kummer_binomial_carry_bit_count

forall p a b C v. ((~(p = 1) /\ forall frm_prime_left_kmckbc_prime frm_prime_right_kmckbc_prime. p = frm_prime_left_kmckbc_prime * frm_prime_right_kmckbc_prime -> frm_prime_left_kmckbc_prime = 1 \/ frm_prime_right_kmckbc_prime = 1)) -> (((exists bcf_lt_gap_kmckbc_choose_out_of_range. bcf_lt_gap_kmckbc_choose_out_of_range + S (a + b) = a) /\ C = 0) \/ ((exists bcf_le_gap_kmckbc_choose_in_range. bcf_le_gap_kmckbc_choose_in_range + (a) = a + b) /\ (exists bcf_row_code_code_kmckbc_choose bcf_row_code_scale_kmckbc_choose bcf_row_scale_code_kmckbc_choose bcf_row_scale_scale_kmckbc_choose bcf_row_code_kmckbc_choose bcf_row_scale_kmckbc_choose. ((forall bcf_row_index_kmckbc_choose_table. (exists bcf_lt_gap_kmckbc_choose_table_row_bound. bcf_lt_gap_kmckbc_choose_table_row_bound + S (bcf_row_index_kmckbc_choose_table) = S (a + b)) -> exists bcf_row_code_kmckbc_choose_table bcf_row_scale_kmckbc_choose_table. ((((exists bcf_height_kmckbc_choose_table_decoded_row_code. bcf_height_kmckbc_choose_table_decoded_row_code + S (bcf_row_code_kmckbc_choose_table) = S ((S (bcf_row_index_kmckbc_choose_table)) * bcf_row_code_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_table_decoded_row_code. bcf_row_code_code_kmckbc_choose = bcf_quotient_kmckbc_choose_table_decoded_row_code * S ((S (bcf_row_index_kmckbc_choose_table)) * bcf_row_code_scale_kmckbc_choose) + (bcf_row_code_kmckbc_choose_table))) /\ ((((exists bcf_height_kmckbc_choose_table_decoded_row_scale. bcf_height_kmckbc_choose_table_decoded_row_scale + S (bcf_row_scale_kmckbc_choose_table) = S ((S (bcf_row_index_kmckbc_choose_table)) * bcf_row_scale_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_table_decoded_row_scale. bcf_row_scale_code_kmckbc_choose = bcf_quotient_kmckbc_choose_table_decoded_row_scale * S ((S (bcf_row_index_kmckbc_choose_table)) * bcf_row_scale_scale_kmckbc_choose) + (bcf_row_scale_kmckbc_choose_table))) /\ ((bcf_row_index_kmckbc_choose_table = 0 /\ (forall bcf_index_kmckbc_choose_table_zero_row. (exists bcf_lt_gap_kmckbc_choose_table_zero_row_bound. bcf_lt_gap_kmckbc_choose_table_zero_row_bound + S (bcf_index_kmckbc_choose_table_zero_row) = S (a + b)) -> exists bcf_value_kmckbc_choose_table_zero_row. ((((exists bcf_height_kmckbc_choose_table_zero_row_entry. bcf_height_kmckbc_choose_table_zero_row_entry + S (bcf_value_kmckbc_choose_table_zero_row) = S ((S (bcf_index_kmckbc_choose_table_zero_row)) * bcf_row_scale_kmckbc_choose_table)) /\ exists bcf_quotient_kmckbc_choose_table_zero_row_entry. bcf_row_code_kmckbc_choose_table = bcf_quotient_kmckbc_choose_table_zero_row_entry * S ((S (bcf_index_kmckbc_choose_table_zero_row)) * bcf_row_scale_kmckbc_choose_table) + (bcf_value_kmckbc_choose_table_zero_row))) /\ ((bcf_index_kmckbc_choose_table_zero_row = 0 /\ bcf_value_kmckbc_choose_table_zero_row = 1) \/ exists bcf_predecessor_kmckbc_choose_table_zero_row. bcf_index_kmckbc_choose_table_zero_row = S bcf_predecessor_kmckbc_choose_table_zero_row /\ bcf_value_kmckbc_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_kmckbc_choose_table bcf_previous_code_kmckbc_choose_table bcf_previous_scale_kmckbc_choose_table. bcf_row_index_kmckbc_choose_table = S bcf_predecessor_kmckbc_choose_table /\ ((((exists bcf_height_kmckbc_choose_table_decoded_previous_code. bcf_height_kmckbc_choose_table_decoded_previous_code + S (bcf_previous_code_kmckbc_choose_table) = S ((S (bcf_predecessor_kmckbc_choose_table)) * bcf_row_code_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_table_decoded_previous_code. bcf_row_code_code_kmckbc_choose = bcf_quotient_kmckbc_choose_table_decoded_previous_code * S ((S (bcf_predecessor_kmckbc_choose_table)) * bcf_row_code_scale_kmckbc_choose) + (bcf_previous_code_kmckbc_choose_table))) /\ ((((exists bcf_height_kmckbc_choose_table_decoded_previous_scale. bcf_height_kmckbc_choose_table_decoded_previous_scale + S (bcf_previous_scale_kmckbc_choose_table) = S ((S (bcf_predecessor_kmckbc_choose_table)) * bcf_row_scale_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_table_decoded_previous_scale. bcf_row_scale_code_kmckbc_choose = bcf_quotient_kmckbc_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_kmckbc_choose_table)) * bcf_row_scale_scale_kmckbc_choose) + (bcf_previous_scale_kmckbc_choose_table))) /\ (forall bcf_index_kmckbc_choose_table_row_step. (exists bcf_lt_gap_kmckbc_choose_table_row_step_bound. bcf_lt_gap_kmckbc_choose_table_row_step_bound + S (bcf_index_kmckbc_choose_table_row_step) = S (a + b)) -> exists bcf_value_kmckbc_choose_table_row_step. ((((exists bcf_height_kmckbc_choose_table_row_step_entry. bcf_height_kmckbc_choose_table_row_step_entry + S (bcf_value_kmckbc_choose_table_row_step) = S ((S (bcf_index_kmckbc_choose_table_row_step)) * bcf_row_scale_kmckbc_choose_table)) /\ exists bcf_quotient_kmckbc_choose_table_row_step_entry. bcf_row_code_kmckbc_choose_table = bcf_quotient_kmckbc_choose_table_row_step_entry * S ((S (bcf_index_kmckbc_choose_table_row_step)) * bcf_row_scale_kmckbc_choose_table) + (bcf_value_kmckbc_choose_table_row_step))) /\ ((bcf_index_kmckbc_choose_table_row_step = 0 /\ bcf_value_kmckbc_choose_table_row_step = 1) \/ exists bcf_predecessor_kmckbc_choose_table_row_step bcf_left_kmckbc_choose_table_row_step bcf_right_kmckbc_choose_table_row_step. bcf_index_kmckbc_choose_table_row_step = S bcf_predecessor_kmckbc_choose_table_row_step /\ ((((exists bcf_height_kmckbc_choose_table_row_step_previous_left. bcf_height_kmckbc_choose_table_row_step_previous_left + S (bcf_left_kmckbc_choose_table_row_step) = S ((S (bcf_predecessor_kmckbc_choose_table_row_step)) * bcf_previous_scale_kmckbc_choose_table)) /\ exists bcf_quotient_kmckbc_choose_table_row_step_previous_left. bcf_previous_code_kmckbc_choose_table = bcf_quotient_kmckbc_choose_table_row_step_previous_left * S ((S (bcf_predecessor_kmckbc_choose_table_row_step)) * bcf_previous_scale_kmckbc_choose_table) + (bcf_left_kmckbc_choose_table_row_step))) /\ ((((exists bcf_height_kmckbc_choose_table_row_step_previous_right. bcf_height_kmckbc_choose_table_row_step_previous_right + S (bcf_right_kmckbc_choose_table_row_step) = S ((S (S (bcf_predecessor_kmckbc_choose_table_row_step))) * bcf_previous_scale_kmckbc_choose_table)) /\ exists bcf_quotient_kmckbc_choose_table_row_step_previous_right. bcf_previous_code_kmckbc_choose_table = bcf_quotient_kmckbc_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_kmckbc_choose_table_row_step))) * bcf_previous_scale_kmckbc_choose_table) + (bcf_right_kmckbc_choose_table_row_step))) /\ bcf_value_kmckbc_choose_table_row_step = bcf_left_kmckbc_choose_table_row_step + bcf_right_kmckbc_choose_table_row_step))))))))))) /\ ((((exists bcf_height_kmckbc_choose_decoded_row_code. bcf_height_kmckbc_choose_decoded_row_code + S (bcf_row_code_kmckbc_choose) = S ((S (a + b)) * bcf_row_code_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_decoded_row_code. bcf_row_code_code_kmckbc_choose = bcf_quotient_kmckbc_choose_decoded_row_code * S ((S (a + b)) * bcf_row_code_scale_kmckbc_choose) + (bcf_row_code_kmckbc_choose))) /\ ((((exists bcf_height_kmckbc_choose_decoded_row_scale. bcf_height_kmckbc_choose_decoded_row_scale + S (bcf_row_scale_kmckbc_choose) = S ((S (a + b)) * bcf_row_scale_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_decoded_row_scale. bcf_row_scale_code_kmckbc_choose = bcf_quotient_kmckbc_choose_decoded_row_scale * S ((S (a + b)) * bcf_row_scale_scale_kmckbc_choose) + (bcf_row_scale_kmckbc_choose))) /\ (((exists bcf_height_kmckbc_choose_decoded_value. bcf_height_kmckbc_choose_decoded_value + S (C) = S ((S (a)) * bcf_row_scale_kmckbc_choose)) /\ exists bcf_quotient_kmckbc_choose_decoded_value. bcf_row_code_kmckbc_choose = bcf_quotient_kmckbc_choose_decoded_value * S ((S (a)) * bcf_row_scale_kmckbc_choose) + (C))))))))) -> (((exists bpv_gap_kmckbc_valuation_exponent_bound. bpv_gap_kmckbc_valuation_exponent_bound + v = C) /\ (exists bpv_result_kmckbc_valuation_selected. ((exists ff_b_kmckbc_valuation_selected_power ff_c_kmckbc_valuation_selected_power. ((forall ff_i_kmckbc_valuation_selected_power_repeat. (exists ff_lt_kmckbc_valuation_selected_power_repeat_bound. ff_lt_kmckbc_valuation_selected_power_repeat_bound + S ff_i_kmckbc_valuation_selected_power_repeat = v) -> (((exists ff_h_kmckbc_valuation_selected_power_repeat_decoded. ff_h_kmckbc_valuation_selected_power_repeat_decoded + S (p) = S ((S (ff_i_kmckbc_valuation_selected_power_repeat)) * ff_c_kmckbc_valuation_selected_power)) /\ exists ff_q_kmckbc_valuation_selected_power_repeat_decoded. ff_b_kmckbc_valuation_selected_power = ff_q_kmckbc_valuation_selected_power_repeat_decoded * S ((S (ff_i_kmckbc_valuation_selected_power_repeat)) * ff_c_kmckbc_valuation_selected_power) + (p)))) /\ (exists ff_u_kmckbc_valuation_selected_power_product ff_v_kmckbc_valuation_selected_power_product. ((((exists ff_h_kmckbc_valuation_selected_power_product_start. ff_h_kmckbc_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_kmckbc_valuation_selected_power_product)) /\ exists ff_q_kmckbc_valuation_selected_power_product_start. ff_u_kmckbc_valuation_selected_power_product = ff_q_kmckbc_valuation_selected_power_product_start * S ((S (0)) * ff_v_kmckbc_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_kmckbc_valuation_selected_power_product_terminal. ff_h_kmckbc_valuation_selected_power_product_terminal + S (bpv_result_kmckbc_valuation_selected) = S ((S (v)) * ff_v_kmckbc_valuation_selected_power_product)) /\ exists ff_q_kmckbc_valuation_selected_power_product_terminal. ff_u_kmckbc_valuation_selected_power_product = ff_q_kmckbc_valuation_selected_power_product_terminal * S ((S (v)) * ff_v_kmckbc_valuation_selected_power_product) + (bpv_result_kmckbc_valuation_selected))) /\ forall ff_i_kmckbc_valuation_selected_power_product. (exists ff_lt_kmckbc_valuation_selected_power_product_bound. ff_lt_kmckbc_valuation_selected_power_product_bound + S ff_i_kmckbc_valuation_selected_power_product = v) -> exists ff_p_kmckbc_valuation_selected_power_product ff_r_kmckbc_valuation_selected_power_product ff_s_kmckbc_valuation_selected_power_product. ((((exists ff_h_kmckbc_valuation_selected_power_product_factor. ff_h_kmckbc_valuation_selected_power_product_factor + S (ff_p_kmckbc_valuation_selected_power_product) = S ((S (ff_i_kmckbc_valuation_selected_power_product)) * ff_c_kmckbc_valuation_selected_power)) /\ exists ff_q_kmckbc_valuation_selected_power_product_factor. ff_b_kmckbc_valuation_selected_power = ff_q_kmckbc_valuation_selected_power_product_factor * S ((S (ff_i_kmckbc_valuation_selected_power_product)) * ff_c_kmckbc_valuation_selected_power) + (ff_p_kmckbc_valuation_selected_power_product))) /\ ((((exists ff_h_kmckbc_valuation_selected_power_product_partial. ff_h_kmckbc_valuation_selected_power_product_partial + S (ff_r_kmckbc_valuation_selected_power_product) = S ((S (ff_i_kmckbc_valuation_selected_power_product)) * ff_v_kmckbc_valuation_selected_power_product)) /\ exists ff_q_kmckbc_valuation_selected_power_product_partial. ff_u_kmckbc_valuation_selected_power_product = ff_q_kmckbc_valuation_selected_power_product_partial * S ((S (ff_i_kmckbc_valuation_selected_power_product)) * ff_v_kmckbc_valuation_selected_power_product) + (ff_r_kmckbc_valuation_selected_power_product))) /\ ((((exists ff_h_kmckbc_valuation_selected_power_product_successor. ff_h_kmckbc_valuation_selected_power_product_successor + S (ff_s_kmckbc_valuation_selected_power_product) = S ((S (S ff_i_kmckbc_valuation_selected_power_product)) * ff_v_kmckbc_valuation_selected_power_product)) /\ exists ff_q_kmckbc_valuation_selected_power_product_successor. ff_u_kmckbc_valuation_selected_power_product = ff_q_kmckbc_valuation_selected_power_product_successor * S ((S (S ff_i_kmckbc_valuation_selected_power_product)) * ff_v_kmckbc_valuation_selected_power_product) + (ff_s_kmckbc_valuation_selected_power_product))) /\ ff_s_kmckbc_valuation_selected_power_product = ff_r_kmckbc_valuation_selected_power_product * ff_p_kmckbc_valuation_selected_power_product)))))))) /\ (exists bpv_factor_kmckbc_valuation_selected_divides. C = bpv_result_kmckbc_valuation_selected * bpv_factor_kmckbc_valuation_selected_divides)))) /\ forall bpv_candidate_kmckbc_valuation. (exists bpv_gap_kmckbc_valuation_candidate_bound. bpv_gap_kmckbc_valuation_candidate_bound + bpv_candidate_kmckbc_valuation = C) -> (exists bpv_result_kmckbc_valuation_candidate. ((exists ff_b_kmckbc_valuation_candidate_power ff_c_kmckbc_valuation_candidate_power. ((forall ff_i_kmckbc_valuation_candidate_power_repeat. (exists ff_lt_kmckbc_valuation_candidate_power_repeat_bound. ff_lt_kmckbc_valuation_candidate_power_repeat_bound + S ff_i_kmckbc_valuation_candidate_power_repeat = bpv_candidate_kmckbc_valuation) -> (((exists ff_h_kmckbc_valuation_candidate_power_repeat_decoded. ff_h_kmckbc_valuation_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_kmckbc_valuation_candidate_power_repeat)) * ff_c_kmckbc_valuation_candidate_power)) /\ exists ff_q_kmckbc_valuation_candidate_power_repeat_decoded. ff_b_kmckbc_valuation_candidate_power = ff_q_kmckbc_valuation_candidate_power_repeat_decoded * S ((S (ff_i_kmckbc_valuation_candidate_power_repeat)) * ff_c_kmckbc_valuation_candidate_power) + (p)))) /\ (exists ff_u_kmckbc_valuation_candidate_power_product ff_v_kmckbc_valuation_candidate_power_product. ((((exists ff_h_kmckbc_valuation_candidate_power_product_start. ff_h_kmckbc_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_kmckbc_valuation_candidate_power_product)) /\ exists ff_q_kmckbc_valuation_candidate_power_product_start. ff_u_kmckbc_valuation_candidate_power_product = ff_q_kmckbc_valuation_candidate_power_product_start * S ((S (0)) * ff_v_kmckbc_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_kmckbc_valuation_candidate_power_product_terminal. ff_h_kmckbc_valuation_candidate_power_product_terminal + S (bpv_result_kmckbc_valuation_candidate) = S ((S (bpv_candidate_kmckbc_valuation)) * ff_v_kmckbc_valuation_candidate_power_product)) /\ exists ff_q_kmckbc_valuation_candidate_power_product_terminal. ff_u_kmckbc_valuation_candidate_power_product = ff_q_kmckbc_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_kmckbc_valuation)) * ff_v_kmckbc_valuation_candidate_power_product) + (bpv_result_kmckbc_valuation_candidate))) /\ forall ff_i_kmckbc_valuation_candidate_power_product. (exists ff_lt_kmckbc_valuation_candidate_power_product_bound. ff_lt_kmckbc_valuation_candidate_power_product_bound + S ff_i_kmckbc_valuation_candidate_power_product = bpv_candidate_kmckbc_valuation) -> exists ff_p_kmckbc_valuation_candidate_power_product ff_r_kmckbc_valuation_candidate_power_product ff_s_kmckbc_valuation_candidate_power_product. ((((exists ff_h_kmckbc_valuation_candidate_power_product_factor. ff_h_kmckbc_valuation_candidate_power_product_factor + S (ff_p_kmckbc_valuation_candidate_power_product) = S ((S (ff_i_kmckbc_valuation_candidate_power_product)) * ff_c_kmckbc_valuation_candidate_power)) /\ exists ff_q_kmckbc_valuation_candidate_power_product_factor. ff_b_kmckbc_valuation_candidate_power = ff_q_kmckbc_valuation_candidate_power_product_factor * S ((S (ff_i_kmckbc_valuation_candidate_power_product)) * ff_c_kmckbc_valuation_candidate_power) + (ff_p_kmckbc_valuation_candidate_power_product))) /\ ((((exists ff_h_kmckbc_valuation_candidate_power_product_partial. ff_h_kmckbc_valuation_candidate_power_product_partial + S (ff_r_kmckbc_valuation_candidate_power_product) = S ((S (ff_i_kmckbc_valuation_candidate_power_product)) * ff_v_kmckbc_valuation_candidate_power_product)) /\ exists ff_q_kmckbc_valuation_candidate_power_product_partial. ff_u_kmckbc_valuation_candidate_power_product = ff_q_kmckbc_valuation_candidate_power_product_partial * S ((S (ff_i_kmckbc_valuation_candidate_power_product)) * ff_v_kmckbc_valuation_candidate_power_product) + (ff_r_kmckbc_valuation_candidate_power_product))) /\ ((((exists ff_h_kmckbc_valuation_candidate_power_product_successor. ff_h_kmckbc_valuation_candidate_power_product_successor + S (ff_s_kmckbc_valuation_candidate_power_product) = S ((S (S ff_i_kmckbc_valuation_candidate_power_product)) * ff_v_kmckbc_valuation_candidate_power_product)) /\ exists ff_q_kmckbc_valuation_candidate_power_product_successor. ff_u_kmckbc_valuation_candidate_power_product = ff_q_kmckbc_valuation_candidate_power_product_successor * S ((S (S ff_i_kmckbc_valuation_candidate_power_product)) * ff_v_kmckbc_valuation_candidate_power_product) + (ff_s_kmckbc_valuation_candidate_power_product))) /\ ff_s_kmckbc_valuation_candidate_power_product = ff_r_kmckbc_valuation_candidate_power_product * ff_p_kmckbc_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_kmckbc_valuation_candidate_divides. C = bpv_result_kmckbc_valuation_candidate * bpv_factor_kmckbc_valuation_candidate_divides))) -> (exists bpv_gap_kmckbc_valuation_maximal. bpv_gap_kmckbc_valuation_maximal + bpv_candidate_kmckbc_valuation = v)) -> exists lb lc rb rc tb tc cb cc. (forall bls_index_kmckbc_left. (exists bls_gap_kmckbc_left_bound. bls_gap_kmckbc_left_bound + S (bls_index_kmckbc_left) = (a + b)) -> exists bls_power_kmckbc_left bls_quotient_kmckbc_left bls_remainder_kmckbc_left. ((exists bpvi_b_bls_kmckbc_left_power bpvi_c_bls_kmckbc_left_power. ((forall bpvi_i_bls_kmckbc_left_power. (exists bpvi_repeat_gap_bls_kmckbc_left_power. bpvi_repeat_gap_bls_kmckbc_left_power + S bpvi_i_bls_kmckbc_left_power = S bls_index_kmckbc_left) -> (((exists bpvi_h_bls_kmckbc_left_power_repeat. bpvi_h_bls_kmckbc_left_power_repeat + S (p) = S ((S (bpvi_i_bls_kmckbc_left_power)) * bpvi_c_bls_kmckbc_left_power)) /\ exists bpvi_q_bls_kmckbc_left_power_repeat. bpvi_b_bls_kmckbc_left_power = bpvi_q_bls_kmckbc_left_power_repeat * S ((S (bpvi_i_bls_kmckbc_left_power)) * bpvi_c_bls_kmckbc_left_power) + (p)))) /\ (exists bpvi_u_bls_kmckbc_left_power bpvi_v_bls_kmckbc_left_power. ((((exists bpvi_h_bls_kmckbc_left_power_start. bpvi_h_bls_kmckbc_left_power_start + S (1) = S ((S (0)) * bpvi_v_bls_kmckbc_left_power)) /\ exists bpvi_q_bls_kmckbc_left_power_start. bpvi_u_bls_kmckbc_left_power = bpvi_q_bls_kmckbc_left_power_start * S ((S (0)) * bpvi_v_bls_kmckbc_left_power) + (1))) /\ ((((exists bpvi_h_bls_kmckbc_left_power_terminal. bpvi_h_bls_kmckbc_left_power_terminal + S (bls_power_kmckbc_left) = S ((S (S bls_index_kmckbc_left)) * bpvi_v_bls_kmckbc_left_power)) /\ exists bpvi_q_bls_kmckbc_left_power_terminal. bpvi_u_bls_kmckbc_left_power = bpvi_q_bls_kmckbc_left_power_terminal * S ((S (S bls_index_kmckbc_left)) * bpvi_v_bls_kmckbc_left_power) + (bls_power_kmckbc_left))) /\ forall bpvi_j_bls_kmckbc_left_power. (exists bpvi_product_gap_bls_kmckbc_left_power. bpvi_product_gap_bls_kmckbc_left_power + S bpvi_j_bls_kmckbc_left_power = S bls_index_kmckbc_left) -> exists bpvi_factor_bls_kmckbc_left_power bpvi_partial_bls_kmckbc_left_power bpvi_successor_bls_kmckbc_left_power. ((((exists bpvi_h_bls_kmckbc_left_power_factor. bpvi_h_bls_kmckbc_left_power_factor + S (bpvi_factor_bls_kmckbc_left_power) = S ((S (bpvi_j_bls_kmckbc_left_power)) * bpvi_c_bls_kmckbc_left_power)) /\ exists bpvi_q_bls_kmckbc_left_power_factor. bpvi_b_bls_kmckbc_left_power = bpvi_q_bls_kmckbc_left_power_factor * S ((S (bpvi_j_bls_kmckbc_left_power)) * bpvi_c_bls_kmckbc_left_power) + (bpvi_factor_bls_kmckbc_left_power))) /\ ((((exists bpvi_h_bls_kmckbc_left_power_partial. bpvi_h_bls_kmckbc_left_power_partial + S (bpvi_partial_bls_kmckbc_left_power) = S ((S (bpvi_j_bls_kmckbc_left_power)) * bpvi_v_bls_kmckbc_left_power)) /\ exists bpvi_q_bls_kmckbc_left_power_partial. bpvi_u_bls_kmckbc_left_power = bpvi_q_bls_kmckbc_left_power_partial * S ((S (bpvi_j_bls_kmckbc_left_power)) * bpvi_v_bls_kmckbc_left_power) + (bpvi_partial_bls_kmckbc_left_power))) /\ ((((exists bpvi_h_bls_kmckbc_left_power_successor. bpvi_h_bls_kmckbc_left_power_successor + S (bpvi_successor_bls_kmckbc_left_power) = S ((S (S bpvi_j_bls_kmckbc_left_power)) * bpvi_v_bls_kmckbc_left_power)) /\ exists bpvi_q_bls_kmckbc_left_power_successor. bpvi_u_bls_kmckbc_left_power = bpvi_q_bls_kmckbc_left_power_successor * S ((S (S bpvi_j_bls_kmckbc_left_power)) * bpvi_v_bls_kmckbc_left_power) + (bpvi_successor_bls_kmckbc_left_power))) /\ bpvi_successor_bls_kmckbc_left_power = bpvi_partial_bls_kmckbc_left_power * bpvi_factor_bls_kmckbc_left_power)))))))) /\ ((((exists ff_h_bls_kmckbc_left_quotient_entry. ff_h_bls_kmckbc_left_quotient_entry + S (bls_quotient_kmckbc_left) = S ((S (bls_index_kmckbc_left)) * lc)) /\ exists ff_q_bls_kmckbc_left_quotient_entry. lb = ff_q_bls_kmckbc_left_quotient_entry * S ((S (bls_index_kmckbc_left)) * lc) + (bls_quotient_kmckbc_left))) /\ ((a = bls_power_kmckbc_left * bls_quotient_kmckbc_left + bls_remainder_kmckbc_left /\ exists bls_remainder_gap_kmckbc_left_division. bls_remainder_gap_kmckbc_left_division + S (bls_remainder_kmckbc_left) = bls_power_kmckbc_left))))) /\ ((forall bls_index_kmckbc_right. (exists bls_gap_kmckbc_right_bound. bls_gap_kmckbc_right_bound + S (bls_index_kmckbc_right) = (a + b)) -> exists bls_power_kmckbc_right bls_quotient_kmckbc_right bls_remainder_kmckbc_right. ((exists bpvi_b_bls_kmckbc_right_power bpvi_c_bls_kmckbc_right_power. ((forall bpvi_i_bls_kmckbc_right_power. (exists bpvi_repeat_gap_bls_kmckbc_right_power. bpvi_repeat_gap_bls_kmckbc_right_power + S bpvi_i_bls_kmckbc_right_power = S bls_index_kmckbc_right) -> (((exists bpvi_h_bls_kmckbc_right_power_repeat. bpvi_h_bls_kmckbc_right_power_repeat + S (p) = S ((S (bpvi_i_bls_kmckbc_right_power)) * bpvi_c_bls_kmckbc_right_power)) /\ exists bpvi_q_bls_kmckbc_right_power_repeat. bpvi_b_bls_kmckbc_right_power = bpvi_q_bls_kmckbc_right_power_repeat * S ((S (bpvi_i_bls_kmckbc_right_power)) * bpvi_c_bls_kmckbc_right_power) + (p)))) /\ (exists bpvi_u_bls_kmckbc_right_power bpvi_v_bls_kmckbc_right_power. ((((exists bpvi_h_bls_kmckbc_right_power_start. bpvi_h_bls_kmckbc_right_power_start + S (1) = S ((S (0)) * bpvi_v_bls_kmckbc_right_power)) /\ exists bpvi_q_bls_kmckbc_right_power_start. bpvi_u_bls_kmckbc_right_power = bpvi_q_bls_kmckbc_right_power_start * S ((S (0)) * bpvi_v_bls_kmckbc_right_power) + (1))) /\ ((((exists bpvi_h_bls_kmckbc_right_power_terminal. bpvi_h_bls_kmckbc_right_power_terminal + S (bls_power_kmckbc_right) = S ((S (S bls_index_kmckbc_right)) * bpvi_v_bls_kmckbc_right_power)) /\ exists bpvi_q_bls_kmckbc_right_power_terminal. bpvi_u_bls_kmckbc_right_power = bpvi_q_bls_kmckbc_right_power_terminal * S ((S (S bls_index_kmckbc_right)) * bpvi_v_bls_kmckbc_right_power) + (bls_power_kmckbc_right))) /\ forall bpvi_j_bls_kmckbc_right_power. (exists bpvi_product_gap_bls_kmckbc_right_power. bpvi_product_gap_bls_kmckbc_right_power + S bpvi_j_bls_kmckbc_right_power = S bls_index_kmckbc_right) -> exists bpvi_factor_bls_kmckbc_right_power bpvi_partial_bls_kmckbc_right_power bpvi_successor_bls_kmckbc_right_power. ((((exists bpvi_h_bls_kmckbc_right_power_factor. bpvi_h_bls_kmckbc_right_power_factor + S (bpvi_factor_bls_kmckbc_right_power) = S ((S (bpvi_j_bls_kmckbc_right_power)) * bpvi_c_bls_kmckbc_right_power)) /\ exists bpvi_q_bls_kmckbc_right_power_factor. bpvi_b_bls_kmckbc_right_power = bpvi_q_bls_kmckbc_right_power_factor * S ((S (bpvi_j_bls_kmckbc_right_power)) * bpvi_c_bls_kmckbc_right_power) + (bpvi_factor_bls_kmckbc_right_power))) /\ ((((exists bpvi_h_bls_kmckbc_right_power_partial. bpvi_h_bls_kmckbc_right_power_partial + S (bpvi_partial_bls_kmckbc_right_power) = S ((S (bpvi_j_bls_kmckbc_right_power)) * bpvi_v_bls_kmckbc_right_power)) /\ exists bpvi_q_bls_kmckbc_right_power_partial. bpvi_u_bls_kmckbc_right_power = bpvi_q_bls_kmckbc_right_power_partial * S ((S (bpvi_j_bls_kmckbc_right_power)) * bpvi_v_bls_kmckbc_right_power) + (bpvi_partial_bls_kmckbc_right_power))) /\ ((((exists bpvi_h_bls_kmckbc_right_power_successor. bpvi_h_bls_kmckbc_right_power_successor + S (bpvi_successor_bls_kmckbc_right_power) = S ((S (S bpvi_j_bls_kmckbc_right_power)) * bpvi_v_bls_kmckbc_right_power)) /\ exists bpvi_q_bls_kmckbc_right_power_successor. bpvi_u_bls_kmckbc_right_power = bpvi_q_bls_kmckbc_right_power_successor * S ((S (S bpvi_j_bls_kmckbc_right_power)) * bpvi_v_bls_kmckbc_right_power) + (bpvi_successor_bls_kmckbc_right_power))) /\ bpvi_successor_bls_kmckbc_right_power = bpvi_partial_bls_kmckbc_right_power * bpvi_factor_bls_kmckbc_right_power)))))))) /\ ((((exists ff_h_bls_kmckbc_right_quotient_entry. ff_h_bls_kmckbc_right_quotient_entry + S (bls_quotient_kmckbc_right) = S ((S (bls_index_kmckbc_right)) * rc)) /\ exists ff_q_bls_kmckbc_right_quotient_entry. rb = ff_q_bls_kmckbc_right_quotient_entry * S ((S (bls_index_kmckbc_right)) * rc) + (bls_quotient_kmckbc_right))) /\ ((b = bls_power_kmckbc_right * bls_quotient_kmckbc_right + bls_remainder_kmckbc_right /\ exists bls_remainder_gap_kmckbc_right_division. bls_remainder_gap_kmckbc_right_division + S (bls_remainder_kmckbc_right) = bls_power_kmckbc_right))))) /\ ((forall bls_index_kmckbc_total. (exists bls_gap_kmckbc_total_bound. bls_gap_kmckbc_total_bound + S (bls_index_kmckbc_total) = (a + b)) -> exists bls_power_kmckbc_total bls_quotient_kmckbc_total bls_remainder_kmckbc_total. ((exists bpvi_b_bls_kmckbc_total_power bpvi_c_bls_kmckbc_total_power. ((forall bpvi_i_bls_kmckbc_total_power. (exists bpvi_repeat_gap_bls_kmckbc_total_power. bpvi_repeat_gap_bls_kmckbc_total_power + S bpvi_i_bls_kmckbc_total_power = S bls_index_kmckbc_total) -> (((exists bpvi_h_bls_kmckbc_total_power_repeat. bpvi_h_bls_kmckbc_total_power_repeat + S (p) = S ((S (bpvi_i_bls_kmckbc_total_power)) * bpvi_c_bls_kmckbc_total_power)) /\ exists bpvi_q_bls_kmckbc_total_power_repeat. bpvi_b_bls_kmckbc_total_power = bpvi_q_bls_kmckbc_total_power_repeat * S ((S (bpvi_i_bls_kmckbc_total_power)) * bpvi_c_bls_kmckbc_total_power) + (p)))) /\ (exists bpvi_u_bls_kmckbc_total_power bpvi_v_bls_kmckbc_total_power. ((((exists bpvi_h_bls_kmckbc_total_power_start. bpvi_h_bls_kmckbc_total_power_start + S (1) = S ((S (0)) * bpvi_v_bls_kmckbc_total_power)) /\ exists bpvi_q_bls_kmckbc_total_power_start. bpvi_u_bls_kmckbc_total_power = bpvi_q_bls_kmckbc_total_power_start * S ((S (0)) * bpvi_v_bls_kmckbc_total_power) + (1))) /\ ((((exists bpvi_h_bls_kmckbc_total_power_terminal. bpvi_h_bls_kmckbc_total_power_terminal + S (bls_power_kmckbc_total) = S ((S (S bls_index_kmckbc_total)) * bpvi_v_bls_kmckbc_total_power)) /\ exists bpvi_q_bls_kmckbc_total_power_terminal. bpvi_u_bls_kmckbc_total_power = bpvi_q_bls_kmckbc_total_power_terminal * S ((S (S bls_index_kmckbc_total)) * bpvi_v_bls_kmckbc_total_power) + (bls_power_kmckbc_total))) /\ forall bpvi_j_bls_kmckbc_total_power. (exists bpvi_product_gap_bls_kmckbc_total_power. bpvi_product_gap_bls_kmckbc_total_power + S bpvi_j_bls_kmckbc_total_power = S bls_index_kmckbc_total) -> exists bpvi_factor_bls_kmckbc_total_power bpvi_partial_bls_kmckbc_total_power bpvi_successor_bls_kmckbc_total_power. ((((exists bpvi_h_bls_kmckbc_total_power_factor. bpvi_h_bls_kmckbc_total_power_factor + S (bpvi_factor_bls_kmckbc_total_power) = S ((S (bpvi_j_bls_kmckbc_total_power)) * bpvi_c_bls_kmckbc_total_power)) /\ exists bpvi_q_bls_kmckbc_total_power_factor. bpvi_b_bls_kmckbc_total_power = bpvi_q_bls_kmckbc_total_power_factor * S ((S (bpvi_j_bls_kmckbc_total_power)) * bpvi_c_bls_kmckbc_total_power) + (bpvi_factor_bls_kmckbc_total_power))) /\ ((((exists bpvi_h_bls_kmckbc_total_power_partial. bpvi_h_bls_kmckbc_total_power_partial + S (bpvi_partial_bls_kmckbc_total_power) = S ((S (bpvi_j_bls_kmckbc_total_power)) * bpvi_v_bls_kmckbc_total_power)) /\ exists bpvi_q_bls_kmckbc_total_power_partial. bpvi_u_bls_kmckbc_total_power = bpvi_q_bls_kmckbc_total_power_partial * S ((S (bpvi_j_bls_kmckbc_total_power)) * bpvi_v_bls_kmckbc_total_power) + (bpvi_partial_bls_kmckbc_total_power))) /\ ((((exists bpvi_h_bls_kmckbc_total_power_successor. bpvi_h_bls_kmckbc_total_power_successor + S (bpvi_successor_bls_kmckbc_total_power) = S ((S (S bpvi_j_bls_kmckbc_total_power)) * bpvi_v_bls_kmckbc_total_power)) /\ exists bpvi_q_bls_kmckbc_total_power_successor. bpvi_u_bls_kmckbc_total_power = bpvi_q_bls_kmckbc_total_power_successor * S ((S (S bpvi_j_bls_kmckbc_total_power)) * bpvi_v_bls_kmckbc_total_power) + (bpvi_successor_bls_kmckbc_total_power))) /\ bpvi_successor_bls_kmckbc_total_power = bpvi_partial_bls_kmckbc_total_power * bpvi_factor_bls_kmckbc_total_power)))))))) /\ ((((exists ff_h_bls_kmckbc_total_quotient_entry. ff_h_bls_kmckbc_total_quotient_entry + S (bls_quotient_kmckbc_total) = S ((S (bls_index_kmckbc_total)) * tc)) /\ exists ff_q_bls_kmckbc_total_quotient_entry. tb = ff_q_bls_kmckbc_total_quotient_entry * S ((S (bls_index_kmckbc_total)) * tc) + (bls_quotient_kmckbc_total))) /\ ((a + b = bls_power_kmckbc_total * bls_quotient_kmckbc_total + bls_remainder_kmckbc_total /\ exists bls_remainder_gap_kmckbc_total_division. bls_remainder_gap_kmckbc_total_division + S (bls_remainder_kmckbc_total) = bls_power_kmckbc_total))))) /\ ((forall kmc_index_kmckbc_carries. (exists bcf_lt_gap_kmckbc_carries_bound. bcf_lt_gap_kmckbc_carries_bound + S (kmc_index_kmckbc_carries) = a + b) -> exists kmc_left_kmckbc_carries kmc_right_kmckbc_carries kmc_total_kmckbc_carries kmc_bit_kmckbc_carries. (((exists fs_h_kmckbc_carries_left. fs_h_kmckbc_carries_left + S (kmc_left_kmckbc_carries) = S ((S (kmc_index_kmckbc_carries)) * lc)) /\ exists fs_q_kmckbc_carries_left. lb = fs_q_kmckbc_carries_left * S ((S (kmc_index_kmckbc_carries)) * lc) + (kmc_left_kmckbc_carries))) /\ ((((exists fs_h_kmckbc_carries_right. fs_h_kmckbc_carries_right + S (kmc_right_kmckbc_carries) = S ((S (kmc_index_kmckbc_carries)) * rc)) /\ exists fs_q_kmckbc_carries_right. rb = fs_q_kmckbc_carries_right * S ((S (kmc_index_kmckbc_carries)) * rc) + (kmc_right_kmckbc_carries))) /\ ((((exists fs_h_kmckbc_carries_total. fs_h_kmckbc_carries_total + S (kmc_total_kmckbc_carries) = S ((S (kmc_index_kmckbc_carries)) * tc)) /\ exists fs_q_kmckbc_carries_total. tb = fs_q_kmckbc_carries_total * S ((S (kmc_index_kmckbc_carries)) * tc) + (kmc_total_kmckbc_carries))) /\ ((((exists fs_h_kmckbc_carries_bit. fs_h_kmckbc_carries_bit + S (kmc_bit_kmckbc_carries) = S ((S (kmc_index_kmckbc_carries)) * cc)) /\ exists fs_q_kmckbc_carries_bit. cb = fs_q_kmckbc_carries_bit * S ((S (kmc_index_kmckbc_carries)) * cc) + (kmc_bit_kmckbc_carries))) /\ (((kmc_bit_kmckbc_carries = 0 /\ kmc_total_kmckbc_carries = kmc_left_kmckbc_carries + kmc_right_kmckbc_carries) \/ (kmc_bit_kmckbc_carries = 1 /\ kmc_total_kmckbc_carries = S (kmc_left_kmckbc_carries + kmc_right_kmckbc_carries)))))))) /\ (((exists ff_u_kmckbc_count_sum ff_v_kmckbc_count_sum. ((((exists ff_h_kmckbc_count_sum_start. ff_h_kmckbc_count_sum_start + S (0) = S ((S (0)) * ff_v_kmckbc_count_sum)) /\ exists ff_q_kmckbc_count_sum_start. ff_u_kmckbc_count_sum = ff_q_kmckbc_count_sum_start * S ((S (0)) * ff_v_kmckbc_count_sum) + (0))) /\ ((((exists ff_h_kmckbc_count_sum_terminal. ff_h_kmckbc_count_sum_terminal + S ((v)) = S ((S ((a + b))) * ff_v_kmckbc_count_sum)) /\ exists ff_q_kmckbc_count_sum_terminal. ff_u_kmckbc_count_sum = ff_q_kmckbc_count_sum_terminal * S ((S ((a + b))) * ff_v_kmckbc_count_sum) + ((v)))) /\ forall ff_i_kmckbc_count_sum. (exists ff_lt_kmckbc_count_sum_bound. ff_lt_kmckbc_count_sum_bound + S ff_i_kmckbc_count_sum = (a + b)) -> exists ff_a_kmckbc_count_sum ff_r_kmckbc_count_sum ff_s_kmckbc_count_sum. ((((exists ff_h_kmckbc_count_sum_summand. ff_h_kmckbc_count_sum_summand + S (ff_a_kmckbc_count_sum) = S ((S (ff_i_kmckbc_count_sum)) * cc)) /\ exists ff_q_kmckbc_count_sum_summand. cb = ff_q_kmckbc_count_sum_summand * S ((S (ff_i_kmckbc_count_sum)) * cc) + (ff_a_kmckbc_count_sum))) /\ ((((exists ff_h_kmckbc_count_sum_partial. ff_h_kmckbc_count_sum_partial + S (ff_r_kmckbc_count_sum) = S ((S (ff_i_kmckbc_count_sum)) * ff_v_kmckbc_count_sum)) /\ exists ff_q_kmckbc_count_sum_partial. ff_u_kmckbc_count_sum = ff_q_kmckbc_count_sum_partial * S ((S (ff_i_kmckbc_count_sum)) * ff_v_kmckbc_count_sum) + (ff_r_kmckbc_count_sum))) /\ ((((exists ff_h_kmckbc_count_sum_successor. ff_h_kmckbc_count_sum_successor + S (ff_s_kmckbc_count_sum) = S ((S (S ff_i_kmckbc_count_sum)) * ff_v_kmckbc_count_sum)) /\ exists ff_q_kmckbc_count_sum_successor. ff_u_kmckbc_count_sum = ff_q_kmckbc_count_sum_successor * S ((S (S ff_i_kmckbc_count_sum)) * ff_v_kmckbc_count_sum) + (ff_s_kmckbc_count_sum))) /\ ff_s_kmckbc_count_sum = ff_r_kmckbc_count_sum + ff_a_kmckbc_count_sum)))))) /\ (forall ff_i_kmckbc_count_bits. (exists ff_lt_kmckbc_count_bits_bound. ff_lt_kmckbc_count_bits_bound + S ff_i_kmckbc_count_bits = (a + b)) -> exists ff_bit_kmckbc_count_bits. ((((exists ff_h_kmckbc_count_bits_decoded. ff_h_kmckbc_count_bits_decoded + S (ff_bit_kmckbc_count_bits) = S ((S (ff_i_kmckbc_count_bits)) * cc)) /\ exists ff_q_kmckbc_count_bits_decoded. cb = ff_q_kmckbc_count_bits_decoded * S ((S (ff_i_kmckbc_count_bits)) * cc) + (ff_bit_kmckbc_count_bits))) /\ (ff_bit_kmckbc_count_bits = 0 \/ ff_bit_kmckbc_count_bits = 1))))))))