multinomial_valuations_give_carry_prefix

Exact expanded first-order arithmetic statement

forall p b c sb sc cb cc vb vc l. ((~(p = 1) /\ forall frm_prime_left_mkm_rows_prime frm_prime_right_mkm_rows_prime. p = frm_prime_left_mkm_rows_prime * frm_prime_right_mkm_rows_prime -> frm_prime_left_mkm_rows_prime = 1 \/ frm_prime_right_mkm_rows_prime = 1)) -> (forall mkm_index_rows_binomial. (exists mkm_lt_rows_binomial_bound. mkm_lt_rows_binomial_bound + S (mkm_index_rows_binomial) = (l)) -> (exists mkm_value_rows_binomial_point mkm_partial_rows_binomial_point mkm_factor_rows_binomial_point. (((exists fs_h_mkm_rows_binomial_point_source. fs_h_mkm_rows_binomial_point_source + S (mkm_value_rows_binomial_point) = S ((S (mkm_index_rows_binomial)) * c)) /\ exists fs_q_mkm_rows_binomial_point_source. b = fs_q_mkm_rows_binomial_point_source * S ((S (mkm_index_rows_binomial)) * c) + (mkm_value_rows_binomial_point))) /\ ((((exists fs_h_mkm_rows_binomial_point_partial. fs_h_mkm_rows_binomial_point_partial + S (mkm_partial_rows_binomial_point) = S ((S (mkm_index_rows_binomial)) * sc)) /\ exists fs_q_mkm_rows_binomial_point_partial. sb = fs_q_mkm_rows_binomial_point_partial * S ((S (mkm_index_rows_binomial)) * sc) + (mkm_partial_rows_binomial_point))) /\ ((((exists bcf_lt_gap_mkm_rows_binomial_point_choose_out_of_range. bcf_lt_gap_mkm_rows_binomial_point_choose_out_of_range + S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point) = mkm_partial_rows_binomial_point) /\ mkm_factor_rows_binomial_point = 0) \/ ((exists bcf_le_gap_mkm_rows_binomial_point_choose_in_range. bcf_le_gap_mkm_rows_binomial_point_choose_in_range + (mkm_partial_rows_binomial_point) = mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point) /\ (exists bcf_row_code_code_mkm_rows_binomial_point_choose bcf_row_code_scale_mkm_rows_binomial_point_choose bcf_row_scale_code_mkm_rows_binomial_point_choose bcf_row_scale_scale_mkm_rows_binomial_point_choose bcf_row_code_mkm_rows_binomial_point_choose bcf_row_scale_mkm_rows_binomial_point_choose. ((forall bcf_row_index_mkm_rows_binomial_point_choose_table. (exists bcf_lt_gap_mkm_rows_binomial_point_choose_table_row_bound. bcf_lt_gap_mkm_rows_binomial_point_choose_table_row_bound + S (bcf_row_index_mkm_rows_binomial_point_choose_table) = S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) -> exists bcf_row_code_mkm_rows_binomial_point_choose_table bcf_row_scale_mkm_rows_binomial_point_choose_table. ((((exists bcf_height_mkm_rows_binomial_point_choose_table_decoded_row_code. bcf_height_mkm_rows_binomial_point_choose_table_decoded_row_code + S (bcf_row_code_mkm_rows_binomial_point_choose_table) = S ((S (bcf_row_index_mkm_rows_binomial_point_choose_table)) * bcf_row_code_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_row_code. bcf_row_code_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_row_code * S ((S (bcf_row_index_mkm_rows_binomial_point_choose_table)) * bcf_row_code_scale_mkm_rows_binomial_point_choose) + (bcf_row_code_mkm_rows_binomial_point_choose_table))) /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_table_decoded_row_scale. bcf_height_mkm_rows_binomial_point_choose_table_decoded_row_scale + S (bcf_row_scale_mkm_rows_binomial_point_choose_table) = S ((S (bcf_row_index_mkm_rows_binomial_point_choose_table)) * bcf_row_scale_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_row_scale. bcf_row_scale_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_row_scale * S ((S (bcf_row_index_mkm_rows_binomial_point_choose_table)) * bcf_row_scale_scale_mkm_rows_binomial_point_choose) + (bcf_row_scale_mkm_rows_binomial_point_choose_table))) /\ ((bcf_row_index_mkm_rows_binomial_point_choose_table = 0 /\ (forall bcf_index_mkm_rows_binomial_point_choose_table_zero_row. (exists bcf_lt_gap_mkm_rows_binomial_point_choose_table_zero_row_bound. bcf_lt_gap_mkm_rows_binomial_point_choose_table_zero_row_bound + S (bcf_index_mkm_rows_binomial_point_choose_table_zero_row) = S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) -> exists bcf_value_mkm_rows_binomial_point_choose_table_zero_row. ((((exists bcf_height_mkm_rows_binomial_point_choose_table_zero_row_entry. bcf_height_mkm_rows_binomial_point_choose_table_zero_row_entry + S (bcf_value_mkm_rows_binomial_point_choose_table_zero_row) = S ((S (bcf_index_mkm_rows_binomial_point_choose_table_zero_row)) * bcf_row_scale_mkm_rows_binomial_point_choose_table)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_zero_row_entry. bcf_row_code_mkm_rows_binomial_point_choose_table = bcf_quotient_mkm_rows_binomial_point_choose_table_zero_row_entry * S ((S (bcf_index_mkm_rows_binomial_point_choose_table_zero_row)) * bcf_row_scale_mkm_rows_binomial_point_choose_table) + (bcf_value_mkm_rows_binomial_point_choose_table_zero_row))) /\ ((bcf_index_mkm_rows_binomial_point_choose_table_zero_row = 0 /\ bcf_value_mkm_rows_binomial_point_choose_table_zero_row = 1) \/ exists bcf_predecessor_mkm_rows_binomial_point_choose_table_zero_row. bcf_index_mkm_rows_binomial_point_choose_table_zero_row = S bcf_predecessor_mkm_rows_binomial_point_choose_table_zero_row /\ bcf_value_mkm_rows_binomial_point_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_mkm_rows_binomial_point_choose_table bcf_previous_code_mkm_rows_binomial_point_choose_table bcf_previous_scale_mkm_rows_binomial_point_choose_table. bcf_row_index_mkm_rows_binomial_point_choose_table = S bcf_predecessor_mkm_rows_binomial_point_choose_table /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_table_decoded_previous_code. bcf_height_mkm_rows_binomial_point_choose_table_decoded_previous_code + S (bcf_previous_code_mkm_rows_binomial_point_choose_table) = S ((S (bcf_predecessor_mkm_rows_binomial_point_choose_table)) * bcf_row_code_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_previous_code. bcf_row_code_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_previous_code * S ((S (bcf_predecessor_mkm_rows_binomial_point_choose_table)) * bcf_row_code_scale_mkm_rows_binomial_point_choose) + (bcf_previous_code_mkm_rows_binomial_point_choose_table))) /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_table_decoded_previous_scale. bcf_height_mkm_rows_binomial_point_choose_table_decoded_previous_scale + S (bcf_previous_scale_mkm_rows_binomial_point_choose_table) = S ((S (bcf_predecessor_mkm_rows_binomial_point_choose_table)) * bcf_row_scale_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_previous_scale. bcf_row_scale_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_mkm_rows_binomial_point_choose_table)) * bcf_row_scale_scale_mkm_rows_binomial_point_choose) + (bcf_previous_scale_mkm_rows_binomial_point_choose_table))) /\ (forall bcf_index_mkm_rows_binomial_point_choose_table_row_step. (exists bcf_lt_gap_mkm_rows_binomial_point_choose_table_row_step_bound. bcf_lt_gap_mkm_rows_binomial_point_choose_table_row_step_bound + S (bcf_index_mkm_rows_binomial_point_choose_table_row_step) = S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) -> exists bcf_value_mkm_rows_binomial_point_choose_table_row_step. ((((exists bcf_height_mkm_rows_binomial_point_choose_table_row_step_entry. bcf_height_mkm_rows_binomial_point_choose_table_row_step_entry + S (bcf_value_mkm_rows_binomial_point_choose_table_row_step) = S ((S (bcf_index_mkm_rows_binomial_point_choose_table_row_step)) * bcf_row_scale_mkm_rows_binomial_point_choose_table)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_row_step_entry. bcf_row_code_mkm_rows_binomial_point_choose_table = bcf_quotient_mkm_rows_binomial_point_choose_table_row_step_entry * S ((S (bcf_index_mkm_rows_binomial_point_choose_table_row_step)) * bcf_row_scale_mkm_rows_binomial_point_choose_table) + (bcf_value_mkm_rows_binomial_point_choose_table_row_step))) /\ ((bcf_index_mkm_rows_binomial_point_choose_table_row_step = 0 /\ bcf_value_mkm_rows_binomial_point_choose_table_row_step = 1) \/ exists bcf_predecessor_mkm_rows_binomial_point_choose_table_row_step bcf_left_mkm_rows_binomial_point_choose_table_row_step bcf_right_mkm_rows_binomial_point_choose_table_row_step. bcf_index_mkm_rows_binomial_point_choose_table_row_step = S bcf_predecessor_mkm_rows_binomial_point_choose_table_row_step /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_table_row_step_previous_left. bcf_height_mkm_rows_binomial_point_choose_table_row_step_previous_left + S (bcf_left_mkm_rows_binomial_point_choose_table_row_step) = S ((S (bcf_predecessor_mkm_rows_binomial_point_choose_table_row_step)) * bcf_previous_scale_mkm_rows_binomial_point_choose_table)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_row_step_previous_left. bcf_previous_code_mkm_rows_binomial_point_choose_table = bcf_quotient_mkm_rows_binomial_point_choose_table_row_step_previous_left * S ((S (bcf_predecessor_mkm_rows_binomial_point_choose_table_row_step)) * bcf_previous_scale_mkm_rows_binomial_point_choose_table) + (bcf_left_mkm_rows_binomial_point_choose_table_row_step))) /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_table_row_step_previous_right. bcf_height_mkm_rows_binomial_point_choose_table_row_step_previous_right + S (bcf_right_mkm_rows_binomial_point_choose_table_row_step) = S ((S (S (bcf_predecessor_mkm_rows_binomial_point_choose_table_row_step))) * bcf_previous_scale_mkm_rows_binomial_point_choose_table)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_table_row_step_previous_right. bcf_previous_code_mkm_rows_binomial_point_choose_table = bcf_quotient_mkm_rows_binomial_point_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_mkm_rows_binomial_point_choose_table_row_step))) * bcf_previous_scale_mkm_rows_binomial_point_choose_table) + (bcf_right_mkm_rows_binomial_point_choose_table_row_step))) /\ bcf_value_mkm_rows_binomial_point_choose_table_row_step = bcf_left_mkm_rows_binomial_point_choose_table_row_step + bcf_right_mkm_rows_binomial_point_choose_table_row_step))))))))))) /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_decoded_row_code. bcf_height_mkm_rows_binomial_point_choose_decoded_row_code + S (bcf_row_code_mkm_rows_binomial_point_choose) = S ((S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) * bcf_row_code_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_decoded_row_code. bcf_row_code_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_decoded_row_code * S ((S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) * bcf_row_code_scale_mkm_rows_binomial_point_choose) + (bcf_row_code_mkm_rows_binomial_point_choose))) /\ ((((exists bcf_height_mkm_rows_binomial_point_choose_decoded_row_scale. bcf_height_mkm_rows_binomial_point_choose_decoded_row_scale + S (bcf_row_scale_mkm_rows_binomial_point_choose) = S ((S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) * bcf_row_scale_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_decoded_row_scale. bcf_row_scale_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_decoded_row_scale * S ((S (mkm_partial_rows_binomial_point + mkm_value_rows_binomial_point)) * bcf_row_scale_scale_mkm_rows_binomial_point_choose) + (bcf_row_scale_mkm_rows_binomial_point_choose))) /\ (((exists bcf_height_mkm_rows_binomial_point_choose_decoded_value. bcf_height_mkm_rows_binomial_point_choose_decoded_value + S (mkm_factor_rows_binomial_point) = S ((S (mkm_partial_rows_binomial_point)) * bcf_row_scale_mkm_rows_binomial_point_choose)) /\ exists bcf_quotient_mkm_rows_binomial_point_choose_decoded_value. bcf_row_code_mkm_rows_binomial_point_choose = bcf_quotient_mkm_rows_binomial_point_choose_decoded_value * S ((S (mkm_partial_rows_binomial_point)) * bcf_row_scale_mkm_rows_binomial_point_choose) + (mkm_factor_rows_binomial_point))))))))) /\ (((exists fs_h_mkm_rows_binomial_point_factor. fs_h_mkm_rows_binomial_point_factor + S (mkm_factor_rows_binomial_point) = S ((S (mkm_index_rows_binomial)) * cc)) /\ exists fs_q_mkm_rows_binomial_point_factor. cb = fs_q_mkm_rows_binomial_point_factor * S ((S (mkm_index_rows_binomial)) * cc) + (mkm_factor_rows_binomial_point))))))) -> (forall mkm_index_rows_valuations. (exists mkm_lt_rows_valuations_bound. mkm_lt_rows_valuations_bound + S (mkm_index_rows_valuations) = (l)) -> (exists mkm_value_rows_valuations_point mkm_exponent_rows_valuations_point. (((exists fs_h_mkm_rows_valuations_point_source. fs_h_mkm_rows_valuations_point_source + S (mkm_value_rows_valuations_point) = S ((S (mkm_index_rows_valuations)) * cc)) /\ exists fs_q_mkm_rows_valuations_point_source. cb = fs_q_mkm_rows_valuations_point_source * S ((S (mkm_index_rows_valuations)) * cc) + (mkm_value_rows_valuations_point))) /\ ((((exists fs_h_mkm_rows_valuations_point_decoded. fs_h_mkm_rows_valuations_point_decoded + S (mkm_exponent_rows_valuations_point) = S ((S (mkm_index_rows_valuations)) * vc)) /\ exists fs_q_mkm_rows_valuations_point_decoded. vb = fs_q_mkm_rows_valuations_point_decoded * S ((S (mkm_index_rows_valuations)) * vc) + (mkm_exponent_rows_valuations_point))) /\ (((exists bpv_gap_mkm_rows_valuations_point_valuation_exponent_bound. bpv_gap_mkm_rows_valuations_point_valuation_exponent_bound + mkm_exponent_rows_valuations_point = (mkm_value_rows_valuations_point)) /\ (exists bpv_result_mkm_rows_valuations_point_valuation_selected. ((exists ff_b_mkm_rows_valuations_point_valuation_selected_power ff_c_mkm_rows_valuations_point_valuation_selected_power. ((forall ff_i_mkm_rows_valuations_point_valuation_selected_power_repeat. (exists ff_lt_mkm_rows_valuations_point_valuation_selected_power_repeat_bound. ff_lt_mkm_rows_valuations_point_valuation_selected_power_repeat_bound + S ff_i_mkm_rows_valuations_point_valuation_selected_power_repeat = mkm_exponent_rows_valuations_point) -> (((exists ff_h_mkm_rows_valuations_point_valuation_selected_power_repeat_decoded. ff_h_mkm_rows_valuations_point_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_mkm_rows_valuations_point_valuation_selected_power_repeat)) * ff_c_mkm_rows_valuations_point_valuation_selected_power)) /\ exists ff_q_mkm_rows_valuations_point_valuation_selected_power_repeat_decoded. ff_b_mkm_rows_valuations_point_valuation_selected_power = ff_q_mkm_rows_valuations_point_valuation_selected_power_repeat_decoded * S ((S (ff_i_mkm_rows_valuations_point_valuation_selected_power_repeat)) * ff_c_mkm_rows_valuations_point_valuation_selected_power) + (p)))) /\ (exists ff_u_mkm_rows_valuations_point_valuation_selected_power_product ff_v_mkm_rows_valuations_point_valuation_selected_power_product. ((((exists ff_h_mkm_rows_valuations_point_valuation_selected_power_product_start. ff_h_mkm_rows_valuations_point_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_selected_power_product_start. ff_u_mkm_rows_valuations_point_valuation_selected_power_product = ff_q_mkm_rows_valuations_point_valuation_selected_power_product_start * S ((S (0)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_mkm_rows_valuations_point_valuation_selected_power_product_terminal. ff_h_mkm_rows_valuations_point_valuation_selected_power_product_terminal + S (bpv_result_mkm_rows_valuations_point_valuation_selected) = S ((S (mkm_exponent_rows_valuations_point)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_selected_power_product_terminal. ff_u_mkm_rows_valuations_point_valuation_selected_power_product = ff_q_mkm_rows_valuations_point_valuation_selected_power_product_terminal * S ((S (mkm_exponent_rows_valuations_point)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product) + (bpv_result_mkm_rows_valuations_point_valuation_selected))) /\ forall ff_i_mkm_rows_valuations_point_valuation_selected_power_product. (exists ff_lt_mkm_rows_valuations_point_valuation_selected_power_product_bound. ff_lt_mkm_rows_valuations_point_valuation_selected_power_product_bound + S ff_i_mkm_rows_valuations_point_valuation_selected_power_product = mkm_exponent_rows_valuations_point) -> exists ff_p_mkm_rows_valuations_point_valuation_selected_power_product ff_r_mkm_rows_valuations_point_valuation_selected_power_product ff_s_mkm_rows_valuations_point_valuation_selected_power_product. ((((exists ff_h_mkm_rows_valuations_point_valuation_selected_power_product_factor. ff_h_mkm_rows_valuations_point_valuation_selected_power_product_factor + S (ff_p_mkm_rows_valuations_point_valuation_selected_power_product) = S ((S (ff_i_mkm_rows_valuations_point_valuation_selected_power_product)) * ff_c_mkm_rows_valuations_point_valuation_selected_power)) /\ exists ff_q_mkm_rows_valuations_point_valuation_selected_power_product_factor. ff_b_mkm_rows_valuations_point_valuation_selected_power = ff_q_mkm_rows_valuations_point_valuation_selected_power_product_factor * S ((S (ff_i_mkm_rows_valuations_point_valuation_selected_power_product)) * ff_c_mkm_rows_valuations_point_valuation_selected_power) + (ff_p_mkm_rows_valuations_point_valuation_selected_power_product))) /\ ((((exists ff_h_mkm_rows_valuations_point_valuation_selected_power_product_partial. ff_h_mkm_rows_valuations_point_valuation_selected_power_product_partial + S (ff_r_mkm_rows_valuations_point_valuation_selected_power_product) = S ((S (ff_i_mkm_rows_valuations_point_valuation_selected_power_product)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_selected_power_product_partial. ff_u_mkm_rows_valuations_point_valuation_selected_power_product = ff_q_mkm_rows_valuations_point_valuation_selected_power_product_partial * S ((S (ff_i_mkm_rows_valuations_point_valuation_selected_power_product)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product) + (ff_r_mkm_rows_valuations_point_valuation_selected_power_product))) /\ ((((exists ff_h_mkm_rows_valuations_point_valuation_selected_power_product_successor. ff_h_mkm_rows_valuations_point_valuation_selected_power_product_successor + S (ff_s_mkm_rows_valuations_point_valuation_selected_power_product) = S ((S (S ff_i_mkm_rows_valuations_point_valuation_selected_power_product)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_selected_power_product_successor. ff_u_mkm_rows_valuations_point_valuation_selected_power_product = ff_q_mkm_rows_valuations_point_valuation_selected_power_product_successor * S ((S (S ff_i_mkm_rows_valuations_point_valuation_selected_power_product)) * ff_v_mkm_rows_valuations_point_valuation_selected_power_product) + (ff_s_mkm_rows_valuations_point_valuation_selected_power_product))) /\ ff_s_mkm_rows_valuations_point_valuation_selected_power_product = ff_r_mkm_rows_valuations_point_valuation_selected_power_product * ff_p_mkm_rows_valuations_point_valuation_selected_power_product)))))))) /\ (exists bpv_factor_mkm_rows_valuations_point_valuation_selected_divides. (mkm_value_rows_valuations_point) = bpv_result_mkm_rows_valuations_point_valuation_selected * bpv_factor_mkm_rows_valuations_point_valuation_selected_divides)))) /\ forall bpv_candidate_mkm_rows_valuations_point_valuation. (exists bpv_gap_mkm_rows_valuations_point_valuation_candidate_bound. bpv_gap_mkm_rows_valuations_point_valuation_candidate_bound + bpv_candidate_mkm_rows_valuations_point_valuation = (mkm_value_rows_valuations_point)) -> (exists bpv_result_mkm_rows_valuations_point_valuation_candidate. ((exists ff_b_mkm_rows_valuations_point_valuation_candidate_power ff_c_mkm_rows_valuations_point_valuation_candidate_power. ((forall ff_i_mkm_rows_valuations_point_valuation_candidate_power_repeat. (exists ff_lt_mkm_rows_valuations_point_valuation_candidate_power_repeat_bound. ff_lt_mkm_rows_valuations_point_valuation_candidate_power_repeat_bound + S ff_i_mkm_rows_valuations_point_valuation_candidate_power_repeat = bpv_candidate_mkm_rows_valuations_point_valuation) -> (((exists ff_h_mkm_rows_valuations_point_valuation_candidate_power_repeat_decoded. ff_h_mkm_rows_valuations_point_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_mkm_rows_valuations_point_valuation_candidate_power_repeat)) * ff_c_mkm_rows_valuations_point_valuation_candidate_power)) /\ exists ff_q_mkm_rows_valuations_point_valuation_candidate_power_repeat_decoded. ff_b_mkm_rows_valuations_point_valuation_candidate_power = ff_q_mkm_rows_valuations_point_valuation_candidate_power_repeat_decoded * S ((S (ff_i_mkm_rows_valuations_point_valuation_candidate_power_repeat)) * ff_c_mkm_rows_valuations_point_valuation_candidate_power) + (p)))) /\ (exists ff_u_mkm_rows_valuations_point_valuation_candidate_power_product ff_v_mkm_rows_valuations_point_valuation_candidate_power_product. ((((exists ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_start. ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_start. ff_u_mkm_rows_valuations_point_valuation_candidate_power_product = ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_start * S ((S (0)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_terminal. ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_terminal + S (bpv_result_mkm_rows_valuations_point_valuation_candidate) = S ((S (bpv_candidate_mkm_rows_valuations_point_valuation)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_terminal. ff_u_mkm_rows_valuations_point_valuation_candidate_power_product = ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_mkm_rows_valuations_point_valuation)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product) + (bpv_result_mkm_rows_valuations_point_valuation_candidate))) /\ forall ff_i_mkm_rows_valuations_point_valuation_candidate_power_product. (exists ff_lt_mkm_rows_valuations_point_valuation_candidate_power_product_bound. ff_lt_mkm_rows_valuations_point_valuation_candidate_power_product_bound + S ff_i_mkm_rows_valuations_point_valuation_candidate_power_product = bpv_candidate_mkm_rows_valuations_point_valuation) -> exists ff_p_mkm_rows_valuations_point_valuation_candidate_power_product ff_r_mkm_rows_valuations_point_valuation_candidate_power_product ff_s_mkm_rows_valuations_point_valuation_candidate_power_product. ((((exists ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_factor. ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_factor + S (ff_p_mkm_rows_valuations_point_valuation_candidate_power_product) = S ((S (ff_i_mkm_rows_valuations_point_valuation_candidate_power_product)) * ff_c_mkm_rows_valuations_point_valuation_candidate_power)) /\ exists ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_factor. ff_b_mkm_rows_valuations_point_valuation_candidate_power = ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_factor * S ((S (ff_i_mkm_rows_valuations_point_valuation_candidate_power_product)) * ff_c_mkm_rows_valuations_point_valuation_candidate_power) + (ff_p_mkm_rows_valuations_point_valuation_candidate_power_product))) /\ ((((exists ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_partial. ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_partial + S (ff_r_mkm_rows_valuations_point_valuation_candidate_power_product) = S ((S (ff_i_mkm_rows_valuations_point_valuation_candidate_power_product)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_partial. ff_u_mkm_rows_valuations_point_valuation_candidate_power_product = ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_partial * S ((S (ff_i_mkm_rows_valuations_point_valuation_candidate_power_product)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product) + (ff_r_mkm_rows_valuations_point_valuation_candidate_power_product))) /\ ((((exists ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_successor. ff_h_mkm_rows_valuations_point_valuation_candidate_power_product_successor + S (ff_s_mkm_rows_valuations_point_valuation_candidate_power_product) = S ((S (S ff_i_mkm_rows_valuations_point_valuation_candidate_power_product)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product)) /\ exists ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_successor. ff_u_mkm_rows_valuations_point_valuation_candidate_power_product = ff_q_mkm_rows_valuations_point_valuation_candidate_power_product_successor * S ((S (S ff_i_mkm_rows_valuations_point_valuation_candidate_power_product)) * ff_v_mkm_rows_valuations_point_valuation_candidate_power_product) + (ff_s_mkm_rows_valuations_point_valuation_candidate_power_product))) /\ ff_s_mkm_rows_valuations_point_valuation_candidate_power_product = ff_r_mkm_rows_valuations_point_valuation_candidate_power_product * ff_p_mkm_rows_valuations_point_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_mkm_rows_valuations_point_valuation_candidate_divides. (mkm_value_rows_valuations_point) = bpv_result_mkm_rows_valuations_point_valuation_candidate * bpv_factor_mkm_rows_valuations_point_valuation_candidate_divides))) -> (exists bpv_gap_mkm_rows_valuations_point_valuation_maximal. bpv_gap_mkm_rows_valuations_point_valuation_maximal + bpv_candidate_mkm_rows_valuations_point_valuation = mkm_exponent_rows_valuations_point))))) -> (forall mkm_index_rows_carries. (exists mkm_lt_rows_carries_bound. mkm_lt_rows_carries_bound + S (mkm_index_rows_carries) = (l)) -> (exists mkm_value_rows_carries_point mkm_partial_rows_carries_point mkm_count_rows_carries_point. (((exists fs_h_mkm_rows_carries_point_source. fs_h_mkm_rows_carries_point_source + S (mkm_value_rows_carries_point) = S ((S (mkm_index_rows_carries)) * c)) /\ exists fs_q_mkm_rows_carries_point_source. b = fs_q_mkm_rows_carries_point_source * S ((S (mkm_index_rows_carries)) * c) + (mkm_value_rows_carries_point))) /\ ((((exists fs_h_mkm_rows_carries_point_partial. fs_h_mkm_rows_carries_point_partial + S (mkm_partial_rows_carries_point) = S ((S (mkm_index_rows_carries)) * sc)) /\ exists fs_q_mkm_rows_carries_point_partial. sb = fs_q_mkm_rows_carries_point_partial * S ((S (mkm_index_rows_carries)) * sc) + (mkm_partial_rows_carries_point))) /\ ((((exists fs_h_mkm_rows_carries_point_stored. fs_h_mkm_rows_carries_point_stored + S (mkm_count_rows_carries_point) = S ((S (mkm_index_rows_carries)) * vc)) /\ exists fs_q_mkm_rows_carries_point_stored. vb = fs_q_mkm_rows_carries_point_stored * S ((S (mkm_index_rows_carries)) * vc) + (mkm_count_rows_carries_point))) /\ (exists mkm_lb_rows_carries_point_binary mkm_lc_rows_carries_point_binary mkm_rb_rows_carries_point_binary mkm_rc_rows_carries_point_binary mkm_tb_rows_carries_point_binary mkm_tc_rows_carries_point_binary mkm_cb_rows_carries_point_binary mkm_cc_rows_carries_point_binary. (forall bls_index_mkm_rows_carries_point_binary_left. (exists bls_gap_mkm_rows_carries_point_binary_left_bound. bls_gap_mkm_rows_carries_point_binary_left_bound + S (bls_index_mkm_rows_carries_point_binary_left) = (mkm_partial_rows_carries_point + mkm_value_rows_carries_point)) -> exists bls_power_mkm_rows_carries_point_binary_left bls_quotient_mkm_rows_carries_point_binary_left bls_remainder_mkm_rows_carries_point_binary_left. ((exists bpvi_b_bls_mkm_rows_carries_point_binary_left_power bpvi_c_bls_mkm_rows_carries_point_binary_left_power. ((forall bpvi_i_bls_mkm_rows_carries_point_binary_left_power. (exists bpvi_repeat_gap_bls_mkm_rows_carries_point_binary_left_power. bpvi_repeat_gap_bls_mkm_rows_carries_point_binary_left_power + S bpvi_i_bls_mkm_rows_carries_point_binary_left_power = S bls_index_mkm_rows_carries_point_binary_left) -> (((exists bpvi_h_bls_mkm_rows_carries_point_binary_left_power_repeat. bpvi_h_bls_mkm_rows_carries_point_binary_left_power_repeat + S (p) = S ((S (bpvi_i_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_left_power_repeat. bpvi_b_bls_mkm_rows_carries_point_binary_left_power = bpvi_q_bls_mkm_rows_carries_point_binary_left_power_repeat * S ((S (bpvi_i_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_left_power) + (p)))) /\ (exists bpvi_u_bls_mkm_rows_carries_point_binary_left_power bpvi_v_bls_mkm_rows_carries_point_binary_left_power. ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_left_power_start. bpvi_h_bls_mkm_rows_carries_point_binary_left_power_start + S (1) = S ((S (0)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_left_power_start. bpvi_u_bls_mkm_rows_carries_point_binary_left_power = bpvi_q_bls_mkm_rows_carries_point_binary_left_power_start * S ((S (0)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power) + (1))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_left_power_terminal. bpvi_h_bls_mkm_rows_carries_point_binary_left_power_terminal + S (bls_power_mkm_rows_carries_point_binary_left) = S ((S (S bls_index_mkm_rows_carries_point_binary_left)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_left_power_terminal. bpvi_u_bls_mkm_rows_carries_point_binary_left_power = bpvi_q_bls_mkm_rows_carries_point_binary_left_power_terminal * S ((S (S bls_index_mkm_rows_carries_point_binary_left)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power) + (bls_power_mkm_rows_carries_point_binary_left))) /\ forall bpvi_j_bls_mkm_rows_carries_point_binary_left_power. (exists bpvi_product_gap_bls_mkm_rows_carries_point_binary_left_power. bpvi_product_gap_bls_mkm_rows_carries_point_binary_left_power + S bpvi_j_bls_mkm_rows_carries_point_binary_left_power = S bls_index_mkm_rows_carries_point_binary_left) -> exists bpvi_factor_bls_mkm_rows_carries_point_binary_left_power bpvi_partial_bls_mkm_rows_carries_point_binary_left_power bpvi_successor_bls_mkm_rows_carries_point_binary_left_power. ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_left_power_factor. bpvi_h_bls_mkm_rows_carries_point_binary_left_power_factor + S (bpvi_factor_bls_mkm_rows_carries_point_binary_left_power) = S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_left_power_factor. bpvi_b_bls_mkm_rows_carries_point_binary_left_power = bpvi_q_bls_mkm_rows_carries_point_binary_left_power_factor * S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_left_power) + (bpvi_factor_bls_mkm_rows_carries_point_binary_left_power))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_left_power_partial. bpvi_h_bls_mkm_rows_carries_point_binary_left_power_partial + S (bpvi_partial_bls_mkm_rows_carries_point_binary_left_power) = S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_left_power_partial. bpvi_u_bls_mkm_rows_carries_point_binary_left_power = bpvi_q_bls_mkm_rows_carries_point_binary_left_power_partial * S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power) + (bpvi_partial_bls_mkm_rows_carries_point_binary_left_power))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_left_power_successor. bpvi_h_bls_mkm_rows_carries_point_binary_left_power_successor + S (bpvi_successor_bls_mkm_rows_carries_point_binary_left_power) = S ((S (S bpvi_j_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_left_power_successor. bpvi_u_bls_mkm_rows_carries_point_binary_left_power = bpvi_q_bls_mkm_rows_carries_point_binary_left_power_successor * S ((S (S bpvi_j_bls_mkm_rows_carries_point_binary_left_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_left_power) + (bpvi_successor_bls_mkm_rows_carries_point_binary_left_power))) /\ bpvi_successor_bls_mkm_rows_carries_point_binary_left_power = bpvi_partial_bls_mkm_rows_carries_point_binary_left_power * bpvi_factor_bls_mkm_rows_carries_point_binary_left_power)))))))) /\ ((((exists ff_h_bls_mkm_rows_carries_point_binary_left_quotient_entry. ff_h_bls_mkm_rows_carries_point_binary_left_quotient_entry + S (bls_quotient_mkm_rows_carries_point_binary_left) = S ((S (bls_index_mkm_rows_carries_point_binary_left)) * mkm_lc_rows_carries_point_binary)) /\ exists ff_q_bls_mkm_rows_carries_point_binary_left_quotient_entry. mkm_lb_rows_carries_point_binary = ff_q_bls_mkm_rows_carries_point_binary_left_quotient_entry * S ((S (bls_index_mkm_rows_carries_point_binary_left)) * mkm_lc_rows_carries_point_binary) + (bls_quotient_mkm_rows_carries_point_binary_left))) /\ ((mkm_partial_rows_carries_point = bls_power_mkm_rows_carries_point_binary_left * bls_quotient_mkm_rows_carries_point_binary_left + bls_remainder_mkm_rows_carries_point_binary_left /\ exists bls_remainder_gap_mkm_rows_carries_point_binary_left_division. bls_remainder_gap_mkm_rows_carries_point_binary_left_division + S (bls_remainder_mkm_rows_carries_point_binary_left) = bls_power_mkm_rows_carries_point_binary_left))))) /\ ((forall bls_index_mkm_rows_carries_point_binary_right. (exists bls_gap_mkm_rows_carries_point_binary_right_bound. bls_gap_mkm_rows_carries_point_binary_right_bound + S (bls_index_mkm_rows_carries_point_binary_right) = (mkm_partial_rows_carries_point + mkm_value_rows_carries_point)) -> exists bls_power_mkm_rows_carries_point_binary_right bls_quotient_mkm_rows_carries_point_binary_right bls_remainder_mkm_rows_carries_point_binary_right. ((exists bpvi_b_bls_mkm_rows_carries_point_binary_right_power bpvi_c_bls_mkm_rows_carries_point_binary_right_power. ((forall bpvi_i_bls_mkm_rows_carries_point_binary_right_power. (exists bpvi_repeat_gap_bls_mkm_rows_carries_point_binary_right_power. bpvi_repeat_gap_bls_mkm_rows_carries_point_binary_right_power + S bpvi_i_bls_mkm_rows_carries_point_binary_right_power = S bls_index_mkm_rows_carries_point_binary_right) -> (((exists bpvi_h_bls_mkm_rows_carries_point_binary_right_power_repeat. bpvi_h_bls_mkm_rows_carries_point_binary_right_power_repeat + S (p) = S ((S (bpvi_i_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_right_power_repeat. bpvi_b_bls_mkm_rows_carries_point_binary_right_power = bpvi_q_bls_mkm_rows_carries_point_binary_right_power_repeat * S ((S (bpvi_i_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_right_power) + (p)))) /\ (exists bpvi_u_bls_mkm_rows_carries_point_binary_right_power bpvi_v_bls_mkm_rows_carries_point_binary_right_power. ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_right_power_start. bpvi_h_bls_mkm_rows_carries_point_binary_right_power_start + S (1) = S ((S (0)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_right_power_start. bpvi_u_bls_mkm_rows_carries_point_binary_right_power = bpvi_q_bls_mkm_rows_carries_point_binary_right_power_start * S ((S (0)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power) + (1))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_right_power_terminal. bpvi_h_bls_mkm_rows_carries_point_binary_right_power_terminal + S (bls_power_mkm_rows_carries_point_binary_right) = S ((S (S bls_index_mkm_rows_carries_point_binary_right)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_right_power_terminal. bpvi_u_bls_mkm_rows_carries_point_binary_right_power = bpvi_q_bls_mkm_rows_carries_point_binary_right_power_terminal * S ((S (S bls_index_mkm_rows_carries_point_binary_right)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power) + (bls_power_mkm_rows_carries_point_binary_right))) /\ forall bpvi_j_bls_mkm_rows_carries_point_binary_right_power. (exists bpvi_product_gap_bls_mkm_rows_carries_point_binary_right_power. bpvi_product_gap_bls_mkm_rows_carries_point_binary_right_power + S bpvi_j_bls_mkm_rows_carries_point_binary_right_power = S bls_index_mkm_rows_carries_point_binary_right) -> exists bpvi_factor_bls_mkm_rows_carries_point_binary_right_power bpvi_partial_bls_mkm_rows_carries_point_binary_right_power bpvi_successor_bls_mkm_rows_carries_point_binary_right_power. ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_right_power_factor. bpvi_h_bls_mkm_rows_carries_point_binary_right_power_factor + S (bpvi_factor_bls_mkm_rows_carries_point_binary_right_power) = S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_right_power_factor. bpvi_b_bls_mkm_rows_carries_point_binary_right_power = bpvi_q_bls_mkm_rows_carries_point_binary_right_power_factor * S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_right_power) + (bpvi_factor_bls_mkm_rows_carries_point_binary_right_power))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_right_power_partial. bpvi_h_bls_mkm_rows_carries_point_binary_right_power_partial + S (bpvi_partial_bls_mkm_rows_carries_point_binary_right_power) = S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_right_power_partial. bpvi_u_bls_mkm_rows_carries_point_binary_right_power = bpvi_q_bls_mkm_rows_carries_point_binary_right_power_partial * S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power) + (bpvi_partial_bls_mkm_rows_carries_point_binary_right_power))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_right_power_successor. bpvi_h_bls_mkm_rows_carries_point_binary_right_power_successor + S (bpvi_successor_bls_mkm_rows_carries_point_binary_right_power) = S ((S (S bpvi_j_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_right_power_successor. bpvi_u_bls_mkm_rows_carries_point_binary_right_power = bpvi_q_bls_mkm_rows_carries_point_binary_right_power_successor * S ((S (S bpvi_j_bls_mkm_rows_carries_point_binary_right_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_right_power) + (bpvi_successor_bls_mkm_rows_carries_point_binary_right_power))) /\ bpvi_successor_bls_mkm_rows_carries_point_binary_right_power = bpvi_partial_bls_mkm_rows_carries_point_binary_right_power * bpvi_factor_bls_mkm_rows_carries_point_binary_right_power)))))))) /\ ((((exists ff_h_bls_mkm_rows_carries_point_binary_right_quotient_entry. ff_h_bls_mkm_rows_carries_point_binary_right_quotient_entry + S (bls_quotient_mkm_rows_carries_point_binary_right) = S ((S (bls_index_mkm_rows_carries_point_binary_right)) * mkm_rc_rows_carries_point_binary)) /\ exists ff_q_bls_mkm_rows_carries_point_binary_right_quotient_entry. mkm_rb_rows_carries_point_binary = ff_q_bls_mkm_rows_carries_point_binary_right_quotient_entry * S ((S (bls_index_mkm_rows_carries_point_binary_right)) * mkm_rc_rows_carries_point_binary) + (bls_quotient_mkm_rows_carries_point_binary_right))) /\ ((mkm_value_rows_carries_point = bls_power_mkm_rows_carries_point_binary_right * bls_quotient_mkm_rows_carries_point_binary_right + bls_remainder_mkm_rows_carries_point_binary_right /\ exists bls_remainder_gap_mkm_rows_carries_point_binary_right_division. bls_remainder_gap_mkm_rows_carries_point_binary_right_division + S (bls_remainder_mkm_rows_carries_point_binary_right) = bls_power_mkm_rows_carries_point_binary_right))))) /\ ((forall bls_index_mkm_rows_carries_point_binary_total. (exists bls_gap_mkm_rows_carries_point_binary_total_bound. bls_gap_mkm_rows_carries_point_binary_total_bound + S (bls_index_mkm_rows_carries_point_binary_total) = (mkm_partial_rows_carries_point + mkm_value_rows_carries_point)) -> exists bls_power_mkm_rows_carries_point_binary_total bls_quotient_mkm_rows_carries_point_binary_total bls_remainder_mkm_rows_carries_point_binary_total. ((exists bpvi_b_bls_mkm_rows_carries_point_binary_total_power bpvi_c_bls_mkm_rows_carries_point_binary_total_power. ((forall bpvi_i_bls_mkm_rows_carries_point_binary_total_power. (exists bpvi_repeat_gap_bls_mkm_rows_carries_point_binary_total_power. bpvi_repeat_gap_bls_mkm_rows_carries_point_binary_total_power + S bpvi_i_bls_mkm_rows_carries_point_binary_total_power = S bls_index_mkm_rows_carries_point_binary_total) -> (((exists bpvi_h_bls_mkm_rows_carries_point_binary_total_power_repeat. bpvi_h_bls_mkm_rows_carries_point_binary_total_power_repeat + S (p) = S ((S (bpvi_i_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_total_power_repeat. bpvi_b_bls_mkm_rows_carries_point_binary_total_power = bpvi_q_bls_mkm_rows_carries_point_binary_total_power_repeat * S ((S (bpvi_i_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_total_power) + (p)))) /\ (exists bpvi_u_bls_mkm_rows_carries_point_binary_total_power bpvi_v_bls_mkm_rows_carries_point_binary_total_power. ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_total_power_start. bpvi_h_bls_mkm_rows_carries_point_binary_total_power_start + S (1) = S ((S (0)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_total_power_start. bpvi_u_bls_mkm_rows_carries_point_binary_total_power = bpvi_q_bls_mkm_rows_carries_point_binary_total_power_start * S ((S (0)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power) + (1))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_total_power_terminal. bpvi_h_bls_mkm_rows_carries_point_binary_total_power_terminal + S (bls_power_mkm_rows_carries_point_binary_total) = S ((S (S bls_index_mkm_rows_carries_point_binary_total)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_total_power_terminal. bpvi_u_bls_mkm_rows_carries_point_binary_total_power = bpvi_q_bls_mkm_rows_carries_point_binary_total_power_terminal * S ((S (S bls_index_mkm_rows_carries_point_binary_total)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power) + (bls_power_mkm_rows_carries_point_binary_total))) /\ forall bpvi_j_bls_mkm_rows_carries_point_binary_total_power. (exists bpvi_product_gap_bls_mkm_rows_carries_point_binary_total_power. bpvi_product_gap_bls_mkm_rows_carries_point_binary_total_power + S bpvi_j_bls_mkm_rows_carries_point_binary_total_power = S bls_index_mkm_rows_carries_point_binary_total) -> exists bpvi_factor_bls_mkm_rows_carries_point_binary_total_power bpvi_partial_bls_mkm_rows_carries_point_binary_total_power bpvi_successor_bls_mkm_rows_carries_point_binary_total_power. ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_total_power_factor. bpvi_h_bls_mkm_rows_carries_point_binary_total_power_factor + S (bpvi_factor_bls_mkm_rows_carries_point_binary_total_power) = S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_total_power_factor. bpvi_b_bls_mkm_rows_carries_point_binary_total_power = bpvi_q_bls_mkm_rows_carries_point_binary_total_power_factor * S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_c_bls_mkm_rows_carries_point_binary_total_power) + (bpvi_factor_bls_mkm_rows_carries_point_binary_total_power))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_total_power_partial. bpvi_h_bls_mkm_rows_carries_point_binary_total_power_partial + S (bpvi_partial_bls_mkm_rows_carries_point_binary_total_power) = S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_total_power_partial. bpvi_u_bls_mkm_rows_carries_point_binary_total_power = bpvi_q_bls_mkm_rows_carries_point_binary_total_power_partial * S ((S (bpvi_j_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power) + (bpvi_partial_bls_mkm_rows_carries_point_binary_total_power))) /\ ((((exists bpvi_h_bls_mkm_rows_carries_point_binary_total_power_successor. bpvi_h_bls_mkm_rows_carries_point_binary_total_power_successor + S (bpvi_successor_bls_mkm_rows_carries_point_binary_total_power) = S ((S (S bpvi_j_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_rows_carries_point_binary_total_power_successor. bpvi_u_bls_mkm_rows_carries_point_binary_total_power = bpvi_q_bls_mkm_rows_carries_point_binary_total_power_successor * S ((S (S bpvi_j_bls_mkm_rows_carries_point_binary_total_power)) * bpvi_v_bls_mkm_rows_carries_point_binary_total_power) + (bpvi_successor_bls_mkm_rows_carries_point_binary_total_power))) /\ bpvi_successor_bls_mkm_rows_carries_point_binary_total_power = bpvi_partial_bls_mkm_rows_carries_point_binary_total_power * bpvi_factor_bls_mkm_rows_carries_point_binary_total_power)))))))) /\ ((((exists ff_h_bls_mkm_rows_carries_point_binary_total_quotient_entry. ff_h_bls_mkm_rows_carries_point_binary_total_quotient_entry + S (bls_quotient_mkm_rows_carries_point_binary_total) = S ((S (bls_index_mkm_rows_carries_point_binary_total)) * mkm_tc_rows_carries_point_binary)) /\ exists ff_q_bls_mkm_rows_carries_point_binary_total_quotient_entry. mkm_tb_rows_carries_point_binary = ff_q_bls_mkm_rows_carries_point_binary_total_quotient_entry * S ((S (bls_index_mkm_rows_carries_point_binary_total)) * mkm_tc_rows_carries_point_binary) + (bls_quotient_mkm_rows_carries_point_binary_total))) /\ ((mkm_partial_rows_carries_point + mkm_value_rows_carries_point = bls_power_mkm_rows_carries_point_binary_total * bls_quotient_mkm_rows_carries_point_binary_total + bls_remainder_mkm_rows_carries_point_binary_total /\ exists bls_remainder_gap_mkm_rows_carries_point_binary_total_division. bls_remainder_gap_mkm_rows_carries_point_binary_total_division + S (bls_remainder_mkm_rows_carries_point_binary_total) = bls_power_mkm_rows_carries_point_binary_total))))) /\ ((forall kmc_index_mkm_rows_carries_point_binary_carries. (exists bcf_lt_gap_mkm_rows_carries_point_binary_carries_bound. bcf_lt_gap_mkm_rows_carries_point_binary_carries_bound + S (kmc_index_mkm_rows_carries_point_binary_carries) = mkm_partial_rows_carries_point + mkm_value_rows_carries_point) -> exists kmc_left_mkm_rows_carries_point_binary_carries kmc_right_mkm_rows_carries_point_binary_carries kmc_total_mkm_rows_carries_point_binary_carries kmc_bit_mkm_rows_carries_point_binary_carries. (((exists fs_h_mkm_rows_carries_point_binary_carries_left. fs_h_mkm_rows_carries_point_binary_carries_left + S (kmc_left_mkm_rows_carries_point_binary_carries) = S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_lc_rows_carries_point_binary)) /\ exists fs_q_mkm_rows_carries_point_binary_carries_left. mkm_lb_rows_carries_point_binary = fs_q_mkm_rows_carries_point_binary_carries_left * S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_lc_rows_carries_point_binary) + (kmc_left_mkm_rows_carries_point_binary_carries))) /\ ((((exists fs_h_mkm_rows_carries_point_binary_carries_right. fs_h_mkm_rows_carries_point_binary_carries_right + S (kmc_right_mkm_rows_carries_point_binary_carries) = S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_rc_rows_carries_point_binary)) /\ exists fs_q_mkm_rows_carries_point_binary_carries_right. mkm_rb_rows_carries_point_binary = fs_q_mkm_rows_carries_point_binary_carries_right * S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_rc_rows_carries_point_binary) + (kmc_right_mkm_rows_carries_point_binary_carries))) /\ ((((exists fs_h_mkm_rows_carries_point_binary_carries_total. fs_h_mkm_rows_carries_point_binary_carries_total + S (kmc_total_mkm_rows_carries_point_binary_carries) = S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_tc_rows_carries_point_binary)) /\ exists fs_q_mkm_rows_carries_point_binary_carries_total. mkm_tb_rows_carries_point_binary = fs_q_mkm_rows_carries_point_binary_carries_total * S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_tc_rows_carries_point_binary) + (kmc_total_mkm_rows_carries_point_binary_carries))) /\ ((((exists fs_h_mkm_rows_carries_point_binary_carries_bit. fs_h_mkm_rows_carries_point_binary_carries_bit + S (kmc_bit_mkm_rows_carries_point_binary_carries) = S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_cc_rows_carries_point_binary)) /\ exists fs_q_mkm_rows_carries_point_binary_carries_bit. mkm_cb_rows_carries_point_binary = fs_q_mkm_rows_carries_point_binary_carries_bit * S ((S (kmc_index_mkm_rows_carries_point_binary_carries)) * mkm_cc_rows_carries_point_binary) + (kmc_bit_mkm_rows_carries_point_binary_carries))) /\ (((kmc_bit_mkm_rows_carries_point_binary_carries = 0 /\ kmc_total_mkm_rows_carries_point_binary_carries = kmc_left_mkm_rows_carries_point_binary_carries + kmc_right_mkm_rows_carries_point_binary_carries) \/ (kmc_bit_mkm_rows_carries_point_binary_carries = 1 /\ kmc_total_mkm_rows_carries_point_binary_carries = S (kmc_left_mkm_rows_carries_point_binary_carries + kmc_right_mkm_rows_carries_point_binary_carries)))))))) /\ (((exists ff_u_mkm_rows_carries_point_binary_count_sum ff_v_mkm_rows_carries_point_binary_count_sum. ((((exists ff_h_mkm_rows_carries_point_binary_count_sum_start. ff_h_mkm_rows_carries_point_binary_count_sum_start + S (0) = S ((S (0)) * ff_v_mkm_rows_carries_point_binary_count_sum)) /\ exists ff_q_mkm_rows_carries_point_binary_count_sum_start. ff_u_mkm_rows_carries_point_binary_count_sum = ff_q_mkm_rows_carries_point_binary_count_sum_start * S ((S (0)) * ff_v_mkm_rows_carries_point_binary_count_sum) + (0))) /\ ((((exists ff_h_mkm_rows_carries_point_binary_count_sum_terminal. ff_h_mkm_rows_carries_point_binary_count_sum_terminal + S ((mkm_count_rows_carries_point)) = S ((S ((mkm_partial_rows_carries_point + mkm_value_rows_carries_point))) * ff_v_mkm_rows_carries_point_binary_count_sum)) /\ exists ff_q_mkm_rows_carries_point_binary_count_sum_terminal. ff_u_mkm_rows_carries_point_binary_count_sum = ff_q_mkm_rows_carries_point_binary_count_sum_terminal * S ((S ((mkm_partial_rows_carries_point + mkm_value_rows_carries_point))) * ff_v_mkm_rows_carries_point_binary_count_sum) + ((mkm_count_rows_carries_point)))) /\ forall ff_i_mkm_rows_carries_point_binary_count_sum. (exists ff_lt_mkm_rows_carries_point_binary_count_sum_bound. ff_lt_mkm_rows_carries_point_binary_count_sum_bound + S ff_i_mkm_rows_carries_point_binary_count_sum = (mkm_partial_rows_carries_point + mkm_value_rows_carries_point)) -> exists ff_a_mkm_rows_carries_point_binary_count_sum ff_r_mkm_rows_carries_point_binary_count_sum ff_s_mkm_rows_carries_point_binary_count_sum. ((((exists ff_h_mkm_rows_carries_point_binary_count_sum_summand. ff_h_mkm_rows_carries_point_binary_count_sum_summand + S (ff_a_mkm_rows_carries_point_binary_count_sum) = S ((S (ff_i_mkm_rows_carries_point_binary_count_sum)) * mkm_cc_rows_carries_point_binary)) /\ exists ff_q_mkm_rows_carries_point_binary_count_sum_summand. mkm_cb_rows_carries_point_binary = ff_q_mkm_rows_carries_point_binary_count_sum_summand * S ((S (ff_i_mkm_rows_carries_point_binary_count_sum)) * mkm_cc_rows_carries_point_binary) + (ff_a_mkm_rows_carries_point_binary_count_sum))) /\ ((((exists ff_h_mkm_rows_carries_point_binary_count_sum_partial. ff_h_mkm_rows_carries_point_binary_count_sum_partial + S (ff_r_mkm_rows_carries_point_binary_count_sum) = S ((S (ff_i_mkm_rows_carries_point_binary_count_sum)) * ff_v_mkm_rows_carries_point_binary_count_sum)) /\ exists ff_q_mkm_rows_carries_point_binary_count_sum_partial. ff_u_mkm_rows_carries_point_binary_count_sum = ff_q_mkm_rows_carries_point_binary_count_sum_partial * S ((S (ff_i_mkm_rows_carries_point_binary_count_sum)) * ff_v_mkm_rows_carries_point_binary_count_sum) + (ff_r_mkm_rows_carries_point_binary_count_sum))) /\ ((((exists ff_h_mkm_rows_carries_point_binary_count_sum_successor. ff_h_mkm_rows_carries_point_binary_count_sum_successor + S (ff_s_mkm_rows_carries_point_binary_count_sum) = S ((S (S ff_i_mkm_rows_carries_point_binary_count_sum)) * ff_v_mkm_rows_carries_point_binary_count_sum)) /\ exists ff_q_mkm_rows_carries_point_binary_count_sum_successor. ff_u_mkm_rows_carries_point_binary_count_sum = ff_q_mkm_rows_carries_point_binary_count_sum_successor * S ((S (S ff_i_mkm_rows_carries_point_binary_count_sum)) * ff_v_mkm_rows_carries_point_binary_count_sum) + (ff_s_mkm_rows_carries_point_binary_count_sum))) /\ ff_s_mkm_rows_carries_point_binary_count_sum = ff_r_mkm_rows_carries_point_binary_count_sum + ff_a_mkm_rows_carries_point_binary_count_sum)))))) /\ (forall ff_i_mkm_rows_carries_point_binary_count_bits. (exists ff_lt_mkm_rows_carries_point_binary_count_bits_bound. ff_lt_mkm_rows_carries_point_binary_count_bits_bound + S ff_i_mkm_rows_carries_point_binary_count_bits = (mkm_partial_rows_carries_point + mkm_value_rows_carries_point)) -> exists ff_bit_mkm_rows_carries_point_binary_count_bits. ((((exists ff_h_mkm_rows_carries_point_binary_count_bits_decoded. ff_h_mkm_rows_carries_point_binary_count_bits_decoded + S (ff_bit_mkm_rows_carries_point_binary_count_bits) = S ((S (ff_i_mkm_rows_carries_point_binary_count_bits)) * mkm_cc_rows_carries_point_binary)) /\ exists ff_q_mkm_rows_carries_point_binary_count_bits_decoded. mkm_cb_rows_carries_point_binary = ff_q_mkm_rows_carries_point_binary_count_bits_decoded * S ((S (ff_i_mkm_rows_carries_point_binary_count_bits)) * mkm_cc_rows_carries_point_binary) + (ff_bit_mkm_rows_carries_point_binary_count_bits))) /\ (ff_bit_mkm_rows_carries_point_binary_count_bits = 0 \/ ff_bit_mkm_rows_carries_point_binary_count_bits = 1)))))))))))))