_legendre_old)) /\ exists ff_q_bls_blfg_agreement_legendre_old_prefix_quotient_entry. bls_code_blfg_agreement_legendre_old = ff_q_bls_blfg_agreement_legendre_old_prefix_quotient_entry * S ((S (bls_index_blfg_agreement_legendre_old_prefix)) * bls_scale_blfg_agreement_legendre_old) + (bls_quotient_blfg_agreement_legendre_old_prefix))) /\ ((n = bls_power_blfg_agreement_legendre_old_prefix * bls_quotient_blfg_agreement_legendre_old_prefix + bls_remainder_blfg_agreement_legendre_old_prefix /\ exists bls_remainder_gap_blfg_agreement_legendre_old_prefix_division. bls_remainder_gap_blfg_agreement_legendre_old_prefix_division + S (bls_remainder_blfg_agreement_legendre_old_prefix) = bls_power_blfg_agreement_legendre_old_prefix))))) /\ (exists ff_u_bls_blfg_agreement_legendre_old_sum ff_v_bls_blfg_agreement_legendre_old_sum. ((((exists ff_h_bls_blfg_agreement_legendre_old_sum_start. ff_h_bls_blfg_agreement_legendre_old_sum_start + S (0) = S ((S (0)) * ff_v_bls_blfg_agreement_legendre_old_sum)) /\ exists ff_q_bls_blfg_agreement_legendre_old_sum_start. ff_u_bls_blfg_agreement_legendre_old_sum = ff_q_bls_blfg_agreement_legendre_old_sum_start * S ((S (0)) * ff_v_bls_blfg_agreement_legendre_old_sum) + (0))) /\ ((((exists ff_h_bls_blfg_agreement_legendre_old_sum_terminal. ff_h_bls_blfg_agreement_legendre_old_sum_terminal + S (c) = S ((S (n)) * ff_v_bls_blfg_agreement_legendre_old_sum)) /\ exists ff_q_bls_blfg_agreement_legendre_old_sum_terminal. ff_u_bls_blfg_agreement_legendre_old_sum = ff_q_bls_blfg_agreement_legendre_old_sum_terminal * S ((S (n)) * ff_v_bls_blfg_agreement_legendre_old_sum) + (c))) /\ forall ff_i_bls_blfg_agreement_legendre_old_sum. (exists ff_lt_bls_blfg_agreement_legendre_old_sum_bound. ff_lt_bls_blfg_agreement_legendre_old_sum_bound + S ff_i_bls_blfg_agreement_legendre_old_sum = n) -> exists ff_a_bls_blfg_agreement_legendre_old_sum ff_r_bls_blfg_agreement_legendre_old_sum ff_s_bls_blfg_agreement_legendre_old_sum. ((((exists ff_h_bls_blfg_agreement_legendre_old_sum_summand. ff_h_bls_blfg_agreement_legendre_old_sum_summand + S (ff_a_bls_blfg_agreement_legendre_old_sum) = S ((S (ff_i_bls_blfg_agreement_legendre_old_sum)) * bls_scale_blfg_agreement_legendre_old)) /\ exists ff_q_bls_blfg_agreement_legendre_old_sum_summand. bls_code_blfg_agreement_legendre_old = ff_q_bls_blfg_agreement_legendre_old_sum_summand * S ((S (ff_i_bls_blfg_agreement_legendre_old_sum)) * bls_scale_blfg_agreement_legendre_old) + (ff_a_bls_blfg_agreement_legendre_old_sum))) /\ ((((exists ff_h_bls_blfg_agreement_legendre_old_sum_partial. ff_h_bls_blfg_agreement_legendre_old_sum_partial + S (ff_r_bls_blfg_agreement_legendre_old_sum) = S ((S (ff_i_bls_blfg_agreement_legendre_old_sum)) * ff_v_bls_blfg_agreement_legendre_old_sum)) /\ exists ff_q_bls_blfg_agreement_legendre_old_sum_partial. ff_u_bls_blfg_agreement_legendre_old_sum = ff_q_bls_blfg_agreement_legendre_old_sum_partial * S ((S (ff_i_bls_blfg_agreement_legendre_old_sum)) * ff_v_bls_blfg_agreement_legendre_old_sum) + (ff_r_bls_blfg_agreement_legendre_old_sum))) /\ ((((exists ff_h_bls_blfg_agreement_legendre_old_sum_successor. ff_h_bls_blfg_agreement_legendre_old_sum_successor + S (ff_s_bls_blfg_agreement_legendre_old_sum) = S ((S (S ff_i_bls_blfg_agreement_legendre_old_sum)) * ff_v_bls_blfg_agreement_legendre_old_sum)) /\ exists ff_q_bls_blfg_agreement_legendre_old_sum_successor. ff_u_bls_blfg_agreement_legendre_old_sum = ff_q_bls_blfg_agreement_legendre_old_sum_successor * S ((S (S ff_i_bls_blfg_agreement_legendre_old_sum)) * ff_v_bls_blfg_agreement_legendre_old_sum) + (ff_s_bls_blfg_agreement_legendre_old_sum))) /\ ff_s_bls_blfg_agreement_legendre_old_sum = ff_r_bls_blfg_agreement_legendre_old_sum + ff_a_bls_blfg_agreement_legendre_old_sum)))))))) -> (exists blrr_code_blfg_agreement_legendre_new blrr_scale_blfg_agreement_legendre_new. ((forall bls_index_blfg_agreement_legendre_new_prefix. (exists bls_gap_blfg_agreement_legendre_new_prefix_bound. bls_gap_blfg_agreement_legendre_new_prefix_bound + S (bls_index_blfg_agreement_legendre_new_prefix) = (S n)) -> exists bls_power_blfg_agreement_legendre_new_prefix bls_quotient_blfg_agreement_legendre_new_prefix bls_remainder_blfg_agreement_legendre_new_prefix. ((exists bpvi_b_bls_blfg_agreement_legendre_new_prefix_power bpvi_c_bls_blfg_agreement_legendre_new_prefix_power. ((forall bpvi_i_bls_blfg_agreement_legendre_new_prefix_power. (exists bpvi_repeat_gap_bls_blfg_agreement_legendre_new_prefix_power. bpvi_repeat_gap_bls_blfg_agreement_legendre_new_prefix_power + S bpvi_i_bls_blfg_agreement_legendre_new_prefix_power = S bls_index_blfg_agreement_legendre_new_prefix) -> (((exists bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_repeat. bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_repeat + S (p) = S ((S (bpvi_i_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_new_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_repeat. bpvi_b_bls_blfg_agreement_legendre_new_prefix_power = bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_repeat * S ((S (bpvi_i_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_new_prefix_power) + (p)))) /\ (exists bpvi_u_bls_blfg_agreement_legendre_new_prefix_power bpvi_v_bls_blfg_agreement_legendre_new_prefix_power. ((((exists bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_start. bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_start + S (1) = S ((S (0)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_start. bpvi_u_bls_blfg_agreement_legendre_new_prefix_power = bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_start * S ((S (0)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power) + (1))) /\ ((((exists bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_terminal. bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_terminal + S (bls_power_blfg_agreement_legendre_new_prefix) = S ((S (S bls_index_blfg_agreement_legendre_new_prefix)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_terminal. bpvi_u_bls_blfg_agreement_legendre_new_prefix_power = bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_terminal * S ((S (S bls_index_blfg_agreement_legendre_new_prefix)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power) + (bls_power_blfg_agreement_legendre_new_prefix))) /\ forall bpvi_j_bls_blfg_agreement_legendre_new_prefix_power. (exists bpvi_product_gap_bls_blfg_agreement_legendre_new_prefix_power. bpvi_product_gap_bls_blfg_agreement_legendre_new_prefix_power + S bpvi_j_bls_blfg_agreement_legendre_new_prefix_power = S bls_index_blfg_agreement_legendre_new_prefix) -> exists bpvi_factor_bls_blfg_agreement_legendre_new_prefix_power bpvi_partial_bls_blfg_agreement_legendre_new_prefix_power bpvi_successor_bls_blfg_agreement_legendre_new_prefix_power. ((((exists bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_factor. bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_factor + S (bpvi_factor_bls_blfg_agreement_legendre_new_prefix_power) = S ((S (bpvi_j_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_new_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_factor. bpvi_b_bls_blfg_agreement_legendre_new_prefix_power = bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_factor * S ((S (bpvi_j_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_c_bls_blfg_agreement_legendre_new_prefix_power) + (bpvi_factor_bls_blfg_agreement_legendre_new_prefix_power))) /\ ((((exists bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_partial. bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_partial + S (bpvi_partial_bls_blfg_agreement_legendre_new_prefix_power) = S ((S (bpvi_j_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_partial. bpvi_u_bls_blfg_agreement_legendre_new_prefix_power = bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_partial * S ((S (bpvi_j_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power) + (bpvi_partial_bls_blfg_agreement_legendre_new_prefix_power))) /\ ((((exists bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_successor. bpvi_h_bls_blfg_agreement_legendre_new_prefix_power_successor + S (bpvi_successor_bls_blfg_agreement_legendre_new_prefix_power) = S ((S (S bpvi_j_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power)) /\ exists bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_successor. bpvi_u_bls_blfg_agreement_legendre_new_prefix_power = bpvi_q_bls_blfg_agreement_legendre_new_prefix_power_successor * S ((S (S bpvi_j_bls_blfg_agreement_legendre_new_prefix_power)) * bpvi_v_bls_blfg_agreement_legendre_new_prefix_power) + (bpvi_successor_bls_blfg_agreement_legendre_new_prefix_power))) /\ bpvi_successor_bls_blfg_agreement_legendre_new_prefix_power = bpvi_partial_bls_blfg_agreement_legendre_new_prefix_power * bpvi_factor_bls_blfg_agreement_legendre_new_prefix_power)))))))) /\ ((((exists ff_h_bls_blfg_agreement_legendre_new_prefix_quotient_entry. ff_h_bls_blfg_agreement_legendre_new_prefix_quotient_entry + S (bls_quotient_blfg_agreement_legendre_new_prefix) = S ((S (bls_index_blfg_agreement_legendre_new_prefix)) * blrr_scale_blfg_agreement_legendre_new)) /\ exists ff_q_bls_blfg_agreement_legendre_new_prefix_quotient_entry. blrr_code_blfg_agreement_legendre_new = ff_q_bls_blfg_agreement_legendre_new_prefix_quotient_entry * S ((S (bls_index_blfg_agreement_legendre_new_prefix)) * blrr_scale_blfg_agreement_legendre_new) + (bls_quotient_blfg_agreement_legendre_new_prefix))) /\ ((S n = bls_power_blfg_agreement_legendre_new_prefix * bls_quotient_blfg_agreement_legendre_new_prefix + bls_remainder_blfg_agreement_legendre_new_prefix /\ exists bls_remainder_gap_blfg_agreement_legendre_new_prefix_division. bls_remainder_gap_blfg_agreement_legendre_new_prefix_division + S (bls_remainder_blfg_agreement_legendre_new_prefix) = bls_power_blfg_agreement_legendre_new_prefix))))) /\ (exists fs_u_blrr_blfg_agreement_legendre_new_sum fs_v_blrr_blfg_agreement_legendre_new_sum. ((((exists fs_h_blrr_blfg_agreement_legendre_new_sum_body_start. fs_h_blrr_blfg_agreement_legendre_new_sum_body_start + S (0) = S ((S (0)) * fs_v_blrr_blfg_agreement_legendre_new_sum)) /\ exists fs_q_blrr_blfg_agreement_legendre_new_sum_body_start. fs_u_blrr_blfg_agreement_legendre_new_sum = fs_q_blrr_blfg_agreement_legendre_new_sum_body_start * S ((S (0)) * fs_v_blrr_blfg_agreement_legendre_new_sum) + (0))) /\ ((((exists fs_h_blrr_blfg_agreement_legendre_new_sum_body_terminal. fs_h_blrr_blfg_agreement_legendre_new_sum_body_terminal + S (d) = S ((S (S n)) * fs_v_blrr_blfg_agreement_legendre_new_sum)) /\ exists fs_q_blrr_blfg_agreement_legendre_new_sum_body_terminal. fs_u_blrr_blfg_agreement_legendre_new_sum = fs_q_blrr_blfg_agreement_legendre_new_sum_body_terminal * S ((S (S n)) * fs_v_blrr_blfg_agreement_legendre_new_sum) + (d))) /\ forall fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps. (exists fs_lt_blrr_blfg_agreement_legendre_new_sum_body_steps_bound. fs_lt_blrr_blfg_agreement_legendre_new_sum_body_steps_bound + S fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps = S n) -> exists fs_a_blrr_blfg_agreement_legendre_new_sum_body_steps fs_r_blrr_blfg_agreement_legendre_new_sum_body_steps fs_s_blrr_blfg_agreement_legendre_new_sum_body_steps. ((((exists fs_h_blrr_blfg_agreement_legendre_new_sum_body_steps_summand. fs_h_blrr_blfg_agreement_legendre_new_sum_body_steps_summand + S (fs_a_blrr_blfg_agreement_legendre_new_sum_body_steps) = S ((S (fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps)) * blrr_scale_blfg_agreement_legendre_new)) /\ exists fs_q_blrr_blfg_agreement_legendre_new_sum_body_steps_summand. blrr_code_blfg_agreement_legendre_new = fs_q_blrr_blfg_agreement_legendre_new_sum_body_steps_summand * S ((S (fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps)) * blrr_scale_blfg_agreement_legendre_new) + (fs_a_blrr_blfg_agreement_legendre_new_sum_body_steps))) /\ ((((exists fs_h_blrr_blfg_agreement_legendre_new_sum_body_steps_partial. fs_h_blrr_blfg_agreement_legendre_new_sum_body_steps_partial + S (fs_r_blrr_blfg_agreement_legendre_new_sum_body_steps) = S ((S (fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps)) * fs_v_blrr_blfg_agreement_legendre_new_sum)) /\ exists fs_q_blrr_blfg_agreement_legendre_new_sum_body_steps_partial. fs_u_blrr_blfg_agreement_legendre_new_sum = fs_q_blrr_blfg_agreement_legendre_new_sum_body_steps_partial * S ((S (fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps)) * fs_v_blrr_blfg_agreement_legendre_new_sum) + (fs_r_blrr_blfg_agreement_legendre_new_sum_body_steps))) /\ ((((exists fs_h_blrr_blfg_agreement_legendre_new_sum_body_steps_successor. fs_h_blrr_blfg_agreement_legendre_new_sum_body_steps_successor + S (fs_s_blrr_blfg_agreement_legendre_new_sum_body_steps) = S ((S (S fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps)) * fs_v_blrr_blfg_agreement_legendre_new_sum)) /\ exists fs_q_blrr_blfg_agreement_legendre_new_sum_body_steps_successor. fs_u_blrr_blfg_agreement_legendre_new_sum = fs_q_blrr_blfg_agreement_legendre_new_sum_body_steps_successor * S ((S (S fs_i_blrr_blfg_agreement_legendre_new_sum_body_steps)) * fs_v_blrr_blfg_agreement_legendre_new_sum) + (fs_s_blrr_blfg_agreement_legendre_new_sum_body_steps))) /\ fs_s_blrr_blfg_agreement_legendre_new_sum_body_steps = fs_r_blrr_blfg_agreement_legendre_new_sum_body_steps + fs_a_blrr_blfg_agreement_legendre_new_sum_body_steps)))))))) -> a = c -> b = d