multinomial_binomial_prefix_extend

Exact expanded first-order arithmetic statement

forall b c sb sc cb cc l a u C. (forall mkm_index_binextend_source. (exists mkm_lt_binextend_source_bound. mkm_lt_binextend_source_bound + S (mkm_index_binextend_source) = (l)) -> (exists mkm_value_binextend_source_point mkm_partial_binextend_source_point mkm_factor_binextend_source_point. (((exists fs_h_mkm_binextend_source_point_source. fs_h_mkm_binextend_source_point_source + S (mkm_value_binextend_source_point) = S ((S (mkm_index_binextend_source)) * c)) /\ exists fs_q_mkm_binextend_source_point_source. b = fs_q_mkm_binextend_source_point_source * S ((S (mkm_index_binextend_source)) * c) + (mkm_value_binextend_source_point))) /\ ((((exists fs_h_mkm_binextend_source_point_partial. fs_h_mkm_binextend_source_point_partial + S (mkm_partial_binextend_source_point) = S ((S (mkm_index_binextend_source)) * sc)) /\ exists fs_q_mkm_binextend_source_point_partial. sb = fs_q_mkm_binextend_source_point_partial * S ((S (mkm_index_binextend_source)) * sc) + (mkm_partial_binextend_source_point))) /\ ((((exists bcf_lt_gap_mkm_binextend_source_point_choose_out_of_range. bcf_lt_gap_mkm_binextend_source_point_choose_out_of_range + S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point) = mkm_partial_binextend_source_point) /\ mkm_factor_binextend_source_point = 0) \/ ((exists bcf_le_gap_mkm_binextend_source_point_choose_in_range. bcf_le_gap_mkm_binextend_source_point_choose_in_range + (mkm_partial_binextend_source_point) = mkm_partial_binextend_source_point + mkm_value_binextend_source_point) /\ (exists bcf_row_code_code_mkm_binextend_source_point_choose bcf_row_code_scale_mkm_binextend_source_point_choose bcf_row_scale_code_mkm_binextend_source_point_choose bcf_row_scale_scale_mkm_binextend_source_point_choose bcf_row_code_mkm_binextend_source_point_choose bcf_row_scale_mkm_binextend_source_point_choose. ((forall bcf_row_index_mkm_binextend_source_point_choose_table. (exists bcf_lt_gap_mkm_binextend_source_point_choose_table_row_bound. bcf_lt_gap_mkm_binextend_source_point_choose_table_row_bound + S (bcf_row_index_mkm_binextend_source_point_choose_table) = S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) -> exists bcf_row_code_mkm_binextend_source_point_choose_table bcf_row_scale_mkm_binextend_source_point_choose_table. ((((exists bcf_height_mkm_binextend_source_point_choose_table_decoded_row_code. bcf_height_mkm_binextend_source_point_choose_table_decoded_row_code + S (bcf_row_code_mkm_binextend_source_point_choose_table) = S ((S (bcf_row_index_mkm_binextend_source_point_choose_table)) * bcf_row_code_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_decoded_row_code. bcf_row_code_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_table_decoded_row_code * S ((S (bcf_row_index_mkm_binextend_source_point_choose_table)) * bcf_row_code_scale_mkm_binextend_source_point_choose) + (bcf_row_code_mkm_binextend_source_point_choose_table))) /\ ((((exists bcf_height_mkm_binextend_source_point_choose_table_decoded_row_scale. bcf_height_mkm_binextend_source_point_choose_table_decoded_row_scale + S (bcf_row_scale_mkm_binextend_source_point_choose_table) = S ((S (bcf_row_index_mkm_binextend_source_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_decoded_row_scale. bcf_row_scale_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_table_decoded_row_scale * S ((S (bcf_row_index_mkm_binextend_source_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_source_point_choose) + (bcf_row_scale_mkm_binextend_source_point_choose_table))) /\ ((bcf_row_index_mkm_binextend_source_point_choose_table = 0 /\ (forall bcf_index_mkm_binextend_source_point_choose_table_zero_row. (exists bcf_lt_gap_mkm_binextend_source_point_choose_table_zero_row_bound. bcf_lt_gap_mkm_binextend_source_point_choose_table_zero_row_bound + S (bcf_index_mkm_binextend_source_point_choose_table_zero_row) = S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) -> exists bcf_value_mkm_binextend_source_point_choose_table_zero_row. ((((exists bcf_height_mkm_binextend_source_point_choose_table_zero_row_entry. bcf_height_mkm_binextend_source_point_choose_table_zero_row_entry + S (bcf_value_mkm_binextend_source_point_choose_table_zero_row) = S ((S (bcf_index_mkm_binextend_source_point_choose_table_zero_row)) * bcf_row_scale_mkm_binextend_source_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_zero_row_entry. bcf_row_code_mkm_binextend_source_point_choose_table = bcf_quotient_mkm_binextend_source_point_choose_table_zero_row_entry * S ((S (bcf_index_mkm_binextend_source_point_choose_table_zero_row)) * bcf_row_scale_mkm_binextend_source_point_choose_table) + (bcf_value_mkm_binextend_source_point_choose_table_zero_row))) /\ ((bcf_index_mkm_binextend_source_point_choose_table_zero_row = 0 /\ bcf_value_mkm_binextend_source_point_choose_table_zero_row = 1) \/ exists bcf_predecessor_mkm_binextend_source_point_choose_table_zero_row. bcf_index_mkm_binextend_source_point_choose_table_zero_row = S bcf_predecessor_mkm_binextend_source_point_choose_table_zero_row /\ bcf_value_mkm_binextend_source_point_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_mkm_binextend_source_point_choose_table bcf_previous_code_mkm_binextend_source_point_choose_table bcf_previous_scale_mkm_binextend_source_point_choose_table. bcf_row_index_mkm_binextend_source_point_choose_table = S bcf_predecessor_mkm_binextend_source_point_choose_table /\ ((((exists bcf_height_mkm_binextend_source_point_choose_table_decoded_previous_code. bcf_height_mkm_binextend_source_point_choose_table_decoded_previous_code + S (bcf_previous_code_mkm_binextend_source_point_choose_table) = S ((S (bcf_predecessor_mkm_binextend_source_point_choose_table)) * bcf_row_code_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_decoded_previous_code. bcf_row_code_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_table_decoded_previous_code * S ((S (bcf_predecessor_mkm_binextend_source_point_choose_table)) * bcf_row_code_scale_mkm_binextend_source_point_choose) + (bcf_previous_code_mkm_binextend_source_point_choose_table))) /\ ((((exists bcf_height_mkm_binextend_source_point_choose_table_decoded_previous_scale. bcf_height_mkm_binextend_source_point_choose_table_decoded_previous_scale + S (bcf_previous_scale_mkm_binextend_source_point_choose_table) = S ((S (bcf_predecessor_mkm_binextend_source_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_decoded_previous_scale. bcf_row_scale_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_mkm_binextend_source_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_source_point_choose) + (bcf_previous_scale_mkm_binextend_source_point_choose_table))) /\ (forall bcf_index_mkm_binextend_source_point_choose_table_row_step. (exists bcf_lt_gap_mkm_binextend_source_point_choose_table_row_step_bound. bcf_lt_gap_mkm_binextend_source_point_choose_table_row_step_bound + S (bcf_index_mkm_binextend_source_point_choose_table_row_step) = S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) -> exists bcf_value_mkm_binextend_source_point_choose_table_row_step. ((((exists bcf_height_mkm_binextend_source_point_choose_table_row_step_entry. bcf_height_mkm_binextend_source_point_choose_table_row_step_entry + S (bcf_value_mkm_binextend_source_point_choose_table_row_step) = S ((S (bcf_index_mkm_binextend_source_point_choose_table_row_step)) * bcf_row_scale_mkm_binextend_source_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_row_step_entry. bcf_row_code_mkm_binextend_source_point_choose_table = bcf_quotient_mkm_binextend_source_point_choose_table_row_step_entry * S ((S (bcf_index_mkm_binextend_source_point_choose_table_row_step)) * bcf_row_scale_mkm_binextend_source_point_choose_table) + (bcf_value_mkm_binextend_source_point_choose_table_row_step))) /\ ((bcf_index_mkm_binextend_source_point_choose_table_row_step = 0 /\ bcf_value_mkm_binextend_source_point_choose_table_row_step = 1) \/ exists bcf_predecessor_mkm_binextend_source_point_choose_table_row_step bcf_left_mkm_binextend_source_point_choose_table_row_step bcf_right_mkm_binextend_source_point_choose_table_row_step. bcf_index_mkm_binextend_source_point_choose_table_row_step = S bcf_predecessor_mkm_binextend_source_point_choose_table_row_step /\ ((((exists bcf_height_mkm_binextend_source_point_choose_table_row_step_previous_left. bcf_height_mkm_binextend_source_point_choose_table_row_step_previous_left + S (bcf_left_mkm_binextend_source_point_choose_table_row_step) = S ((S (bcf_predecessor_mkm_binextend_source_point_choose_table_row_step)) * bcf_previous_scale_mkm_binextend_source_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_row_step_previous_left. bcf_previous_code_mkm_binextend_source_point_choose_table = bcf_quotient_mkm_binextend_source_point_choose_table_row_step_previous_left * S ((S (bcf_predecessor_mkm_binextend_source_point_choose_table_row_step)) * bcf_previous_scale_mkm_binextend_source_point_choose_table) + (bcf_left_mkm_binextend_source_point_choose_table_row_step))) /\ ((((exists bcf_height_mkm_binextend_source_point_choose_table_row_step_previous_right. bcf_height_mkm_binextend_source_point_choose_table_row_step_previous_right + S (bcf_right_mkm_binextend_source_point_choose_table_row_step) = S ((S (S (bcf_predecessor_mkm_binextend_source_point_choose_table_row_step))) * bcf_previous_scale_mkm_binextend_source_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_table_row_step_previous_right. bcf_previous_code_mkm_binextend_source_point_choose_table = bcf_quotient_mkm_binextend_source_point_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_mkm_binextend_source_point_choose_table_row_step))) * bcf_previous_scale_mkm_binextend_source_point_choose_table) + (bcf_right_mkm_binextend_source_point_choose_table_row_step))) /\ bcf_value_mkm_binextend_source_point_choose_table_row_step = bcf_left_mkm_binextend_source_point_choose_table_row_step + bcf_right_mkm_binextend_source_point_choose_table_row_step))))))))))) /\ ((((exists bcf_height_mkm_binextend_source_point_choose_decoded_row_code. bcf_height_mkm_binextend_source_point_choose_decoded_row_code + S (bcf_row_code_mkm_binextend_source_point_choose) = S ((S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) * bcf_row_code_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_decoded_row_code. bcf_row_code_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_decoded_row_code * S ((S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) * bcf_row_code_scale_mkm_binextend_source_point_choose) + (bcf_row_code_mkm_binextend_source_point_choose))) /\ ((((exists bcf_height_mkm_binextend_source_point_choose_decoded_row_scale. bcf_height_mkm_binextend_source_point_choose_decoded_row_scale + S (bcf_row_scale_mkm_binextend_source_point_choose) = S ((S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) * bcf_row_scale_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_decoded_row_scale. bcf_row_scale_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_decoded_row_scale * S ((S (mkm_partial_binextend_source_point + mkm_value_binextend_source_point)) * bcf_row_scale_scale_mkm_binextend_source_point_choose) + (bcf_row_scale_mkm_binextend_source_point_choose))) /\ (((exists bcf_height_mkm_binextend_source_point_choose_decoded_value. bcf_height_mkm_binextend_source_point_choose_decoded_value + S (mkm_factor_binextend_source_point) = S ((S (mkm_partial_binextend_source_point)) * bcf_row_scale_mkm_binextend_source_point_choose)) /\ exists bcf_quotient_mkm_binextend_source_point_choose_decoded_value. bcf_row_code_mkm_binextend_source_point_choose = bcf_quotient_mkm_binextend_source_point_choose_decoded_value * S ((S (mkm_partial_binextend_source_point)) * bcf_row_scale_mkm_binextend_source_point_choose) + (mkm_factor_binextend_source_point))))))))) /\ (((exists fs_h_mkm_binextend_source_point_factor. fs_h_mkm_binextend_source_point_factor + S (mkm_factor_binextend_source_point) = S ((S (mkm_index_binextend_source)) * cc)) /\ exists fs_q_mkm_binextend_source_point_factor. cb = fs_q_mkm_binextend_source_point_factor * S ((S (mkm_index_binextend_source)) * cc) + (mkm_factor_binextend_source_point))))))) -> (((exists fs_h_mkm_binextend_a. fs_h_mkm_binextend_a + S (a) = S ((S (l)) * c)) /\ exists fs_q_mkm_binextend_a. b = fs_q_mkm_binextend_a * S ((S (l)) * c) + (a))) -> (((exists fs_h_mkm_binextend_u. fs_h_mkm_binextend_u + S (u) = S ((S (l)) * sc)) /\ exists fs_q_mkm_binextend_u. sb = fs_q_mkm_binextend_u * S ((S (l)) * sc) + (u))) -> (((exists bcf_lt_gap_mkm_binextend_choose_out_of_range. bcf_lt_gap_mkm_binextend_choose_out_of_range + S (u + a) = u) /\ C = 0) \/ ((exists bcf_le_gap_mkm_binextend_choose_in_range. bcf_le_gap_mkm_binextend_choose_in_range + (u) = u + a) /\ (exists bcf_row_code_code_mkm_binextend_choose bcf_row_code_scale_mkm_binextend_choose bcf_row_scale_code_mkm_binextend_choose bcf_row_scale_scale_mkm_binextend_choose bcf_row_code_mkm_binextend_choose bcf_row_scale_mkm_binextend_choose. ((forall bcf_row_index_mkm_binextend_choose_table. (exists bcf_lt_gap_mkm_binextend_choose_table_row_bound. bcf_lt_gap_mkm_binextend_choose_table_row_bound + S (bcf_row_index_mkm_binextend_choose_table) = S (u + a)) -> exists bcf_row_code_mkm_binextend_choose_table bcf_row_scale_mkm_binextend_choose_table. ((((exists bcf_height_mkm_binextend_choose_table_decoded_row_code. bcf_height_mkm_binextend_choose_table_decoded_row_code + S (bcf_row_code_mkm_binextend_choose_table) = S ((S (bcf_row_index_mkm_binextend_choose_table)) * bcf_row_code_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_table_decoded_row_code. bcf_row_code_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_table_decoded_row_code * S ((S (bcf_row_index_mkm_binextend_choose_table)) * bcf_row_code_scale_mkm_binextend_choose) + (bcf_row_code_mkm_binextend_choose_table))) /\ ((((exists bcf_height_mkm_binextend_choose_table_decoded_row_scale. bcf_height_mkm_binextend_choose_table_decoded_row_scale + S (bcf_row_scale_mkm_binextend_choose_table) = S ((S (bcf_row_index_mkm_binextend_choose_table)) * bcf_row_scale_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_table_decoded_row_scale. bcf_row_scale_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_table_decoded_row_scale * S ((S (bcf_row_index_mkm_binextend_choose_table)) * bcf_row_scale_scale_mkm_binextend_choose) + (bcf_row_scale_mkm_binextend_choose_table))) /\ ((bcf_row_index_mkm_binextend_choose_table = 0 /\ (forall bcf_index_mkm_binextend_choose_table_zero_row. (exists bcf_lt_gap_mkm_binextend_choose_table_zero_row_bound. bcf_lt_gap_mkm_binextend_choose_table_zero_row_bound + S (bcf_index_mkm_binextend_choose_table_zero_row) = S (u + a)) -> exists bcf_value_mkm_binextend_choose_table_zero_row. ((((exists bcf_height_mkm_binextend_choose_table_zero_row_entry. bcf_height_mkm_binextend_choose_table_zero_row_entry + S (bcf_value_mkm_binextend_choose_table_zero_row) = S ((S (bcf_index_mkm_binextend_choose_table_zero_row)) * bcf_row_scale_mkm_binextend_choose_table)) /\ exists bcf_quotient_mkm_binextend_choose_table_zero_row_entry. bcf_row_code_mkm_binextend_choose_table = bcf_quotient_mkm_binextend_choose_table_zero_row_entry * S ((S (bcf_index_mkm_binextend_choose_table_zero_row)) * bcf_row_scale_mkm_binextend_choose_table) + (bcf_value_mkm_binextend_choose_table_zero_row))) /\ ((bcf_index_mkm_binextend_choose_table_zero_row = 0 /\ bcf_value_mkm_binextend_choose_table_zero_row = 1) \/ exists bcf_predecessor_mkm_binextend_choose_table_zero_row. bcf_index_mkm_binextend_choose_table_zero_row = S bcf_predecessor_mkm_binextend_choose_table_zero_row /\ bcf_value_mkm_binextend_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_mkm_binextend_choose_table bcf_previous_code_mkm_binextend_choose_table bcf_previous_scale_mkm_binextend_choose_table. bcf_row_index_mkm_binextend_choose_table = S bcf_predecessor_mkm_binextend_choose_table /\ ((((exists bcf_height_mkm_binextend_choose_table_decoded_previous_code. bcf_height_mkm_binextend_choose_table_decoded_previous_code + S (bcf_previous_code_mkm_binextend_choose_table) = S ((S (bcf_predecessor_mkm_binextend_choose_table)) * bcf_row_code_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_table_decoded_previous_code. bcf_row_code_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_table_decoded_previous_code * S ((S (bcf_predecessor_mkm_binextend_choose_table)) * bcf_row_code_scale_mkm_binextend_choose) + (bcf_previous_code_mkm_binextend_choose_table))) /\ ((((exists bcf_height_mkm_binextend_choose_table_decoded_previous_scale. bcf_height_mkm_binextend_choose_table_decoded_previous_scale + S (bcf_previous_scale_mkm_binextend_choose_table) = S ((S (bcf_predecessor_mkm_binextend_choose_table)) * bcf_row_scale_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_table_decoded_previous_scale. bcf_row_scale_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_mkm_binextend_choose_table)) * bcf_row_scale_scale_mkm_binextend_choose) + (bcf_previous_scale_mkm_binextend_choose_table))) /\ (forall bcf_index_mkm_binextend_choose_table_row_step. (exists bcf_lt_gap_mkm_binextend_choose_table_row_step_bound. bcf_lt_gap_mkm_binextend_choose_table_row_step_bound + S (bcf_index_mkm_binextend_choose_table_row_step) = S (u + a)) -> exists bcf_value_mkm_binextend_choose_table_row_step. ((((exists bcf_height_mkm_binextend_choose_table_row_step_entry. bcf_height_mkm_binextend_choose_table_row_step_entry + S (bcf_value_mkm_binextend_choose_table_row_step) = S ((S (bcf_index_mkm_binextend_choose_table_row_step)) * bcf_row_scale_mkm_binextend_choose_table)) /\ exists bcf_quotient_mkm_binextend_choose_table_row_step_entry. bcf_row_code_mkm_binextend_choose_table = bcf_quotient_mkm_binextend_choose_table_row_step_entry * S ((S (bcf_index_mkm_binextend_choose_table_row_step)) * bcf_row_scale_mkm_binextend_choose_table) + (bcf_value_mkm_binextend_choose_table_row_step))) /\ ((bcf_index_mkm_binextend_choose_table_row_step = 0 /\ bcf_value_mkm_binextend_choose_table_row_step = 1) \/ exists bcf_predecessor_mkm_binextend_choose_table_row_step bcf_left_mkm_binextend_choose_table_row_step bcf_right_mkm_binextend_choose_table_row_step. bcf_index_mkm_binextend_choose_table_row_step = S bcf_predecessor_mkm_binextend_choose_table_row_step /\ ((((exists bcf_height_mkm_binextend_choose_table_row_step_previous_left. bcf_height_mkm_binextend_choose_table_row_step_previous_left + S (bcf_left_mkm_binextend_choose_table_row_step) = S ((S (bcf_predecessor_mkm_binextend_choose_table_row_step)) * bcf_previous_scale_mkm_binextend_choose_table)) /\ exists bcf_quotient_mkm_binextend_choose_table_row_step_previous_left. bcf_previous_code_mkm_binextend_choose_table = bcf_quotient_mkm_binextend_choose_table_row_step_previous_left * S ((S (bcf_predecessor_mkm_binextend_choose_table_row_step)) * bcf_previous_scale_mkm_binextend_choose_table) + (bcf_left_mkm_binextend_choose_table_row_step))) /\ ((((exists bcf_height_mkm_binextend_choose_table_row_step_previous_right. bcf_height_mkm_binextend_choose_table_row_step_previous_right + S (bcf_right_mkm_binextend_choose_table_row_step) = S ((S (S (bcf_predecessor_mkm_binextend_choose_table_row_step))) * bcf_previous_scale_mkm_binextend_choose_table)) /\ exists bcf_quotient_mkm_binextend_choose_table_row_step_previous_right. bcf_previous_code_mkm_binextend_choose_table = bcf_quotient_mkm_binextend_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_mkm_binextend_choose_table_row_step))) * bcf_previous_scale_mkm_binextend_choose_table) + (bcf_right_mkm_binextend_choose_table_row_step))) /\ bcf_value_mkm_binextend_choose_table_row_step = bcf_left_mkm_binextend_choose_table_row_step + bcf_right_mkm_binextend_choose_table_row_step))))))))))) /\ ((((exists bcf_height_mkm_binextend_choose_decoded_row_code. bcf_height_mkm_binextend_choose_decoded_row_code + S (bcf_row_code_mkm_binextend_choose) = S ((S (u + a)) * bcf_row_code_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_decoded_row_code. bcf_row_code_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_decoded_row_code * S ((S (u + a)) * bcf_row_code_scale_mkm_binextend_choose) + (bcf_row_code_mkm_binextend_choose))) /\ ((((exists bcf_height_mkm_binextend_choose_decoded_row_scale. bcf_height_mkm_binextend_choose_decoded_row_scale + S (bcf_row_scale_mkm_binextend_choose) = S ((S (u + a)) * bcf_row_scale_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_decoded_row_scale. bcf_row_scale_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_decoded_row_scale * S ((S (u + a)) * bcf_row_scale_scale_mkm_binextend_choose) + (bcf_row_scale_mkm_binextend_choose))) /\ (((exists bcf_height_mkm_binextend_choose_decoded_value. bcf_height_mkm_binextend_choose_decoded_value + S (C) = S ((S (u)) * bcf_row_scale_mkm_binextend_choose)) /\ exists bcf_quotient_mkm_binextend_choose_decoded_value. bcf_row_code_mkm_binextend_choose = bcf_quotient_mkm_binextend_choose_decoded_value * S ((S (u)) * bcf_row_scale_mkm_binextend_choose) + (C))))))))) -> exists nb nc. (forall mkm_index_binextend_target. (exists mkm_lt_binextend_target_bound. mkm_lt_binextend_target_bound + S (mkm_index_binextend_target) = (S l)) -> (exists mkm_value_binextend_target_point mkm_partial_binextend_target_point mkm_factor_binextend_target_point. (((exists fs_h_mkm_binextend_target_point_source. fs_h_mkm_binextend_target_point_source + S (mkm_value_binextend_target_point) = S ((S (mkm_index_binextend_target)) * c)) /\ exists fs_q_mkm_binextend_target_point_source. b = fs_q_mkm_binextend_target_point_source * S ((S (mkm_index_binextend_target)) * c) + (mkm_value_binextend_target_point))) /\ ((((exists fs_h_mkm_binextend_target_point_partial. fs_h_mkm_binextend_target_point_partial + S (mkm_partial_binextend_target_point) = S ((S (mkm_index_binextend_target)) * sc)) /\ exists fs_q_mkm_binextend_target_point_partial. sb = fs_q_mkm_binextend_target_point_partial * S ((S (mkm_index_binextend_target)) * sc) + (mkm_partial_binextend_target_point))) /\ ((((exists bcf_lt_gap_mkm_binextend_target_point_choose_out_of_range. bcf_lt_gap_mkm_binextend_target_point_choose_out_of_range + S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point) = mkm_partial_binextend_target_point) /\ mkm_factor_binextend_target_point = 0) \/ ((exists bcf_le_gap_mkm_binextend_target_point_choose_in_range. bcf_le_gap_mkm_binextend_target_point_choose_in_range + (mkm_partial_binextend_target_point) = mkm_partial_binextend_target_point + mkm_value_binextend_target_point) /\ (exists bcf_row_code_code_mkm_binextend_target_point_choose bcf_row_code_scale_mkm_binextend_target_point_choose bcf_row_scale_code_mkm_binextend_target_point_choose bcf_row_scale_scale_mkm_binextend_target_point_choose bcf_row_code_mkm_binextend_target_point_choose bcf_row_scale_mkm_binextend_target_point_choose. ((forall bcf_row_index_mkm_binextend_target_point_choose_table. (exists bcf_lt_gap_mkm_binextend_target_point_choose_table_row_bound. bcf_lt_gap_mkm_binextend_target_point_choose_table_row_bound + S (bcf_row_index_mkm_binextend_target_point_choose_table) = S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) -> exists bcf_row_code_mkm_binextend_target_point_choose_table bcf_row_scale_mkm_binextend_target_point_choose_table. ((((exists bcf_height_mkm_binextend_target_point_choose_table_decoded_row_code. bcf_height_mkm_binextend_target_point_choose_table_decoded_row_code + S (bcf_row_code_mkm_binextend_target_point_choose_table) = S ((S (bcf_row_index_mkm_binextend_target_point_choose_table)) * bcf_row_code_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_decoded_row_code. bcf_row_code_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_table_decoded_row_code * S ((S (bcf_row_index_mkm_binextend_target_point_choose_table)) * bcf_row_code_scale_mkm_binextend_target_point_choose) + (bcf_row_code_mkm_binextend_target_point_choose_table))) /\ ((((exists bcf_height_mkm_binextend_target_point_choose_table_decoded_row_scale. bcf_height_mkm_binextend_target_point_choose_table_decoded_row_scale + S (bcf_row_scale_mkm_binextend_target_point_choose_table) = S ((S (bcf_row_index_mkm_binextend_target_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_decoded_row_scale. bcf_row_scale_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_table_decoded_row_scale * S ((S (bcf_row_index_mkm_binextend_target_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_target_point_choose) + (bcf_row_scale_mkm_binextend_target_point_choose_table))) /\ ((bcf_row_index_mkm_binextend_target_point_choose_table = 0 /\ (forall bcf_index_mkm_binextend_target_point_choose_table_zero_row. (exists bcf_lt_gap_mkm_binextend_target_point_choose_table_zero_row_bound. bcf_lt_gap_mkm_binextend_target_point_choose_table_zero_row_bound + S (bcf_index_mkm_binextend_target_point_choose_table_zero_row) = S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) -> exists bcf_value_mkm_binextend_target_point_choose_table_zero_row. ((((exists bcf_height_mkm_binextend_target_point_choose_table_zero_row_entry. bcf_height_mkm_binextend_target_point_choose_table_zero_row_entry + S (bcf_value_mkm_binextend_target_point_choose_table_zero_row) = S ((S (bcf_index_mkm_binextend_target_point_choose_table_zero_row)) * bcf_row_scale_mkm_binextend_target_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_zero_row_entry. bcf_row_code_mkm_binextend_target_point_choose_table = bcf_quotient_mkm_binextend_target_point_choose_table_zero_row_entry * S ((S (bcf_index_mkm_binextend_target_point_choose_table_zero_row)) * bcf_row_scale_mkm_binextend_target_point_choose_table) + (bcf_value_mkm_binextend_target_point_choose_table_zero_row))) /\ ((bcf_index_mkm_binextend_target_point_choose_table_zero_row = 0 /\ bcf_value_mkm_binextend_target_point_choose_table_zero_row = 1) \/ exists bcf_predecessor_mkm_binextend_target_point_choose_table_zero_row. bcf_index_mkm_binextend_target_point_choose_table_zero_row = S bcf_predecessor_mkm_binextend_target_point_choose_table_zero_row /\ bcf_value_mkm_binextend_target_point_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_mkm_binextend_target_point_choose_table bcf_previous_code_mkm_binextend_target_point_choose_table bcf_previous_scale_mkm_binextend_target_point_choose_table. bcf_row_index_mkm_binextend_target_point_choose_table = S bcf_predecessor_mkm_binextend_target_point_choose_table /\ ((((exists bcf_height_mkm_binextend_target_point_choose_table_decoded_previous_code. bcf_height_mkm_binextend_target_point_choose_table_decoded_previous_code + S (bcf_previous_code_mkm_binextend_target_point_choose_table) = S ((S (bcf_predecessor_mkm_binextend_target_point_choose_table)) * bcf_row_code_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_decoded_previous_code. bcf_row_code_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_table_decoded_previous_code * S ((S (bcf_predecessor_mkm_binextend_target_point_choose_table)) * bcf_row_code_scale_mkm_binextend_target_point_choose) + (bcf_previous_code_mkm_binextend_target_point_choose_table))) /\ ((((exists bcf_height_mkm_binextend_target_point_choose_table_decoded_previous_scale. bcf_height_mkm_binextend_target_point_choose_table_decoded_previous_scale + S (bcf_previous_scale_mkm_binextend_target_point_choose_table) = S ((S (bcf_predecessor_mkm_binextend_target_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_decoded_previous_scale. bcf_row_scale_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_mkm_binextend_target_point_choose_table)) * bcf_row_scale_scale_mkm_binextend_target_point_choose) + (bcf_previous_scale_mkm_binextend_target_point_choose_table))) /\ (forall bcf_index_mkm_binextend_target_point_choose_table_row_step. (exists bcf_lt_gap_mkm_binextend_target_point_choose_table_row_step_bound. bcf_lt_gap_mkm_binextend_target_point_choose_table_row_step_bound + S (bcf_index_mkm_binextend_target_point_choose_table_row_step) = S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) -> exists bcf_value_mkm_binextend_target_point_choose_table_row_step. ((((exists bcf_height_mkm_binextend_target_point_choose_table_row_step_entry. bcf_height_mkm_binextend_target_point_choose_table_row_step_entry + S (bcf_value_mkm_binextend_target_point_choose_table_row_step) = S ((S (bcf_index_mkm_binextend_target_point_choose_table_row_step)) * bcf_row_scale_mkm_binextend_target_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_row_step_entry. bcf_row_code_mkm_binextend_target_point_choose_table = bcf_quotient_mkm_binextend_target_point_choose_table_row_step_entry * S ((S (bcf_index_mkm_binextend_target_point_choose_table_row_step)) * bcf_row_scale_mkm_binextend_target_point_choose_table) + (bcf_value_mkm_binextend_target_point_choose_table_row_step))) /\ ((bcf_index_mkm_binextend_target_point_choose_table_row_step = 0 /\ bcf_value_mkm_binextend_target_point_choose_table_row_step = 1) \/ exists bcf_predecessor_mkm_binextend_target_point_choose_table_row_step bcf_left_mkm_binextend_target_point_choose_table_row_step bcf_right_mkm_binextend_target_point_choose_table_row_step. bcf_index_mkm_binextend_target_point_choose_table_row_step = S bcf_predecessor_mkm_binextend_target_point_choose_table_row_step /\ ((((exists bcf_height_mkm_binextend_target_point_choose_table_row_step_previous_left. bcf_height_mkm_binextend_target_point_choose_table_row_step_previous_left + S (bcf_left_mkm_binextend_target_point_choose_table_row_step) = S ((S (bcf_predecessor_mkm_binextend_target_point_choose_table_row_step)) * bcf_previous_scale_mkm_binextend_target_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_row_step_previous_left. bcf_previous_code_mkm_binextend_target_point_choose_table = bcf_quotient_mkm_binextend_target_point_choose_table_row_step_previous_left * S ((S (bcf_predecessor_mkm_binextend_target_point_choose_table_row_step)) * bcf_previous_scale_mkm_binextend_target_point_choose_table) + (bcf_left_mkm_binextend_target_point_choose_table_row_step))) /\ ((((exists bcf_height_mkm_binextend_target_point_choose_table_row_step_previous_right. bcf_height_mkm_binextend_target_point_choose_table_row_step_previous_right + S (bcf_right_mkm_binextend_target_point_choose_table_row_step) = S ((S (S (bcf_predecessor_mkm_binextend_target_point_choose_table_row_step))) * bcf_previous_scale_mkm_binextend_target_point_choose_table)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_table_row_step_previous_right. bcf_previous_code_mkm_binextend_target_point_choose_table = bcf_quotient_mkm_binextend_target_point_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_mkm_binextend_target_point_choose_table_row_step))) * bcf_previous_scale_mkm_binextend_target_point_choose_table) + (bcf_right_mkm_binextend_target_point_choose_table_row_step))) /\ bcf_value_mkm_binextend_target_point_choose_table_row_step = bcf_left_mkm_binextend_target_point_choose_table_row_step + bcf_right_mkm_binextend_target_point_choose_table_row_step))))))))))) /\ ((((exists bcf_height_mkm_binextend_target_point_choose_decoded_row_code. bcf_height_mkm_binextend_target_point_choose_decoded_row_code + S (bcf_row_code_mkm_binextend_target_point_choose) = S ((S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) * bcf_row_code_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_decoded_row_code. bcf_row_code_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_decoded_row_code * S ((S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) * bcf_row_code_scale_mkm_binextend_target_point_choose) + (bcf_row_code_mkm_binextend_target_point_choose))) /\ ((((exists bcf_height_mkm_binextend_target_point_choose_decoded_row_scale. bcf_height_mkm_binextend_target_point_choose_decoded_row_scale + S (bcf_row_scale_mkm_binextend_target_point_choose) = S ((S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) * bcf_row_scale_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_decoded_row_scale. bcf_row_scale_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_decoded_row_scale * S ((S (mkm_partial_binextend_target_point + mkm_value_binextend_target_point)) * bcf_row_scale_scale_mkm_binextend_target_point_choose) + (bcf_row_scale_mkm_binextend_target_point_choose))) /\ (((exists bcf_height_mkm_binextend_target_point_choose_decoded_value. bcf_height_mkm_binextend_target_point_choose_decoded_value + S (mkm_factor_binextend_target_point) = S ((S (mkm_partial_binextend_target_point)) * bcf_row_scale_mkm_binextend_target_point_choose)) /\ exists bcf_quotient_mkm_binextend_target_point_choose_decoded_value. bcf_row_code_mkm_binextend_target_point_choose = bcf_quotient_mkm_binextend_target_point_choose_decoded_value * S ((S (mkm_partial_binextend_target_point)) * bcf_row_scale_mkm_binextend_target_point_choose) + (mkm_factor_binextend_target_point))))))))) /\ (((exists fs_h_mkm_binextend_target_point_factor. fs_h_mkm_binextend_target_point_factor + S (mkm_factor_binextend_target_point) = S ((S (mkm_index_binextend_target)) * nc)) /\ exists fs_q_mkm_binextend_target_point_factor. nb = fs_q_mkm_binextend_target_point_factor * S ((S (mkm_index_binextend_target)) * nc) + (mkm_factor_binextend_target_point)))))))