choose_factorial_valuation_balance

Statement with defined notation

forall p n k j c e A B D. k + j = n -> ((~(p = 1) /\ forall frm_prime_left_kmvcfvb_prime frm_prime_right_kmvcfvb_prime. p = frm_prime_left_kmvcfvb_prime * frm_prime_right_kmvcfvb_prime -> frm_prime_left_kmvcfvb_prime = 1 \/ frm_prime_right_kmvcfvb_prime = 1)) -> (((exists bcf_lt_gap_kmvcfvb_choose_out_of_range. bcf_lt_gap_kmvcfvb_choose_out_of_range + S (n) = k) /\ c = 0) \/ ((exists bcf_le_gap_kmvcfvb_choose_in_range. bcf_le_gap_kmvcfvb_choose_in_range + (k) = n) /\ (exists bcf_row_code_code_kmvcfvb_choose bcf_row_code_scale_kmvcfvb_choose bcf_row_scale_code_kmvcfvb_choose bcf_row_scale_scale_kmvcfvb_choose bcf_row_code_kmvcfvb_choose bcf_row_scale_kmvcfvb_choose. ((forall bcf_row_index_kmvcfvb_choose_table. (exists bcf_lt_gap_kmvcfvb_choose_table_row_bound. bcf_lt_gap_kmvcfvb_choose_table_row_bound + S (bcf_row_index_kmvcfvb_choose_table) = S (n)) -> exists bcf_row_code_kmvcfvb_choose_table bcf_row_scale_kmvcfvb_choose_table. ((((exists bcf_height_kmvcfvb_choose_table_decoded_row_code. bcf_height_kmvcfvb_choose_table_decoded_row_code + S (bcf_row_code_kmvcfvb_choose_table) = S ((S (bcf_row_index_kmvcfvb_choose_table)) * bcf_row_code_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_table_decoded_row_code. bcf_row_code_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_table_decoded_row_code * S ((S (bcf_row_index_kmvcfvb_choose_table)) * bcf_row_code_scale_kmvcfvb_choose) + (bcf_row_code_kmvcfvb_choose_table))) /\ ((((exists bcf_height_kmvcfvb_choose_table_decoded_row_scale. bcf_height_kmvcfvb_choose_table_decoded_row_scale + S (bcf_row_scale_kmvcfvb_choose_table) = S ((S (bcf_row_index_kmvcfvb_choose_table)) * bcf_row_scale_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_table_decoded_row_scale. bcf_row_scale_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_table_decoded_row_scale * S ((S (bcf_row_index_kmvcfvb_choose_table)) * bcf_row_scale_scale_kmvcfvb_choose) + (bcf_row_scale_kmvcfvb_choose_table))) /\ ((bcf_row_index_kmvcfvb_choose_table = 0 /\ (forall bcf_index_kmvcfvb_choose_table_zero_row. (exists bcf_lt_gap_kmvcfvb_choose_table_zero_row_bound. bcf_lt_gap_kmvcfvb_choose_table_zero_row_bound + S (bcf_index_kmvcfvb_choose_table_zero_row) = S (n)) -> exists bcf_value_kmvcfvb_choose_table_zero_row. ((((exists bcf_height_kmvcfvb_choose_table_zero_row_entry. bcf_height_kmvcfvb_choose_table_zero_row_entry + S (bcf_value_kmvcfvb_choose_table_zero_row) = S ((S (bcf_index_kmvcfvb_choose_table_zero_row)) * bcf_row_scale_kmvcfvb_choose_table)) /\ exists bcf_quotient_kmvcfvb_choose_table_zero_row_entry. bcf_row_code_kmvcfvb_choose_table = bcf_quotient_kmvcfvb_choose_table_zero_row_entry * S ((S (bcf_index_kmvcfvb_choose_table_zero_row)) * bcf_row_scale_kmvcfvb_choose_table) + (bcf_value_kmvcfvb_choose_table_zero_row))) /\ ((bcf_index_kmvcfvb_choose_table_zero_row = 0 /\ bcf_value_kmvcfvb_choose_table_zero_row = 1) \/ exists bcf_predecessor_kmvcfvb_choose_table_zero_row. bcf_index_kmvcfvb_choose_table_zero_row = S bcf_predecessor_kmvcfvb_choose_table_zero_row /\ bcf_value_kmvcfvb_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_kmvcfvb_choose_table bcf_previous_code_kmvcfvb_choose_table bcf_previous_scale_kmvcfvb_choose_table. bcf_row_index_kmvcfvb_choose_table = S bcf_predecessor_kmvcfvb_choose_table /\ ((((exists bcf_height_kmvcfvb_choose_table_decoded_previous_code. bcf_height_kmvcfvb_choose_table_decoded_previous_code + S (bcf_previous_code_kmvcfvb_choose_table) = S ((S (bcf_predecessor_kmvcfvb_choose_table)) * bcf_row_code_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_table_decoded_previous_code. bcf_row_code_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_table_decoded_previous_code * S ((S (bcf_predecessor_kmvcfvb_choose_table)) * bcf_row_code_scale_kmvcfvb_choose) + (bcf_previous_code_kmvcfvb_choose_table))) /\ ((((exists bcf_height_kmvcfvb_choose_table_decoded_previous_scale. bcf_height_kmvcfvb_choose_table_decoded_previous_scale + S (bcf_previous_scale_kmvcfvb_choose_table) = S ((S (bcf_predecessor_kmvcfvb_choose_table)) * bcf_row_scale_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_table_decoded_previous_scale. bcf_row_scale_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_kmvcfvb_choose_table)) * bcf_row_scale_scale_kmvcfvb_choose) + (bcf_previous_scale_kmvcfvb_choose_table))) /\ (forall bcf_index_kmvcfvb_choose_table_row_step. (exists bcf_lt_gap_kmvcfvb_choose_table_row_step_bound. bcf_lt_gap_kmvcfvb_choose_table_row_step_bound + S (bcf_index_kmvcfvb_choose_table_row_step) = S (n)) -> exists bcf_value_kmvcfvb_choose_table_row_step. ((((exists bcf_height_kmvcfvb_choose_table_row_step_entry. bcf_height_kmvcfvb_choose_table_row_step_entry + S (bcf_value_kmvcfvb_choose_table_row_step) = S ((S (bcf_index_kmvcfvb_choose_table_row_step)) * bcf_row_scale_kmvcfvb_choose_table)) /\ exists bcf_quotient_kmvcfvb_choose_table_row_step_entry. bcf_row_code_kmvcfvb_choose_table = bcf_quotient_kmvcfvb_choose_table_row_step_entry * S ((S (bcf_index_kmvcfvb_choose_table_row_step)) * bcf_row_scale_kmvcfvb_choose_table) + (bcf_value_kmvcfvb_choose_table_row_step))) /\ ((bcf_index_kmvcfvb_choose_table_row_step = 0 /\ bcf_value_kmvcfvb_choose_table_row_step = 1) \/ exists bcf_predecessor_kmvcfvb_choose_table_row_step bcf_left_kmvcfvb_choose_table_row_step bcf_right_kmvcfvb_choose_table_row_step. bcf_index_kmvcfvb_choose_table_row_step = S bcf_predecessor_kmvcfvb_choose_table_row_step /\ ((((exists bcf_height_kmvcfvb_choose_table_row_step_previous_left. bcf_height_kmvcfvb_choose_table_row_step_previous_left + S (bcf_left_kmvcfvb_choose_table_row_step) = S ((S (bcf_predecessor_kmvcfvb_choose_table_row_step)) * bcf_previous_scale_kmvcfvb_choose_table)) /\ exists bcf_quotient_kmvcfvb_choose_table_row_step_previous_left. bcf_previous_code_kmvcfvb_choose_table = bcf_quotient_kmvcfvb_choose_table_row_step_previous_left * S ((S (bcf_predecessor_kmvcfvb_choose_table_row_step)) * bcf_previous_scale_kmvcfvb_choose_table) + (bcf_left_kmvcfvb_choose_table_row_step))) /\ ((((exists bcf_height_kmvcfvb_choose_table_row_step_previous_right. bcf_height_kmvcfvb_choose_table_row_step_previous_right + S (bcf_right_kmvcfvb_choose_table_row_step) = S ((S (S (bcf_predecessor_kmvcfvb_choose_table_row_step))) * bcf_previous_scale_kmvcfvb_choose_table)) /\ exists bcf_quotient_kmvcfvb_choose_table_row_step_previous_right. bcf_previous_code_kmvcfvb_choose_table = bcf_quotient_kmvcfvb_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_kmvcfvb_choose_table_row_step))) * bcf_previous_scale_kmvcfvb_choose_table) + (bcf_right_kmvcfvb_choose_table_row_step))) /\ bcf_value_kmvcfvb_choose_table_row_step = bcf_left_kmvcfvb_choose_table_row_step + bcf_right_kmvcfvb_choose_table_row_step))))))))))) /\ ((((exists bcf_height_kmvcfvb_choose_decoded_row_code. bcf_height_kmvcfvb_choose_decoded_row_code + S (bcf_row_code_kmvcfvb_choose) = S ((S (n)) * bcf_row_code_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_decoded_row_code. bcf_row_code_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_decoded_row_code * S ((S (n)) * bcf_row_code_scale_kmvcfvb_choose) + (bcf_row_code_kmvcfvb_choose))) /\ ((((exists bcf_height_kmvcfvb_choose_decoded_row_scale. bcf_height_kmvcfvb_choose_decoded_row_scale + S (bcf_row_scale_kmvcfvb_choose) = S ((S (n)) * bcf_row_scale_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_decoded_row_scale. bcf_row_scale_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_decoded_row_scale * S ((S (n)) * bcf_row_scale_scale_kmvcfvb_choose) + (bcf_row_scale_kmvcfvb_choose))) /\ (((exists bcf_height_kmvcfvb_choose_decoded_value. bcf_height_kmvcfvb_choose_decoded_value + S (c) = S ((S (k)) * bcf_row_scale_kmvcfvb_choose)) /\ exists bcf_quotient_kmvcfvb_choose_decoded_value. bcf_row_code_kmvcfvb_choose = bcf_quotient_kmvcfvb_choose_decoded_value * S ((S (k)) * bcf_row_scale_kmvcfvb_choose) + (c))))))))) -> (((exists bpv_gap_kmvcfvb_value_exponent_bound. bpv_gap_kmvcfvb_value_exponent_bound + e = c) /\ (exists bpv_result_kmvcfvb_value_selected. ((exists ff_b_kmvcfvb_value_selected_power ff_c_kmvcfvb_value_selected_power. ((forall ff_i_kmvcfvb_value_selected_power_repeat. (exists ff_lt_kmvcfvb_value_selected_power_repeat_bound. ff_lt_kmvcfvb_value_selected_power_repeat_bound + S ff_i_kmvcfvb_value_selected_power_repeat = e) -> (((exists ff_h_kmvcfvb_value_selected_power_repeat_decoded. ff_h_kmvcfvb_value_selected_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_value_selected_power_repeat)) * ff_c_kmvcfvb_value_selected_power)) /\ exists ff_q_kmvcfvb_value_selected_power_repeat_decoded. ff_b_kmvcfvb_value_selected_power = ff_q_kmvcfvb_value_selected_power_repeat_decoded * S ((S (ff_i_kmvcfvb_value_selected_power_repeat)) * ff_c_kmvcfvb_value_selected_power) + (p)))) /\ (exists ff_u_kmvcfvb_value_selected_power_product ff_v_kmvcfvb_value_selected_power_product. ((((exists ff_h_kmvcfvb_value_selected_power_product_start. ff_h_kmvcfvb_value_selected_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_value_selected_power_product)) /\ exists ff_q_kmvcfvb_value_selected_power_product_start. ff_u_kmvcfvb_value_selected_power_product = ff_q_kmvcfvb_value_selected_power_product_start * S ((S (0)) * ff_v_kmvcfvb_value_selected_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_value_selected_power_product_terminal. ff_h_kmvcfvb_value_selected_power_product_terminal + S (bpv_result_kmvcfvb_value_selected) = S ((S (e)) * ff_v_kmvcfvb_value_selected_power_product)) /\ exists ff_q_kmvcfvb_value_selected_power_product_terminal. ff_u_kmvcfvb_value_selected_power_product = ff_q_kmvcfvb_value_selected_power_product_terminal * S ((S (e)) * ff_v_kmvcfvb_value_selected_power_product) + (bpv_result_kmvcfvb_value_selected))) /\ forall ff_i_kmvcfvb_value_selected_power_product. (exists ff_lt_kmvcfvb_value_selected_power_product_bound. ff_lt_kmvcfvb_value_selected_power_product_bound + S ff_i_kmvcfvb_value_selected_power_product = e) -> exists ff_p_kmvcfvb_value_selected_power_product ff_r_kmvcfvb_value_selected_power_product ff_s_kmvcfvb_value_selected_power_product. ((((exists ff_h_kmvcfvb_value_selected_power_product_factor. ff_h_kmvcfvb_value_selected_power_product_factor + S (ff_p_kmvcfvb_value_selected_power_product) = S ((S (ff_i_kmvcfvb_value_selected_power_product)) * ff_c_kmvcfvb_value_selected_power)) /\ exists ff_q_kmvcfvb_value_selected_power_product_factor. ff_b_kmvcfvb_value_selected_power = ff_q_kmvcfvb_value_selected_power_product_factor * S ((S (ff_i_kmvcfvb_value_selected_power_product)) * ff_c_kmvcfvb_value_selected_power) + (ff_p_kmvcfvb_value_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_value_selected_power_product_partial. ff_h_kmvcfvb_value_selected_power_product_partial + S (ff_r_kmvcfvb_value_selected_power_product) = S ((S (ff_i_kmvcfvb_value_selected_power_product)) * ff_v_kmvcfvb_value_selected_power_product)) /\ exists ff_q_kmvcfvb_value_selected_power_product_partial. ff_u_kmvcfvb_value_selected_power_product = ff_q_kmvcfvb_value_selected_power_product_partial * S ((S (ff_i_kmvcfvb_value_selected_power_product)) * ff_v_kmvcfvb_value_selected_power_product) + (ff_r_kmvcfvb_value_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_value_selected_power_product_successor. ff_h_kmvcfvb_value_selected_power_product_successor + S (ff_s_kmvcfvb_value_selected_power_product) = S ((S (S ff_i_kmvcfvb_value_selected_power_product)) * ff_v_kmvcfvb_value_selected_power_product)) /\ exists ff_q_kmvcfvb_value_selected_power_product_successor. ff_u_kmvcfvb_value_selected_power_product = ff_q_kmvcfvb_value_selected_power_product_successor * S ((S (S ff_i_kmvcfvb_value_selected_power_product)) * ff_v_kmvcfvb_value_selected_power_product) + (ff_s_kmvcfvb_value_selected_power_product))) /\ ff_s_kmvcfvb_value_selected_power_product = ff_r_kmvcfvb_value_selected_power_product * ff_p_kmvcfvb_value_selected_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_value_selected_divides. c = bpv_result_kmvcfvb_value_selected * bpv_factor_kmvcfvb_value_selected_divides)))) /\ forall bpv_candidate_kmvcfvb_value. (exists bpv_gap_kmvcfvb_value_candidate_bound. bpv_gap_kmvcfvb_value_candidate_bound + bpv_candidate_kmvcfvb_value = c) -> (exists bpv_result_kmvcfvb_value_candidate. ((exists ff_b_kmvcfvb_value_candidate_power ff_c_kmvcfvb_value_candidate_power. ((forall ff_i_kmvcfvb_value_candidate_power_repeat. (exists ff_lt_kmvcfvb_value_candidate_power_repeat_bound. ff_lt_kmvcfvb_value_candidate_power_repeat_bound + S ff_i_kmvcfvb_value_candidate_power_repeat = bpv_candidate_kmvcfvb_value) -> (((exists ff_h_kmvcfvb_value_candidate_power_repeat_decoded. ff_h_kmvcfvb_value_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_value_candidate_power_repeat)) * ff_c_kmvcfvb_value_candidate_power)) /\ exists ff_q_kmvcfvb_value_candidate_power_repeat_decoded. ff_b_kmvcfvb_value_candidate_power = ff_q_kmvcfvb_value_candidate_power_repeat_decoded * S ((S (ff_i_kmvcfvb_value_candidate_power_repeat)) * ff_c_kmvcfvb_value_candidate_power) + (p)))) /\ (exists ff_u_kmvcfvb_value_candidate_power_product ff_v_kmvcfvb_value_candidate_power_product. ((((exists ff_h_kmvcfvb_value_candidate_power_product_start. ff_h_kmvcfvb_value_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_value_candidate_power_product)) /\ exists ff_q_kmvcfvb_value_candidate_power_product_start. ff_u_kmvcfvb_value_candidate_power_product = ff_q_kmvcfvb_value_candidate_power_product_start * S ((S (0)) * ff_v_kmvcfvb_value_candidate_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_value_candidate_power_product_terminal. ff_h_kmvcfvb_value_candidate_power_product_terminal + S (bpv_result_kmvcfvb_value_candidate) = S ((S (bpv_candidate_kmvcfvb_value)) * ff_v_kmvcfvb_value_candidate_power_product)) /\ exists ff_q_kmvcfvb_value_candidate_power_product_terminal. ff_u_kmvcfvb_value_candidate_power_product = ff_q_kmvcfvb_value_candidate_power_product_terminal * S ((S (bpv_candidate_kmvcfvb_value)) * ff_v_kmvcfvb_value_candidate_power_product) + (bpv_result_kmvcfvb_value_candidate))) /\ forall ff_i_kmvcfvb_value_candidate_power_product. (exists ff_lt_kmvcfvb_value_candidate_power_product_bound. ff_lt_kmvcfvb_value_candidate_power_product_bound + S ff_i_kmvcfvb_value_candidate_power_product = bpv_candidate_kmvcfvb_value) -> exists ff_p_kmvcfvb_value_candidate_power_product ff_r_kmvcfvb_value_candidate_power_product ff_s_kmvcfvb_value_candidate_power_product. ((((exists ff_h_kmvcfvb_value_candidate_power_product_factor. ff_h_kmvcfvb_value_candidate_power_product_factor + S (ff_p_kmvcfvb_value_candidate_power_product) = S ((S (ff_i_kmvcfvb_value_candidate_power_product)) * ff_c_kmvcfvb_value_candidate_power)) /\ exists ff_q_kmvcfvb_value_candidate_power_product_factor. ff_b_kmvcfvb_value_candidate_power = ff_q_kmvcfvb_value_candidate_power_product_factor * S ((S (ff_i_kmvcfvb_value_candidate_power_product)) * ff_c_kmvcfvb_value_candidate_power) + (ff_p_kmvcfvb_value_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_value_candidate_power_product_partial. ff_h_kmvcfvb_value_candidate_power_product_partial + S (ff_r_kmvcfvb_value_candidate_power_product) = S ((S (ff_i_kmvcfvb_value_candidate_power_product)) * ff_v_kmvcfvb_value_candidate_power_product)) /\ exists ff_q_kmvcfvb_value_candidate_power_product_partial. ff_u_kmvcfvb_value_candidate_power_product = ff_q_kmvcfvb_value_candidate_power_product_partial * S ((S (ff_i_kmvcfvb_value_candidate_power_product)) * ff_v_kmvcfvb_value_candidate_power_product) + (ff_r_kmvcfvb_value_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_value_candidate_power_product_successor. ff_h_kmvcfvb_value_candidate_power_product_successor + S (ff_s_kmvcfvb_value_candidate_power_product) = S ((S (S ff_i_kmvcfvb_value_candidate_power_product)) * ff_v_kmvcfvb_value_candidate_power_product)) /\ exists ff_q_kmvcfvb_value_candidate_power_product_successor. ff_u_kmvcfvb_value_candidate_power_product = ff_q_kmvcfvb_value_candidate_power_product_successor * S ((S (S ff_i_kmvcfvb_value_candidate_power_product)) * ff_v_kmvcfvb_value_candidate_power_product) + (ff_s_kmvcfvb_value_candidate_power_product))) /\ ff_s_kmvcfvb_value_candidate_power_product = ff_r_kmvcfvb_value_candidate_power_product * ff_p_kmvcfvb_value_candidate_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_value_candidate_divides. c = bpv_result_kmvcfvb_value_candidate * bpv_factor_kmvcfvb_value_candidate_divides))) -> (exists bpv_gap_kmvcfvb_value_maximal. bpv_gap_kmvcfvb_value_maximal + bpv_candidate_kmvcfvb_value = e)) -> (exists bfv_factorial_kmvcfvb_total. ((exists ff_b_kmvcfvb_total_factorial ff_c_kmvcfvb_total_factorial. ((forall ff_i_kmvcfvb_total_factorial_range. (exists ff_lt_kmvcfvb_total_factorial_range_bound. ff_lt_kmvcfvb_total_factorial_range_bound + S ff_i_kmvcfvb_total_factorial_range = n) -> (((exists ff_h_kmvcfvb_total_factorial_range_decoded. ff_h_kmvcfvb_total_factorial_range_decoded + S (1 + ff_i_kmvcfvb_total_factorial_range) = S ((S (ff_i_kmvcfvb_total_factorial_range)) * ff_c_kmvcfvb_total_factorial)) /\ exists ff_q_kmvcfvb_total_factorial_range_decoded. ff_b_kmvcfvb_total_factorial = ff_q_kmvcfvb_total_factorial_range_decoded * S ((S (ff_i_kmvcfvb_total_factorial_range)) * ff_c_kmvcfvb_total_factorial) + (1 + ff_i_kmvcfvb_total_factorial_range)))) /\ (exists ff_u_kmvcfvb_total_factorial_product ff_v_kmvcfvb_total_factorial_product. ((((exists ff_h_kmvcfvb_total_factorial_product_start. ff_h_kmvcfvb_total_factorial_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_total_factorial_product)) /\ exists ff_q_kmvcfvb_total_factorial_product_start. ff_u_kmvcfvb_total_factorial_product = ff_q_kmvcfvb_total_factorial_product_start * S ((S (0)) * ff_v_kmvcfvb_total_factorial_product) + (1))) /\ ((((exists ff_h_kmvcfvb_total_factorial_product_terminal. ff_h_kmvcfvb_total_factorial_product_terminal + S (bfv_factorial_kmvcfvb_total) = S ((S (n)) * ff_v_kmvcfvb_total_factorial_product)) /\ exists ff_q_kmvcfvb_total_factorial_product_terminal. ff_u_kmvcfvb_total_factorial_product = ff_q_kmvcfvb_total_factorial_product_terminal * S ((S (n)) * ff_v_kmvcfvb_total_factorial_product) + (bfv_factorial_kmvcfvb_total))) /\ forall ff_i_kmvcfvb_total_factorial_product. (exists ff_lt_kmvcfvb_total_factorial_product_bound. ff_lt_kmvcfvb_total_factorial_product_bound + S ff_i_kmvcfvb_total_factorial_product = n) -> exists ff_p_kmvcfvb_total_factorial_product ff_r_kmvcfvb_total_factorial_product ff_s_kmvcfvb_total_factorial_product. ((((exists ff_h_kmvcfvb_total_factorial_product_factor. ff_h_kmvcfvb_total_factorial_product_factor + S (ff_p_kmvcfvb_total_factorial_product) = S ((S (ff_i_kmvcfvb_total_factorial_product)) * ff_c_kmvcfvb_total_factorial)) /\ exists ff_q_kmvcfvb_total_factorial_product_factor. ff_b_kmvcfvb_total_factorial = ff_q_kmvcfvb_total_factorial_product_factor * S ((S (ff_i_kmvcfvb_total_factorial_product)) * ff_c_kmvcfvb_total_factorial) + (ff_p_kmvcfvb_total_factorial_product))) /\ ((((exists ff_h_kmvcfvb_total_factorial_product_partial. ff_h_kmvcfvb_total_factorial_product_partial + S (ff_r_kmvcfvb_total_factorial_product) = S ((S (ff_i_kmvcfvb_total_factorial_product)) * ff_v_kmvcfvb_total_factorial_product)) /\ exists ff_q_kmvcfvb_total_factorial_product_partial. ff_u_kmvcfvb_total_factorial_product = ff_q_kmvcfvb_total_factorial_product_partial * S ((S (ff_i_kmvcfvb_total_factorial_product)) * ff_v_kmvcfvb_total_factorial_product) + (ff_r_kmvcfvb_total_factorial_product))) /\ ((((exists ff_h_kmvcfvb_total_factorial_product_successor. ff_h_kmvcfvb_total_factorial_product_successor + S (ff_s_kmvcfvb_total_factorial_product) = S ((S (S ff_i_kmvcfvb_total_factorial_product)) * ff_v_kmvcfvb_total_factorial_product)) /\ exists ff_q_kmvcfvb_total_factorial_product_successor. ff_u_kmvcfvb_total_factorial_product = ff_q_kmvcfvb_total_factorial_product_successor * S ((S (S ff_i_kmvcfvb_total_factorial_product)) * ff_v_kmvcfvb_total_factorial_product) + (ff_s_kmvcfvb_total_factorial_product))) /\ ff_s_kmvcfvb_total_factorial_product = ff_r_kmvcfvb_total_factorial_product * ff_p_kmvcfvb_total_factorial_product)))))))) /\ (((exists bpv_gap_kmvcfvb_total_valuation_exponent_bound. bpv_gap_kmvcfvb_total_valuation_exponent_bound + A = bfv_factorial_kmvcfvb_total) /\ (exists bpv_result_kmvcfvb_total_valuation_selected. ((exists ff_b_kmvcfvb_total_valuation_selected_power ff_c_kmvcfvb_total_valuation_selected_power. ((forall ff_i_kmvcfvb_total_valuation_selected_power_repeat. (exists ff_lt_kmvcfvb_total_valuation_selected_power_repeat_bound. ff_lt_kmvcfvb_total_valuation_selected_power_repeat_bound + S ff_i_kmvcfvb_total_valuation_selected_power_repeat = A) -> (((exists ff_h_kmvcfvb_total_valuation_selected_power_repeat_decoded. ff_h_kmvcfvb_total_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_total_valuation_selected_power_repeat)) * ff_c_kmvcfvb_total_valuation_selected_power)) /\ exists ff_q_kmvcfvb_total_valuation_selected_power_repeat_decoded. ff_b_kmvcfvb_total_valuation_selected_power = ff_q_kmvcfvb_total_valuation_selected_power_repeat_decoded * S ((S (ff_i_kmvcfvb_total_valuation_selected_power_repeat)) * ff_c_kmvcfvb_total_valuation_selected_power) + (p)))) /\ (exists ff_u_kmvcfvb_total_valuation_selected_power_product ff_v_kmvcfvb_total_valuation_selected_power_product. ((((exists ff_h_kmvcfvb_total_valuation_selected_power_product_start. ff_h_kmvcfvb_total_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_total_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_selected_power_product_start. ff_u_kmvcfvb_total_valuation_selected_power_product = ff_q_kmvcfvb_total_valuation_selected_power_product_start * S ((S (0)) * ff_v_kmvcfvb_total_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_total_valuation_selected_power_product_terminal. ff_h_kmvcfvb_total_valuation_selected_power_product_terminal + S (bpv_result_kmvcfvb_total_valuation_selected) = S ((S (A)) * ff_v_kmvcfvb_total_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_selected_power_product_terminal. ff_u_kmvcfvb_total_valuation_selected_power_product = ff_q_kmvcfvb_total_valuation_selected_power_product_terminal * S ((S (A)) * ff_v_kmvcfvb_total_valuation_selected_power_product) + (bpv_result_kmvcfvb_total_valuation_selected))) /\ forall ff_i_kmvcfvb_total_valuation_selected_power_product. (exists ff_lt_kmvcfvb_total_valuation_selected_power_product_bound. ff_lt_kmvcfvb_total_valuation_selected_power_product_bound + S ff_i_kmvcfvb_total_valuation_selected_power_product = A) -> exists ff_p_kmvcfvb_total_valuation_selected_power_product ff_r_kmvcfvb_total_valuation_selected_power_product ff_s_kmvcfvb_total_valuation_selected_power_product. ((((exists ff_h_kmvcfvb_total_valuation_selected_power_product_factor. ff_h_kmvcfvb_total_valuation_selected_power_product_factor + S (ff_p_kmvcfvb_total_valuation_selected_power_product) = S ((S (ff_i_kmvcfvb_total_valuation_selected_power_product)) * ff_c_kmvcfvb_total_valuation_selected_power)) /\ exists ff_q_kmvcfvb_total_valuation_selected_power_product_factor. ff_b_kmvcfvb_total_valuation_selected_power = ff_q_kmvcfvb_total_valuation_selected_power_product_factor * S ((S (ff_i_kmvcfvb_total_valuation_selected_power_product)) * ff_c_kmvcfvb_total_valuation_selected_power) + (ff_p_kmvcfvb_total_valuation_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_total_valuation_selected_power_product_partial. ff_h_kmvcfvb_total_valuation_selected_power_product_partial + S (ff_r_kmvcfvb_total_valuation_selected_power_product) = S ((S (ff_i_kmvcfvb_total_valuation_selected_power_product)) * ff_v_kmvcfvb_total_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_selected_power_product_partial. ff_u_kmvcfvb_total_valuation_selected_power_product = ff_q_kmvcfvb_total_valuation_selected_power_product_partial * S ((S (ff_i_kmvcfvb_total_valuation_selected_power_product)) * ff_v_kmvcfvb_total_valuation_selected_power_product) + (ff_r_kmvcfvb_total_valuation_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_total_valuation_selected_power_product_successor. ff_h_kmvcfvb_total_valuation_selected_power_product_successor + S (ff_s_kmvcfvb_total_valuation_selected_power_product) = S ((S (S ff_i_kmvcfvb_total_valuation_selected_power_product)) * ff_v_kmvcfvb_total_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_selected_power_product_successor. ff_u_kmvcfvb_total_valuation_selected_power_product = ff_q_kmvcfvb_total_valuation_selected_power_product_successor * S ((S (S ff_i_kmvcfvb_total_valuation_selected_power_product)) * ff_v_kmvcfvb_total_valuation_selected_power_product) + (ff_s_kmvcfvb_total_valuation_selected_power_product))) /\ ff_s_kmvcfvb_total_valuation_selected_power_product = ff_r_kmvcfvb_total_valuation_selected_power_product * ff_p_kmvcfvb_total_valuation_selected_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_total_valuation_selected_divides. bfv_factorial_kmvcfvb_total = bpv_result_kmvcfvb_total_valuation_selected * bpv_factor_kmvcfvb_total_valuation_selected_divides)))) /\ forall bpv_candidate_kmvcfvb_total_valuation. (exists bpv_gap_kmvcfvb_total_valuation_candidate_bound. bpv_gap_kmvcfvb_total_valuation_candidate_bound + bpv_candidate_kmvcfvb_total_valuation = bfv_factorial_kmvcfvb_total) -> (exists bpv_result_kmvcfvb_total_valuation_candidate. ((exists ff_b_kmvcfvb_total_valuation_candidate_power ff_c_kmvcfvb_total_valuation_candidate_power. ((forall ff_i_kmvcfvb_total_valuation_candidate_power_repeat. (exists ff_lt_kmvcfvb_total_valuation_candidate_power_repeat_bound. ff_lt_kmvcfvb_total_valuation_candidate_power_repeat_bound + S ff_i_kmvcfvb_total_valuation_candidate_power_repeat = bpv_candidate_kmvcfvb_total_valuation) -> (((exists ff_h_kmvcfvb_total_valuation_candidate_power_repeat_decoded. ff_h_kmvcfvb_total_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_total_valuation_candidate_power_repeat)) * ff_c_kmvcfvb_total_valuation_candidate_power)) /\ exists ff_q_kmvcfvb_total_valuation_candidate_power_repeat_decoded. ff_b_kmvcfvb_total_valuation_candidate_power = ff_q_kmvcfvb_total_valuation_candidate_power_repeat_decoded * S ((S (ff_i_kmvcfvb_total_valuation_candidate_power_repeat)) * ff_c_kmvcfvb_total_valuation_candidate_power) + (p)))) /\ (exists ff_u_kmvcfvb_total_valuation_candidate_power_product ff_v_kmvcfvb_total_valuation_candidate_power_product. ((((exists ff_h_kmvcfvb_total_valuation_candidate_power_product_start. ff_h_kmvcfvb_total_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_total_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_candidate_power_product_start. ff_u_kmvcfvb_total_valuation_candidate_power_product = ff_q_kmvcfvb_total_valuation_candidate_power_product_start * S ((S (0)) * ff_v_kmvcfvb_total_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_total_valuation_candidate_power_product_terminal. ff_h_kmvcfvb_total_valuation_candidate_power_product_terminal + S (bpv_result_kmvcfvb_total_valuation_candidate) = S ((S (bpv_candidate_kmvcfvb_total_valuation)) * ff_v_kmvcfvb_total_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_candidate_power_product_terminal. ff_u_kmvcfvb_total_valuation_candidate_power_product = ff_q_kmvcfvb_total_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_kmvcfvb_total_valuation)) * ff_v_kmvcfvb_total_valuation_candidate_power_product) + (bpv_result_kmvcfvb_total_valuation_candidate))) /\ forall ff_i_kmvcfvb_total_valuation_candidate_power_product. (exists ff_lt_kmvcfvb_total_valuation_candidate_power_product_bound. ff_lt_kmvcfvb_total_valuation_candidate_power_product_bound + S ff_i_kmvcfvb_total_valuation_candidate_power_product = bpv_candidate_kmvcfvb_total_valuation) -> exists ff_p_kmvcfvb_total_valuation_candidate_power_product ff_r_kmvcfvb_total_valuation_candidate_power_product ff_s_kmvcfvb_total_valuation_candidate_power_product. ((((exists ff_h_kmvcfvb_total_valuation_candidate_power_product_factor. ff_h_kmvcfvb_total_valuation_candidate_power_product_factor + S (ff_p_kmvcfvb_total_valuation_candidate_power_product) = S ((S (ff_i_kmvcfvb_total_valuation_candidate_power_product)) * ff_c_kmvcfvb_total_valuation_candidate_power)) /\ exists ff_q_kmvcfvb_total_valuation_candidate_power_product_factor. ff_b_kmvcfvb_total_valuation_candidate_power = ff_q_kmvcfvb_total_valuation_candidate_power_product_factor * S ((S (ff_i_kmvcfvb_total_valuation_candidate_power_product)) * ff_c_kmvcfvb_total_valuation_candidate_power) + (ff_p_kmvcfvb_total_valuation_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_total_valuation_candidate_power_product_partial. ff_h_kmvcfvb_total_valuation_candidate_power_product_partial + S (ff_r_kmvcfvb_total_valuation_candidate_power_product) = S ((S (ff_i_kmvcfvb_total_valuation_candidate_power_product)) * ff_v_kmvcfvb_total_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_candidate_power_product_partial. ff_u_kmvcfvb_total_valuation_candidate_power_product = ff_q_kmvcfvb_total_valuation_candidate_power_product_partial * S ((S (ff_i_kmvcfvb_total_valuation_candidate_power_product)) * ff_v_kmvcfvb_total_valuation_candidate_power_product) + (ff_r_kmvcfvb_total_valuation_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_total_valuation_candidate_power_product_successor. ff_h_kmvcfvb_total_valuation_candidate_power_product_successor + S (ff_s_kmvcfvb_total_valuation_candidate_power_product) = S ((S (S ff_i_kmvcfvb_total_valuation_candidate_power_product)) * ff_v_kmvcfvb_total_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_total_valuation_candidate_power_product_successor. ff_u_kmvcfvb_total_valuation_candidate_power_product = ff_q_kmvcfvb_total_valuation_candidate_power_product_successor * S ((S (S ff_i_kmvcfvb_total_valuation_candidate_power_product)) * ff_v_kmvcfvb_total_valuation_candidate_power_product) + (ff_s_kmvcfvb_total_valuation_candidate_power_product))) /\ ff_s_kmvcfvb_total_valuation_candidate_power_product = ff_r_kmvcfvb_total_valuation_candidate_power_product * ff_p_kmvcfvb_total_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_total_valuation_candidate_divides. bfv_factorial_kmvcfvb_total = bpv_result_kmvcfvb_total_valuation_candidate * bpv_factor_kmvcfvb_total_valuation_candidate_divides))) -> (exists bpv_gap_kmvcfvb_total_valuation_maximal. bpv_gap_kmvcfvb_total_valuation_maximal + bpv_candidate_kmvcfvb_total_valuation = A)))) -> (exists bfv_factorial_kmvcfvb_left. ((exists ff_b_kmvcfvb_left_factorial ff_c_kmvcfvb_left_factorial. ((forall ff_i_kmvcfvb_left_factorial_range. (exists ff_lt_kmvcfvb_left_factorial_range_bound. ff_lt_kmvcfvb_left_factorial_range_bound + S ff_i_kmvcfvb_left_factorial_range = k) -> (((exists ff_h_kmvcfvb_left_factorial_range_decoded. ff_h_kmvcfvb_left_factorial_range_decoded + S (1 + ff_i_kmvcfvb_left_factorial_range) = S ((S (ff_i_kmvcfvb_left_factorial_range)) * ff_c_kmvcfvb_left_factorial)) /\ exists ff_q_kmvcfvb_left_factorial_range_decoded. ff_b_kmvcfvb_left_factorial = ff_q_kmvcfvb_left_factorial_range_decoded * S ((S (ff_i_kmvcfvb_left_factorial_range)) * ff_c_kmvcfvb_left_factorial) + (1 + ff_i_kmvcfvb_left_factorial_range)))) /\ (exists ff_u_kmvcfvb_left_factorial_product ff_v_kmvcfvb_left_factorial_product. ((((exists ff_h_kmvcfvb_left_factorial_product_start. ff_h_kmvcfvb_left_factorial_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_left_factorial_product)) /\ exists ff_q_kmvcfvb_left_factorial_product_start. ff_u_kmvcfvb_left_factorial_product = ff_q_kmvcfvb_left_factorial_product_start * S ((S (0)) * ff_v_kmvcfvb_left_factorial_product) + (1))) /\ ((((exists ff_h_kmvcfvb_left_factorial_product_terminal. ff_h_kmvcfvb_left_factorial_product_terminal + S (bfv_factorial_kmvcfvb_left) = S ((S (k)) * ff_v_kmvcfvb_left_factorial_product)) /\ exists ff_q_kmvcfvb_left_factorial_product_terminal. ff_u_kmvcfvb_left_factorial_product = ff_q_kmvcfvb_left_factorial_product_terminal * S ((S (k)) * ff_v_kmvcfvb_left_factorial_product) + (bfv_factorial_kmvcfvb_left))) /\ forall ff_i_kmvcfvb_left_factorial_product. (exists ff_lt_kmvcfvb_left_factorial_product_bound. ff_lt_kmvcfvb_left_factorial_product_bound + S ff_i_kmvcfvb_left_factorial_product = k) -> exists ff_p_kmvcfvb_left_factorial_product ff_r_kmvcfvb_left_factorial_product ff_s_kmvcfvb_left_factorial_product. ((((exists ff_h_kmvcfvb_left_factorial_product_factor. ff_h_kmvcfvb_left_factorial_product_factor + S (ff_p_kmvcfvb_left_factorial_product) = S ((S (ff_i_kmvcfvb_left_factorial_product)) * ff_c_kmvcfvb_left_factorial)) /\ exists ff_q_kmvcfvb_left_factorial_product_factor. ff_b_kmvcfvb_left_factorial = ff_q_kmvcfvb_left_factorial_product_factor * S ((S (ff_i_kmvcfvb_left_factorial_product)) * ff_c_kmvcfvb_left_factorial) + (ff_p_kmvcfvb_left_factorial_product))) /\ ((((exists ff_h_kmvcfvb_left_factorial_product_partial. ff_h_kmvcfvb_left_factorial_product_partial + S (ff_r_kmvcfvb_left_factorial_product) = S ((S (ff_i_kmvcfvb_left_factorial_product)) * ff_v_kmvcfvb_left_factorial_product)) /\ exists ff_q_kmvcfvb_left_factorial_product_partial. ff_u_kmvcfvb_left_factorial_product = ff_q_kmvcfvb_left_factorial_product_partial * S ((S (ff_i_kmvcfvb_left_factorial_product)) * ff_v_kmvcfvb_left_factorial_product) + (ff_r_kmvcfvb_left_factorial_product))) /\ ((((exists ff_h_kmvcfvb_left_factorial_product_successor. ff_h_kmvcfvb_left_factorial_product_successor + S (ff_s_kmvcfvb_left_factorial_product) = S ((S (S ff_i_kmvcfvb_left_factorial_product)) * ff_v_kmvcfvb_left_factorial_product)) /\ exists ff_q_kmvcfvb_left_factorial_product_successor. ff_u_kmvcfvb_left_factorial_product = ff_q_kmvcfvb_left_factorial_product_successor * S ((S (S ff_i_kmvcfvb_left_factorial_product)) * ff_v_kmvcfvb_left_factorial_product) + (ff_s_kmvcfvb_left_factorial_product))) /\ ff_s_kmvcfvb_left_factorial_product = ff_r_kmvcfvb_left_factorial_product * ff_p_kmvcfvb_left_factorial_product)))))))) /\ (((exists bpv_gap_kmvcfvb_left_valuation_exponent_bound. bpv_gap_kmvcfvb_left_valuation_exponent_bound + B = bfv_factorial_kmvcfvb_left) /\ (exists bpv_result_kmvcfvb_left_valuation_selected. ((exists ff_b_kmvcfvb_left_valuation_selected_power ff_c_kmvcfvb_left_valuation_selected_power. ((forall ff_i_kmvcfvb_left_valuation_selected_power_repeat. (exists ff_lt_kmvcfvb_left_valuation_selected_power_repeat_bound. ff_lt_kmvcfvb_left_valuation_selected_power_repeat_bound + S ff_i_kmvcfvb_left_valuation_selected_power_repeat = B) -> (((exists ff_h_kmvcfvb_left_valuation_selected_power_repeat_decoded. ff_h_kmvcfvb_left_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_left_valuation_selected_power_repeat)) * ff_c_kmvcfvb_left_valuation_selected_power)) /\ exists ff_q_kmvcfvb_left_valuation_selected_power_repeat_decoded. ff_b_kmvcfvb_left_valuation_selected_power = ff_q_kmvcfvb_left_valuation_selected_power_repeat_decoded * S ((S (ff_i_kmvcfvb_left_valuation_selected_power_repeat)) * ff_c_kmvcfvb_left_valuation_selected_power) + (p)))) /\ (exists ff_u_kmvcfvb_left_valuation_selected_power_product ff_v_kmvcfvb_left_valuation_selected_power_product. ((((exists ff_h_kmvcfvb_left_valuation_selected_power_product_start. ff_h_kmvcfvb_left_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_left_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_selected_power_product_start. ff_u_kmvcfvb_left_valuation_selected_power_product = ff_q_kmvcfvb_left_valuation_selected_power_product_start * S ((S (0)) * ff_v_kmvcfvb_left_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_left_valuation_selected_power_product_terminal. ff_h_kmvcfvb_left_valuation_selected_power_product_terminal + S (bpv_result_kmvcfvb_left_valuation_selected) = S ((S (B)) * ff_v_kmvcfvb_left_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_selected_power_product_terminal. ff_u_kmvcfvb_left_valuation_selected_power_product = ff_q_kmvcfvb_left_valuation_selected_power_product_terminal * S ((S (B)) * ff_v_kmvcfvb_left_valuation_selected_power_product) + (bpv_result_kmvcfvb_left_valuation_selected))) /\ forall ff_i_kmvcfvb_left_valuation_selected_power_product. (exists ff_lt_kmvcfvb_left_valuation_selected_power_product_bound. ff_lt_kmvcfvb_left_valuation_selected_power_product_bound + S ff_i_kmvcfvb_left_valuation_selected_power_product = B) -> exists ff_p_kmvcfvb_left_valuation_selected_power_product ff_r_kmvcfvb_left_valuation_selected_power_product ff_s_kmvcfvb_left_valuation_selected_power_product. ((((exists ff_h_kmvcfvb_left_valuation_selected_power_product_factor. ff_h_kmvcfvb_left_valuation_selected_power_product_factor + S (ff_p_kmvcfvb_left_valuation_selected_power_product) = S ((S (ff_i_kmvcfvb_left_valuation_selected_power_product)) * ff_c_kmvcfvb_left_valuation_selected_power)) /\ exists ff_q_kmvcfvb_left_valuation_selected_power_product_factor. ff_b_kmvcfvb_left_valuation_selected_power = ff_q_kmvcfvb_left_valuation_selected_power_product_factor * S ((S (ff_i_kmvcfvb_left_valuation_selected_power_product)) * ff_c_kmvcfvb_left_valuation_selected_power) + (ff_p_kmvcfvb_left_valuation_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_left_valuation_selected_power_product_partial. ff_h_kmvcfvb_left_valuation_selected_power_product_partial + S (ff_r_kmvcfvb_left_valuation_selected_power_product) = S ((S (ff_i_kmvcfvb_left_valuation_selected_power_product)) * ff_v_kmvcfvb_left_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_selected_power_product_partial. ff_u_kmvcfvb_left_valuation_selected_power_product = ff_q_kmvcfvb_left_valuation_selected_power_product_partial * S ((S (ff_i_kmvcfvb_left_valuation_selected_power_product)) * ff_v_kmvcfvb_left_valuation_selected_power_product) + (ff_r_kmvcfvb_left_valuation_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_left_valuation_selected_power_product_successor. ff_h_kmvcfvb_left_valuation_selected_power_product_successor + S (ff_s_kmvcfvb_left_valuation_selected_power_product) = S ((S (S ff_i_kmvcfvb_left_valuation_selected_power_product)) * ff_v_kmvcfvb_left_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_selected_power_product_successor. ff_u_kmvcfvb_left_valuation_selected_power_product = ff_q_kmvcfvb_left_valuation_selected_power_product_successor * S ((S (S ff_i_kmvcfvb_left_valuation_selected_power_product)) * ff_v_kmvcfvb_left_valuation_selected_power_product) + (ff_s_kmvcfvb_left_valuation_selected_power_product))) /\ ff_s_kmvcfvb_left_valuation_selected_power_product = ff_r_kmvcfvb_left_valuation_selected_power_product * ff_p_kmvcfvb_left_valuation_selected_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_left_valuation_selected_divides. bfv_factorial_kmvcfvb_left = bpv_result_kmvcfvb_left_valuation_selected * bpv_factor_kmvcfvb_left_valuation_selected_divides)))) /\ forall bpv_candidate_kmvcfvb_left_valuation. (exists bpv_gap_kmvcfvb_left_valuation_candidate_bound. bpv_gap_kmvcfvb_left_valuation_candidate_bound + bpv_candidate_kmvcfvb_left_valuation = bfv_factorial_kmvcfvb_left) -> (exists bpv_result_kmvcfvb_left_valuation_candidate. ((exists ff_b_kmvcfvb_left_valuation_candidate_power ff_c_kmvcfvb_left_valuation_candidate_power. ((forall ff_i_kmvcfvb_left_valuation_candidate_power_repeat. (exists ff_lt_kmvcfvb_left_valuation_candidate_power_repeat_bound. ff_lt_kmvcfvb_left_valuation_candidate_power_repeat_bound + S ff_i_kmvcfvb_left_valuation_candidate_power_repeat = bpv_candidate_kmvcfvb_left_valuation) -> (((exists ff_h_kmvcfvb_left_valuation_candidate_power_repeat_decoded. ff_h_kmvcfvb_left_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_left_valuation_candidate_power_repeat)) * ff_c_kmvcfvb_left_valuation_candidate_power)) /\ exists ff_q_kmvcfvb_left_valuation_candidate_power_repeat_decoded. ff_b_kmvcfvb_left_valuation_candidate_power = ff_q_kmvcfvb_left_valuation_candidate_power_repeat_decoded * S ((S (ff_i_kmvcfvb_left_valuation_candidate_power_repeat)) * ff_c_kmvcfvb_left_valuation_candidate_power) + (p)))) /\ (exists ff_u_kmvcfvb_left_valuation_candidate_power_product ff_v_kmvcfvb_left_valuation_candidate_power_product. ((((exists ff_h_kmvcfvb_left_valuation_candidate_power_product_start. ff_h_kmvcfvb_left_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_left_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_candidate_power_product_start. ff_u_kmvcfvb_left_valuation_candidate_power_product = ff_q_kmvcfvb_left_valuation_candidate_power_product_start * S ((S (0)) * ff_v_kmvcfvb_left_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_left_valuation_candidate_power_product_terminal. ff_h_kmvcfvb_left_valuation_candidate_power_product_terminal + S (bpv_result_kmvcfvb_left_valuation_candidate) = S ((S (bpv_candidate_kmvcfvb_left_valuation)) * ff_v_kmvcfvb_left_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_candidate_power_product_terminal. ff_u_kmvcfvb_left_valuation_candidate_power_product = ff_q_kmvcfvb_left_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_kmvcfvb_left_valuation)) * ff_v_kmvcfvb_left_valuation_candidate_power_product) + (bpv_result_kmvcfvb_left_valuation_candidate))) /\ forall ff_i_kmvcfvb_left_valuation_candidate_power_product. (exists ff_lt_kmvcfvb_left_valuation_candidate_power_product_bound. ff_lt_kmvcfvb_left_valuation_candidate_power_product_bound + S ff_i_kmvcfvb_left_valuation_candidate_power_product = bpv_candidate_kmvcfvb_left_valuation) -> exists ff_p_kmvcfvb_left_valuation_candidate_power_product ff_r_kmvcfvb_left_valuation_candidate_power_product ff_s_kmvcfvb_left_valuation_candidate_power_product. ((((exists ff_h_kmvcfvb_left_valuation_candidate_power_product_factor. ff_h_kmvcfvb_left_valuation_candidate_power_product_factor + S (ff_p_kmvcfvb_left_valuation_candidate_power_product) = S ((S (ff_i_kmvcfvb_left_valuation_candidate_power_product)) * ff_c_kmvcfvb_left_valuation_candidate_power)) /\ exists ff_q_kmvcfvb_left_valuation_candidate_power_product_factor. ff_b_kmvcfvb_left_valuation_candidate_power = ff_q_kmvcfvb_left_valuation_candidate_power_product_factor * S ((S (ff_i_kmvcfvb_left_valuation_candidate_power_product)) * ff_c_kmvcfvb_left_valuation_candidate_power) + (ff_p_kmvcfvb_left_valuation_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_left_valuation_candidate_power_product_partial. ff_h_kmvcfvb_left_valuation_candidate_power_product_partial + S (ff_r_kmvcfvb_left_valuation_candidate_power_product) = S ((S (ff_i_kmvcfvb_left_valuation_candidate_power_product)) * ff_v_kmvcfvb_left_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_candidate_power_product_partial. ff_u_kmvcfvb_left_valuation_candidate_power_product = ff_q_kmvcfvb_left_valuation_candidate_power_product_partial * S ((S (ff_i_kmvcfvb_left_valuation_candidate_power_product)) * ff_v_kmvcfvb_left_valuation_candidate_power_product) + (ff_r_kmvcfvb_left_valuation_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_left_valuation_candidate_power_product_successor. ff_h_kmvcfvb_left_valuation_candidate_power_product_successor + S (ff_s_kmvcfvb_left_valuation_candidate_power_product) = S ((S (S ff_i_kmvcfvb_left_valuation_candidate_power_product)) * ff_v_kmvcfvb_left_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_left_valuation_candidate_power_product_successor. ff_u_kmvcfvb_left_valuation_candidate_power_product = ff_q_kmvcfvb_left_valuation_candidate_power_product_successor * S ((S (S ff_i_kmvcfvb_left_valuation_candidate_power_product)) * ff_v_kmvcfvb_left_valuation_candidate_power_product) + (ff_s_kmvcfvb_left_valuation_candidate_power_product))) /\ ff_s_kmvcfvb_left_valuation_candidate_power_product = ff_r_kmvcfvb_left_valuation_candidate_power_product * ff_p_kmvcfvb_left_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_left_valuation_candidate_divides. bfv_factorial_kmvcfvb_left = bpv_result_kmvcfvb_left_valuation_candidate * bpv_factor_kmvcfvb_left_valuation_candidate_divides))) -> (exists bpv_gap_kmvcfvb_left_valuation_maximal. bpv_gap_kmvcfvb_left_valuation_maximal + bpv_candidate_kmvcfvb_left_valuation = B)))) -> (exists bfv_factorial_kmvcfvb_right. ((exists ff_b_kmvcfvb_right_factorial ff_c_kmvcfvb_right_factorial. ((forall ff_i_kmvcfvb_right_factorial_range. (exists ff_lt_kmvcfvb_right_factorial_range_bound. ff_lt_kmvcfvb_right_factorial_range_bound + S ff_i_kmvcfvb_right_factorial_range = j) -> (((exists ff_h_kmvcfvb_right_factorial_range_decoded. ff_h_kmvcfvb_right_factorial_range_decoded + S (1 + ff_i_kmvcfvb_right_factorial_range) = S ((S (ff_i_kmvcfvb_right_factorial_range)) * ff_c_kmvcfvb_right_factorial)) /\ exists ff_q_kmvcfvb_right_factorial_range_decoded. ff_b_kmvcfvb_right_factorial = ff_q_kmvcfvb_right_factorial_range_decoded * S ((S (ff_i_kmvcfvb_right_factorial_range)) * ff_c_kmvcfvb_right_factorial) + (1 + ff_i_kmvcfvb_right_factorial_range)))) /\ (exists ff_u_kmvcfvb_right_factorial_product ff_v_kmvcfvb_right_factorial_product. ((((exists ff_h_kmvcfvb_right_factorial_product_start. ff_h_kmvcfvb_right_factorial_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_right_factorial_product)) /\ exists ff_q_kmvcfvb_right_factorial_product_start. ff_u_kmvcfvb_right_factorial_product = ff_q_kmvcfvb_right_factorial_product_start * S ((S (0)) * ff_v_kmvcfvb_right_factorial_product) + (1))) /\ ((((exists ff_h_kmvcfvb_right_factorial_product_terminal. ff_h_kmvcfvb_right_factorial_product_terminal + S (bfv_factorial_kmvcfvb_right) = S ((S (j)) * ff_v_kmvcfvb_right_factorial_product)) /\ exists ff_q_kmvcfvb_right_factorial_product_terminal. ff_u_kmvcfvb_right_factorial_product = ff_q_kmvcfvb_right_factorial_product_terminal * S ((S (j)) * ff_v_kmvcfvb_right_factorial_product) + (bfv_factorial_kmvcfvb_right))) /\ forall ff_i_kmvcfvb_right_factorial_product. (exists ff_lt_kmvcfvb_right_factorial_product_bound. ff_lt_kmvcfvb_right_factorial_product_bound + S ff_i_kmvcfvb_right_factorial_product = j) -> exists ff_p_kmvcfvb_right_factorial_product ff_r_kmvcfvb_right_factorial_product ff_s_kmvcfvb_right_factorial_product. ((((exists ff_h_kmvcfvb_right_factorial_product_factor. ff_h_kmvcfvb_right_factorial_product_factor + S (ff_p_kmvcfvb_right_factorial_product) = S ((S (ff_i_kmvcfvb_right_factorial_product)) * ff_c_kmvcfvb_right_factorial)) /\ exists ff_q_kmvcfvb_right_factorial_product_factor. ff_b_kmvcfvb_right_factorial = ff_q_kmvcfvb_right_factorial_product_factor * S ((S (ff_i_kmvcfvb_right_factorial_product)) * ff_c_kmvcfvb_right_factorial) + (ff_p_kmvcfvb_right_factorial_product))) /\ ((((exists ff_h_kmvcfvb_right_factorial_product_partial. ff_h_kmvcfvb_right_factorial_product_partial + S (ff_r_kmvcfvb_right_factorial_product) = S ((S (ff_i_kmvcfvb_right_factorial_product)) * ff_v_kmvcfvb_right_factorial_product)) /\ exists ff_q_kmvcfvb_right_factorial_product_partial. ff_u_kmvcfvb_right_factorial_product = ff_q_kmvcfvb_right_factorial_product_partial * S ((S (ff_i_kmvcfvb_right_factorial_product)) * ff_v_kmvcfvb_right_factorial_product) + (ff_r_kmvcfvb_right_factorial_product))) /\ ((((exists ff_h_kmvcfvb_right_factorial_product_successor. ff_h_kmvcfvb_right_factorial_product_successor + S (ff_s_kmvcfvb_right_factorial_product) = S ((S (S ff_i_kmvcfvb_right_factorial_product)) * ff_v_kmvcfvb_right_factorial_product)) /\ exists ff_q_kmvcfvb_right_factorial_product_successor. ff_u_kmvcfvb_right_factorial_product = ff_q_kmvcfvb_right_factorial_product_successor * S ((S (S ff_i_kmvcfvb_right_factorial_product)) * ff_v_kmvcfvb_right_factorial_product) + (ff_s_kmvcfvb_right_factorial_product))) /\ ff_s_kmvcfvb_right_factorial_product = ff_r_kmvcfvb_right_factorial_product * ff_p_kmvcfvb_right_factorial_product)))))))) /\ (((exists bpv_gap_kmvcfvb_right_valuation_exponent_bound. bpv_gap_kmvcfvb_right_valuation_exponent_bound + D = bfv_factorial_kmvcfvb_right) /\ (exists bpv_result_kmvcfvb_right_valuation_selected. ((exists ff_b_kmvcfvb_right_valuation_selected_power ff_c_kmvcfvb_right_valuation_selected_power. ((forall ff_i_kmvcfvb_right_valuation_selected_power_repeat. (exists ff_lt_kmvcfvb_right_valuation_selected_power_repeat_bound. ff_lt_kmvcfvb_right_valuation_selected_power_repeat_bound + S ff_i_kmvcfvb_right_valuation_selected_power_repeat = D) -> (((exists ff_h_kmvcfvb_right_valuation_selected_power_repeat_decoded. ff_h_kmvcfvb_right_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_right_valuation_selected_power_repeat)) * ff_c_kmvcfvb_right_valuation_selected_power)) /\ exists ff_q_kmvcfvb_right_valuation_selected_power_repeat_decoded. ff_b_kmvcfvb_right_valuation_selected_power = ff_q_kmvcfvb_right_valuation_selected_power_repeat_decoded * S ((S (ff_i_kmvcfvb_right_valuation_selected_power_repeat)) * ff_c_kmvcfvb_right_valuation_selected_power) + (p)))) /\ (exists ff_u_kmvcfvb_right_valuation_selected_power_product ff_v_kmvcfvb_right_valuation_selected_power_product. ((((exists ff_h_kmvcfvb_right_valuation_selected_power_product_start. ff_h_kmvcfvb_right_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_right_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_selected_power_product_start. ff_u_kmvcfvb_right_valuation_selected_power_product = ff_q_kmvcfvb_right_valuation_selected_power_product_start * S ((S (0)) * ff_v_kmvcfvb_right_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_right_valuation_selected_power_product_terminal. ff_h_kmvcfvb_right_valuation_selected_power_product_terminal + S (bpv_result_kmvcfvb_right_valuation_selected) = S ((S (D)) * ff_v_kmvcfvb_right_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_selected_power_product_terminal. ff_u_kmvcfvb_right_valuation_selected_power_product = ff_q_kmvcfvb_right_valuation_selected_power_product_terminal * S ((S (D)) * ff_v_kmvcfvb_right_valuation_selected_power_product) + (bpv_result_kmvcfvb_right_valuation_selected))) /\ forall ff_i_kmvcfvb_right_valuation_selected_power_product. (exists ff_lt_kmvcfvb_right_valuation_selected_power_product_bound. ff_lt_kmvcfvb_right_valuation_selected_power_product_bound + S ff_i_kmvcfvb_right_valuation_selected_power_product = D) -> exists ff_p_kmvcfvb_right_valuation_selected_power_product ff_r_kmvcfvb_right_valuation_selected_power_product ff_s_kmvcfvb_right_valuation_selected_power_product. ((((exists ff_h_kmvcfvb_right_valuation_selected_power_product_factor. ff_h_kmvcfvb_right_valuation_selected_power_product_factor + S (ff_p_kmvcfvb_right_valuation_selected_power_product) = S ((S (ff_i_kmvcfvb_right_valuation_selected_power_product)) * ff_c_kmvcfvb_right_valuation_selected_power)) /\ exists ff_q_kmvcfvb_right_valuation_selected_power_product_factor. ff_b_kmvcfvb_right_valuation_selected_power = ff_q_kmvcfvb_right_valuation_selected_power_product_factor * S ((S (ff_i_kmvcfvb_right_valuation_selected_power_product)) * ff_c_kmvcfvb_right_valuation_selected_power) + (ff_p_kmvcfvb_right_valuation_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_right_valuation_selected_power_product_partial. ff_h_kmvcfvb_right_valuation_selected_power_product_partial + S (ff_r_kmvcfvb_right_valuation_selected_power_product) = S ((S (ff_i_kmvcfvb_right_valuation_selected_power_product)) * ff_v_kmvcfvb_right_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_selected_power_product_partial. ff_u_kmvcfvb_right_valuation_selected_power_product = ff_q_kmvcfvb_right_valuation_selected_power_product_partial * S ((S (ff_i_kmvcfvb_right_valuation_selected_power_product)) * ff_v_kmvcfvb_right_valuation_selected_power_product) + (ff_r_kmvcfvb_right_valuation_selected_power_product))) /\ ((((exists ff_h_kmvcfvb_right_valuation_selected_power_product_successor. ff_h_kmvcfvb_right_valuation_selected_power_product_successor + S (ff_s_kmvcfvb_right_valuation_selected_power_product) = S ((S (S ff_i_kmvcfvb_right_valuation_selected_power_product)) * ff_v_kmvcfvb_right_valuation_selected_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_selected_power_product_successor. ff_u_kmvcfvb_right_valuation_selected_power_product = ff_q_kmvcfvb_right_valuation_selected_power_product_successor * S ((S (S ff_i_kmvcfvb_right_valuation_selected_power_product)) * ff_v_kmvcfvb_right_valuation_selected_power_product) + (ff_s_kmvcfvb_right_valuation_selected_power_product))) /\ ff_s_kmvcfvb_right_valuation_selected_power_product = ff_r_kmvcfvb_right_valuation_selected_power_product * ff_p_kmvcfvb_right_valuation_selected_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_right_valuation_selected_divides. bfv_factorial_kmvcfvb_right = bpv_result_kmvcfvb_right_valuation_selected * bpv_factor_kmvcfvb_right_valuation_selected_divides)))) /\ forall bpv_candidate_kmvcfvb_right_valuation. (exists bpv_gap_kmvcfvb_right_valuation_candidate_bound. bpv_gap_kmvcfvb_right_valuation_candidate_bound + bpv_candidate_kmvcfvb_right_valuation = bfv_factorial_kmvcfvb_right) -> (exists bpv_result_kmvcfvb_right_valuation_candidate. ((exists ff_b_kmvcfvb_right_valuation_candidate_power ff_c_kmvcfvb_right_valuation_candidate_power. ((forall ff_i_kmvcfvb_right_valuation_candidate_power_repeat. (exists ff_lt_kmvcfvb_right_valuation_candidate_power_repeat_bound. ff_lt_kmvcfvb_right_valuation_candidate_power_repeat_bound + S ff_i_kmvcfvb_right_valuation_candidate_power_repeat = bpv_candidate_kmvcfvb_right_valuation) -> (((exists ff_h_kmvcfvb_right_valuation_candidate_power_repeat_decoded. ff_h_kmvcfvb_right_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_kmvcfvb_right_valuation_candidate_power_repeat)) * ff_c_kmvcfvb_right_valuation_candidate_power)) /\ exists ff_q_kmvcfvb_right_valuation_candidate_power_repeat_decoded. ff_b_kmvcfvb_right_valuation_candidate_power = ff_q_kmvcfvb_right_valuation_candidate_power_repeat_decoded * S ((S (ff_i_kmvcfvb_right_valuation_candidate_power_repeat)) * ff_c_kmvcfvb_right_valuation_candidate_power) + (p)))) /\ (exists ff_u_kmvcfvb_right_valuation_candidate_power_product ff_v_kmvcfvb_right_valuation_candidate_power_product. ((((exists ff_h_kmvcfvb_right_valuation_candidate_power_product_start. ff_h_kmvcfvb_right_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_kmvcfvb_right_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_candidate_power_product_start. ff_u_kmvcfvb_right_valuation_candidate_power_product = ff_q_kmvcfvb_right_valuation_candidate_power_product_start * S ((S (0)) * ff_v_kmvcfvb_right_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_kmvcfvb_right_valuation_candidate_power_product_terminal. ff_h_kmvcfvb_right_valuation_candidate_power_product_terminal + S (bpv_result_kmvcfvb_right_valuation_candidate) = S ((S (bpv_candidate_kmvcfvb_right_valuation)) * ff_v_kmvcfvb_right_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_candidate_power_product_terminal. ff_u_kmvcfvb_right_valuation_candidate_power_product = ff_q_kmvcfvb_right_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_kmvcfvb_right_valuation)) * ff_v_kmvcfvb_right_valuation_candidate_power_product) + (bpv_result_kmvcfvb_right_valuation_candidate))) /\ forall ff_i_kmvcfvb_right_valuation_candidate_power_product. (exists ff_lt_kmvcfvb_right_valuation_candidate_power_product_bound. ff_lt_kmvcfvb_right_valuation_candidate_power_product_bound + S ff_i_kmvcfvb_right_valuation_candidate_power_product = bpv_candidate_kmvcfvb_right_valuation) -> exists ff_p_kmvcfvb_right_valuation_candidate_power_product ff_r_kmvcfvb_right_valuation_candidate_power_product ff_s_kmvcfvb_right_valuation_candidate_power_product. ((((exists ff_h_kmvcfvb_right_valuation_candidate_power_product_factor. ff_h_kmvcfvb_right_valuation_candidate_power_product_factor + S (ff_p_kmvcfvb_right_valuation_candidate_power_product) = S ((S (ff_i_kmvcfvb_right_valuation_candidate_power_product)) * ff_c_kmvcfvb_right_valuation_candidate_power)) /\ exists ff_q_kmvcfvb_right_valuation_candidate_power_product_factor. ff_b_kmvcfvb_right_valuation_candidate_power = ff_q_kmvcfvb_right_valuation_candidate_power_product_factor * S ((S (ff_i_kmvcfvb_right_valuation_candidate_power_product)) * ff_c_kmvcfvb_right_valuation_candidate_power) + (ff_p_kmvcfvb_right_valuation_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_right_valuation_candidate_power_product_partial. ff_h_kmvcfvb_right_valuation_candidate_power_product_partial + S (ff_r_kmvcfvb_right_valuation_candidate_power_product) = S ((S (ff_i_kmvcfvb_right_valuation_candidate_power_product)) * ff_v_kmvcfvb_right_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_candidate_power_product_partial. ff_u_kmvcfvb_right_valuation_candidate_power_product = ff_q_kmvcfvb_right_valuation_candidate_power_product_partial * S ((S (ff_i_kmvcfvb_right_valuation_candidate_power_product)) * ff_v_kmvcfvb_right_valuation_candidate_power_product) + (ff_r_kmvcfvb_right_valuation_candidate_power_product))) /\ ((((exists ff_h_kmvcfvb_right_valuation_candidate_power_product_successor. ff_h_kmvcfvb_right_valuation_candidate_power_product_successor + S (ff_s_kmvcfvb_right_valuation_candidate_power_product) = S ((S (S ff_i_kmvcfvb_right_valuation_candidate_power_product)) * ff_v_kmvcfvb_right_valuation_candidate_power_product)) /\ exists ff_q_kmvcfvb_right_valuation_candidate_power_product_successor. ff_u_kmvcfvb_right_valuation_candidate_power_product = ff_q_kmvcfvb_right_valuation_candidate_power_product_successor * S ((S (S ff_i_kmvcfvb_right_valuation_candidate_power_product)) * ff_v_kmvcfvb_right_valuation_candidate_power_product) + (ff_s_kmvcfvb_right_valuation_candidate_power_product))) /\ ff_s_kmvcfvb_right_valuation_candidate_power_product = ff_r_kmvcfvb_right_valuation_candidate_power_product * ff_p_kmvcfvb_right_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_kmvcfvb_right_valuation_candidate_divides. bfv_factorial_kmvcfvb_right = bpv_result_kmvcfvb_right_valuation_candidate * bpv_factor_kmvcfvb_right_valuation_candidate_divides))) -> (exists bpv_gap_kmvcfvb_right_valuation_maximal. bpv_gap_kmvcfvb_right_valuation_maximal + bpv_candidate_kmvcfvb_right_valuation = D)))) -> A = (B + D) + e

Every purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.

Definitions used by this theorem

In the theorem statement

In local proof propositions

Proof neighborhood

Direct theorem prerequisites

Direct theorem dependents

Definition-aware tactic body

Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay command.