Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Exact expanded first-order arithmetic statement
forall b c sb sc cb cc l. (forall mkm_index_bindrop_source. (exists mkm_lt_bindrop_source_bound. mkm_lt_bindrop_source_bound + S (mkm_index_bindrop_source) = (S l)) -> (exists mkm_value_bindrop_source_point mkm_partial_bindrop_source_point mkm_factor_bindrop_source_point. (((exists fs_h_mkm_bindrop_source_point_source. fs_h_mkm_bindrop_source_point_source + S (mkm_value_bindrop_source_point) = S ((S (mkm_index_bindrop_source)) * c)) /\ exists fs_q_mkm_bindrop_source_point_source. b = fs_q_mkm_bindrop_source_point_source * S ((S (mkm_index_bindrop_source)) * c) + (mkm_value_bindrop_source_point))) /\ ((((exists fs_h_mkm_bindrop_source_point_partial. fs_h_mkm_bindrop_source_point_partial + S (mkm_partial_bindrop_source_point) = S ((S (mkm_index_bindrop_source)) * sc)) /\ exists fs_q_mkm_bindrop_source_point_partial. sb = fs_q_mkm_bindrop_source_point_partial * S ((S (mkm_index_bindrop_source)) * sc) + (mkm_partial_bindrop_source_point))) /\ ((((exists bcf_lt_gap_mkm_bindrop_source_point_choose_out_of_range. bcf_lt_gap_mkm_bindrop_source_point_choose_out_of_range + S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point) = mkm_partial_bindrop_source_point) /\ mkm_factor_bindrop_source_point = 0) \/ ((exists bcf_le_gap_mkm_bindrop_source_point_choose_in_range. bcf_le_gap_mkm_bindrop_source_point_choose_in_range + (mkm_partial_bindrop_source_point) = mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point) /\ (exists bcf_row_code_code_mkm_bindrop_source_point_choose bcf_row_code_scale_mkm_bindrop_source_point_choose bcf_row_scale_code_mkm_bindrop_source_point_choose bcf_row_scale_scale_mkm_bindrop_source_point_choose bcf_row_code_mkm_bindrop_source_point_choose bcf_row_scale_mkm_bindrop_source_point_choose. ((forall bcf_row_index_mkm_bindrop_source_point_choose_table. (exists bcf_lt_gap_mkm_bindrop_source_point_choose_table_row_bound. bcf_lt_gap_mkm_bindrop_source_point_choose_table_row_bound + S (bcf_row_index_mkm_bindrop_source_point_choose_table) = S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) -> exists bcf_row_code_mkm_bindrop_source_point_choose_table bcf_row_scale_mkm_bindrop_source_point_choose_table. ((((exists bcf_height_mkm_bindrop_source_point_choose_table_decoded_row_code. bcf_height_mkm_bindrop_source_point_choose_table_decoded_row_code + S (bcf_row_code_mkm_bindrop_source_point_choose_table) = S ((S (bcf_row_index_mkm_bindrop_source_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_row_code. bcf_row_code_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_row_code * S ((S (bcf_row_index_mkm_bindrop_source_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_source_point_choose) + (bcf_row_code_mkm_bindrop_source_point_choose_table))) /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_table_decoded_row_scale. bcf_height_mkm_bindrop_source_point_choose_table_decoded_row_scale + S (bcf_row_scale_mkm_bindrop_source_point_choose_table) = S ((S (bcf_row_index_mkm_bindrop_source_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_row_scale. bcf_row_scale_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_row_scale * S ((S (bcf_row_index_mkm_bindrop_source_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_source_point_choose) + (bcf_row_scale_mkm_bindrop_source_point_choose_table))) /\ ((bcf_row_index_mkm_bindrop_source_point_choose_table = 0 /\ (forall bcf_index_mkm_bindrop_source_point_choose_table_zero_row. (exists bcf_lt_gap_mkm_bindrop_source_point_choose_table_zero_row_bound. bcf_lt_gap_mkm_bindrop_source_point_choose_table_zero_row_bound + S (bcf_index_mkm_bindrop_source_point_choose_table_zero_row) = S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) -> exists bcf_value_mkm_bindrop_source_point_choose_table_zero_row. ((((exists bcf_height_mkm_bindrop_source_point_choose_table_zero_row_entry. bcf_height_mkm_bindrop_source_point_choose_table_zero_row_entry + S (bcf_value_mkm_bindrop_source_point_choose_table_zero_row) = S ((S (bcf_index_mkm_bindrop_source_point_choose_table_zero_row)) * bcf_row_scale_mkm_bindrop_source_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_zero_row_entry. bcf_row_code_mkm_bindrop_source_point_choose_table = bcf_quotient_mkm_bindrop_source_point_choose_table_zero_row_entry * S ((S (bcf_index_mkm_bindrop_source_point_choose_table_zero_row)) * bcf_row_scale_mkm_bindrop_source_point_choose_table) + (bcf_value_mkm_bindrop_source_point_choose_table_zero_row))) /\ ((bcf_index_mkm_bindrop_source_point_choose_table_zero_row = 0 /\ bcf_value_mkm_bindrop_source_point_choose_table_zero_row = 1) \/ exists bcf_predecessor_mkm_bindrop_source_point_choose_table_zero_row. bcf_index_mkm_bindrop_source_point_choose_table_zero_row = S bcf_predecessor_mkm_bindrop_source_point_choose_table_zero_row /\ bcf_value_mkm_bindrop_source_point_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_mkm_bindrop_source_point_choose_table bcf_previous_code_mkm_bindrop_source_point_choose_table bcf_previous_scale_mkm_bindrop_source_point_choose_table. bcf_row_index_mkm_bindrop_source_point_choose_table = S bcf_predecessor_mkm_bindrop_source_point_choose_table /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_table_decoded_previous_code. bcf_height_mkm_bindrop_source_point_choose_table_decoded_previous_code + S (bcf_previous_code_mkm_bindrop_source_point_choose_table) = S ((S (bcf_predecessor_mkm_bindrop_source_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_previous_code. bcf_row_code_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_previous_code * S ((S (bcf_predecessor_mkm_bindrop_source_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_source_point_choose) + (bcf_previous_code_mkm_bindrop_source_point_choose_table))) /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_table_decoded_previous_scale. bcf_height_mkm_bindrop_source_point_choose_table_decoded_previous_scale + S (bcf_previous_scale_mkm_bindrop_source_point_choose_table) = S ((S (bcf_predecessor_mkm_bindrop_source_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_previous_scale. bcf_row_scale_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_mkm_bindrop_source_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_source_point_choose) + (bcf_previous_scale_mkm_bindrop_source_point_choose_table))) /\ (forall bcf_index_mkm_bindrop_source_point_choose_table_row_step. (exists bcf_lt_gap_mkm_bindrop_source_point_choose_table_row_step_bound. bcf_lt_gap_mkm_bindrop_source_point_choose_table_row_step_bound + S (bcf_index_mkm_bindrop_source_point_choose_table_row_step) = S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) -> exists bcf_value_mkm_bindrop_source_point_choose_table_row_step. ((((exists bcf_height_mkm_bindrop_source_point_choose_table_row_step_entry. bcf_height_mkm_bindrop_source_point_choose_table_row_step_entry + S (bcf_value_mkm_bindrop_source_point_choose_table_row_step) = S ((S (bcf_index_mkm_bindrop_source_point_choose_table_row_step)) * bcf_row_scale_mkm_bindrop_source_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_row_step_entry. bcf_row_code_mkm_bindrop_source_point_choose_table = bcf_quotient_mkm_bindrop_source_point_choose_table_row_step_entry * S ((S (bcf_index_mkm_bindrop_source_point_choose_table_row_step)) * bcf_row_scale_mkm_bindrop_source_point_choose_table) + (bcf_value_mkm_bindrop_source_point_choose_table_row_step))) /\ ((bcf_index_mkm_bindrop_source_point_choose_table_row_step = 0 /\ bcf_value_mkm_bindrop_source_point_choose_table_row_step = 1) \/ exists bcf_predecessor_mkm_bindrop_source_point_choose_table_row_step bcf_left_mkm_bindrop_source_point_choose_table_row_step bcf_right_mkm_bindrop_source_point_choose_table_row_step. bcf_index_mkm_bindrop_source_point_choose_table_row_step = S bcf_predecessor_mkm_bindrop_source_point_choose_table_row_step /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_table_row_step_previous_left. bcf_height_mkm_bindrop_source_point_choose_table_row_step_previous_left + S (bcf_left_mkm_bindrop_source_point_choose_table_row_step) = S ((S (bcf_predecessor_mkm_bindrop_source_point_choose_table_row_step)) * bcf_previous_scale_mkm_bindrop_source_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_row_step_previous_left. bcf_previous_code_mkm_bindrop_source_point_choose_table = bcf_quotient_mkm_bindrop_source_point_choose_table_row_step_previous_left * S ((S (bcf_predecessor_mkm_bindrop_source_point_choose_table_row_step)) * bcf_previous_scale_mkm_bindrop_source_point_choose_table) + (bcf_left_mkm_bindrop_source_point_choose_table_row_step))) /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_table_row_step_previous_right. bcf_height_mkm_bindrop_source_point_choose_table_row_step_previous_right + S (bcf_right_mkm_bindrop_source_point_choose_table_row_step) = S ((S (S (bcf_predecessor_mkm_bindrop_source_point_choose_table_row_step))) * bcf_previous_scale_mkm_bindrop_source_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_table_row_step_previous_right. bcf_previous_code_mkm_bindrop_source_point_choose_table = bcf_quotient_mkm_bindrop_source_point_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_mkm_bindrop_source_point_choose_table_row_step))) * bcf_previous_scale_mkm_bindrop_source_point_choose_table) + (bcf_right_mkm_bindrop_source_point_choose_table_row_step))) /\ bcf_value_mkm_bindrop_source_point_choose_table_row_step = bcf_left_mkm_bindrop_source_point_choose_table_row_step + bcf_right_mkm_bindrop_source_point_choose_table_row_step))))))))))) /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_decoded_row_code. bcf_height_mkm_bindrop_source_point_choose_decoded_row_code + S (bcf_row_code_mkm_bindrop_source_point_choose) = S ((S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) * bcf_row_code_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_decoded_row_code. bcf_row_code_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_decoded_row_code * S ((S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) * bcf_row_code_scale_mkm_bindrop_source_point_choose) + (bcf_row_code_mkm_bindrop_source_point_choose))) /\ ((((exists bcf_height_mkm_bindrop_source_point_choose_decoded_row_scale. bcf_height_mkm_bindrop_source_point_choose_decoded_row_scale + S (bcf_row_scale_mkm_bindrop_source_point_choose) = S ((S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) * bcf_row_scale_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_decoded_row_scale. bcf_row_scale_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_decoded_row_scale * S ((S (mkm_partial_bindrop_source_point + mkm_value_bindrop_source_point)) * bcf_row_scale_scale_mkm_bindrop_source_point_choose) + (bcf_row_scale_mkm_bindrop_source_point_choose))) /\ (((exists bcf_height_mkm_bindrop_source_point_choose_decoded_value. bcf_height_mkm_bindrop_source_point_choose_decoded_value + S (mkm_factor_bindrop_source_point) = S ((S (mkm_partial_bindrop_source_point)) * bcf_row_scale_mkm_bindrop_source_point_choose)) /\ exists bcf_quotient_mkm_bindrop_source_point_choose_decoded_value. bcf_row_code_mkm_bindrop_source_point_choose = bcf_quotient_mkm_bindrop_source_point_choose_decoded_value * S ((S (mkm_partial_bindrop_source_point)) * bcf_row_scale_mkm_bindrop_source_point_choose) + (mkm_factor_bindrop_source_point))))))))) /\ (((exists fs_h_mkm_bindrop_source_point_factor. fs_h_mkm_bindrop_source_point_factor + S (mkm_factor_bindrop_source_point) = S ((S (mkm_index_bindrop_source)) * cc)) /\ exists fs_q_mkm_bindrop_source_point_factor. cb = fs_q_mkm_bindrop_source_point_factor * S ((S (mkm_index_bindrop_source)) * cc) + (mkm_factor_bindrop_source_point))))))) -> (forall mkm_index_bindrop_target. (exists mkm_lt_bindrop_target_bound. mkm_lt_bindrop_target_bound + S (mkm_index_bindrop_target) = (l)) -> (exists mkm_value_bindrop_target_point mkm_partial_bindrop_target_point mkm_factor_bindrop_target_point. (((exists fs_h_mkm_bindrop_target_point_source. fs_h_mkm_bindrop_target_point_source + S (mkm_value_bindrop_target_point) = S ((S (mkm_index_bindrop_target)) * c)) /\ exists fs_q_mkm_bindrop_target_point_source. b = fs_q_mkm_bindrop_target_point_source * S ((S (mkm_index_bindrop_target)) * c) + (mkm_value_bindrop_target_point))) /\ ((((exists fs_h_mkm_bindrop_target_point_partial. fs_h_mkm_bindrop_target_point_partial + S (mkm_partial_bindrop_target_point) = S ((S (mkm_index_bindrop_target)) * sc)) /\ exists fs_q_mkm_bindrop_target_point_partial. sb = fs_q_mkm_bindrop_target_point_partial * S ((S (mkm_index_bindrop_target)) * sc) + (mkm_partial_bindrop_target_point))) /\ ((((exists bcf_lt_gap_mkm_bindrop_target_point_choose_out_of_range. bcf_lt_gap_mkm_bindrop_target_point_choose_out_of_range + S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point) = mkm_partial_bindrop_target_point) /\ mkm_factor_bindrop_target_point = 0) \/ ((exists bcf_le_gap_mkm_bindrop_target_point_choose_in_range. bcf_le_gap_mkm_bindrop_target_point_choose_in_range + (mkm_partial_bindrop_target_point) = mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point) /\ (exists bcf_row_code_code_mkm_bindrop_target_point_choose bcf_row_code_scale_mkm_bindrop_target_point_choose bcf_row_scale_code_mkm_bindrop_target_point_choose bcf_row_scale_scale_mkm_bindrop_target_point_choose bcf_row_code_mkm_bindrop_target_point_choose bcf_row_scale_mkm_bindrop_target_point_choose. ((forall bcf_row_index_mkm_bindrop_target_point_choose_table. (exists bcf_lt_gap_mkm_bindrop_target_point_choose_table_row_bound. bcf_lt_gap_mkm_bindrop_target_point_choose_table_row_bound + S (bcf_row_index_mkm_bindrop_target_point_choose_table) = S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) -> exists bcf_row_code_mkm_bindrop_target_point_choose_table bcf_row_scale_mkm_bindrop_target_point_choose_table. ((((exists bcf_height_mkm_bindrop_target_point_choose_table_decoded_row_code. bcf_height_mkm_bindrop_target_point_choose_table_decoded_row_code + S (bcf_row_code_mkm_bindrop_target_point_choose_table) = S ((S (bcf_row_index_mkm_bindrop_target_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_row_code. bcf_row_code_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_row_code * S ((S (bcf_row_index_mkm_bindrop_target_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_target_point_choose) + (bcf_row_code_mkm_bindrop_target_point_choose_table))) /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_table_decoded_row_scale. bcf_height_mkm_bindrop_target_point_choose_table_decoded_row_scale + S (bcf_row_scale_mkm_bindrop_target_point_choose_table) = S ((S (bcf_row_index_mkm_bindrop_target_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_row_scale. bcf_row_scale_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_row_scale * S ((S (bcf_row_index_mkm_bindrop_target_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_target_point_choose) + (bcf_row_scale_mkm_bindrop_target_point_choose_table))) /\ ((bcf_row_index_mkm_bindrop_target_point_choose_table = 0 /\ (forall bcf_index_mkm_bindrop_target_point_choose_table_zero_row. (exists bcf_lt_gap_mkm_bindrop_target_point_choose_table_zero_row_bound. bcf_lt_gap_mkm_bindrop_target_point_choose_table_zero_row_bound + S (bcf_index_mkm_bindrop_target_point_choose_table_zero_row) = S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) -> exists bcf_value_mkm_bindrop_target_point_choose_table_zero_row. ((((exists bcf_height_mkm_bindrop_target_point_choose_table_zero_row_entry. bcf_height_mkm_bindrop_target_point_choose_table_zero_row_entry + S (bcf_value_mkm_bindrop_target_point_choose_table_zero_row) = S ((S (bcf_index_mkm_bindrop_target_point_choose_table_zero_row)) * bcf_row_scale_mkm_bindrop_target_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_zero_row_entry. bcf_row_code_mkm_bindrop_target_point_choose_table = bcf_quotient_mkm_bindrop_target_point_choose_table_zero_row_entry * S ((S (bcf_index_mkm_bindrop_target_point_choose_table_zero_row)) * bcf_row_scale_mkm_bindrop_target_point_choose_table) + (bcf_value_mkm_bindrop_target_point_choose_table_zero_row))) /\ ((bcf_index_mkm_bindrop_target_point_choose_table_zero_row = 0 /\ bcf_value_mkm_bindrop_target_point_choose_table_zero_row = 1) \/ exists bcf_predecessor_mkm_bindrop_target_point_choose_table_zero_row. bcf_index_mkm_bindrop_target_point_choose_table_zero_row = S bcf_predecessor_mkm_bindrop_target_point_choose_table_zero_row /\ bcf_value_mkm_bindrop_target_point_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_mkm_bindrop_target_point_choose_table bcf_previous_code_mkm_bindrop_target_point_choose_table bcf_previous_scale_mkm_bindrop_target_point_choose_table. bcf_row_index_mkm_bindrop_target_point_choose_table = S bcf_predecessor_mkm_bindrop_target_point_choose_table /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_table_decoded_previous_code. bcf_height_mkm_bindrop_target_point_choose_table_decoded_previous_code + S (bcf_previous_code_mkm_bindrop_target_point_choose_table) = S ((S (bcf_predecessor_mkm_bindrop_target_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_previous_code. bcf_row_code_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_previous_code * S ((S (bcf_predecessor_mkm_bindrop_target_point_choose_table)) * bcf_row_code_scale_mkm_bindrop_target_point_choose) + (bcf_previous_code_mkm_bindrop_target_point_choose_table))) /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_table_decoded_previous_scale. bcf_height_mkm_bindrop_target_point_choose_table_decoded_previous_scale + S (bcf_previous_scale_mkm_bindrop_target_point_choose_table) = S ((S (bcf_predecessor_mkm_bindrop_target_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_previous_scale. bcf_row_scale_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_mkm_bindrop_target_point_choose_table)) * bcf_row_scale_scale_mkm_bindrop_target_point_choose) + (bcf_previous_scale_mkm_bindrop_target_point_choose_table))) /\ (forall bcf_index_mkm_bindrop_target_point_choose_table_row_step. (exists bcf_lt_gap_mkm_bindrop_target_point_choose_table_row_step_bound. bcf_lt_gap_mkm_bindrop_target_point_choose_table_row_step_bound + S (bcf_index_mkm_bindrop_target_point_choose_table_row_step) = S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) -> exists bcf_value_mkm_bindrop_target_point_choose_table_row_step. ((((exists bcf_height_mkm_bindrop_target_point_choose_table_row_step_entry. bcf_height_mkm_bindrop_target_point_choose_table_row_step_entry + S (bcf_value_mkm_bindrop_target_point_choose_table_row_step) = S ((S (bcf_index_mkm_bindrop_target_point_choose_table_row_step)) * bcf_row_scale_mkm_bindrop_target_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_row_step_entry. bcf_row_code_mkm_bindrop_target_point_choose_table = bcf_quotient_mkm_bindrop_target_point_choose_table_row_step_entry * S ((S (bcf_index_mkm_bindrop_target_point_choose_table_row_step)) * bcf_row_scale_mkm_bindrop_target_point_choose_table) + (bcf_value_mkm_bindrop_target_point_choose_table_row_step))) /\ ((bcf_index_mkm_bindrop_target_point_choose_table_row_step = 0 /\ bcf_value_mkm_bindrop_target_point_choose_table_row_step = 1) \/ exists bcf_predecessor_mkm_bindrop_target_point_choose_table_row_step bcf_left_mkm_bindrop_target_point_choose_table_row_step bcf_right_mkm_bindrop_target_point_choose_table_row_step. bcf_index_mkm_bindrop_target_point_choose_table_row_step = S bcf_predecessor_mkm_bindrop_target_point_choose_table_row_step /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_table_row_step_previous_left. bcf_height_mkm_bindrop_target_point_choose_table_row_step_previous_left + S (bcf_left_mkm_bindrop_target_point_choose_table_row_step) = S ((S (bcf_predecessor_mkm_bindrop_target_point_choose_table_row_step)) * bcf_previous_scale_mkm_bindrop_target_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_row_step_previous_left. bcf_previous_code_mkm_bindrop_target_point_choose_table = bcf_quotient_mkm_bindrop_target_point_choose_table_row_step_previous_left * S ((S (bcf_predecessor_mkm_bindrop_target_point_choose_table_row_step)) * bcf_previous_scale_mkm_bindrop_target_point_choose_table) + (bcf_left_mkm_bindrop_target_point_choose_table_row_step))) /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_table_row_step_previous_right. bcf_height_mkm_bindrop_target_point_choose_table_row_step_previous_right + S (bcf_right_mkm_bindrop_target_point_choose_table_row_step) = S ((S (S (bcf_predecessor_mkm_bindrop_target_point_choose_table_row_step))) * bcf_previous_scale_mkm_bindrop_target_point_choose_table)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_table_row_step_previous_right. bcf_previous_code_mkm_bindrop_target_point_choose_table = bcf_quotient_mkm_bindrop_target_point_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_mkm_bindrop_target_point_choose_table_row_step))) * bcf_previous_scale_mkm_bindrop_target_point_choose_table) + (bcf_right_mkm_bindrop_target_point_choose_table_row_step))) /\ bcf_value_mkm_bindrop_target_point_choose_table_row_step = bcf_left_mkm_bindrop_target_point_choose_table_row_step + bcf_right_mkm_bindrop_target_point_choose_table_row_step))))))))))) /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_decoded_row_code. bcf_height_mkm_bindrop_target_point_choose_decoded_row_code + S (bcf_row_code_mkm_bindrop_target_point_choose) = S ((S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) * bcf_row_code_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_decoded_row_code. bcf_row_code_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_decoded_row_code * S ((S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) * bcf_row_code_scale_mkm_bindrop_target_point_choose) + (bcf_row_code_mkm_bindrop_target_point_choose))) /\ ((((exists bcf_height_mkm_bindrop_target_point_choose_decoded_row_scale. bcf_height_mkm_bindrop_target_point_choose_decoded_row_scale + S (bcf_row_scale_mkm_bindrop_target_point_choose) = S ((S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) * bcf_row_scale_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_decoded_row_scale. bcf_row_scale_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_decoded_row_scale * S ((S (mkm_partial_bindrop_target_point + mkm_value_bindrop_target_point)) * bcf_row_scale_scale_mkm_bindrop_target_point_choose) + (bcf_row_scale_mkm_bindrop_target_point_choose))) /\ (((exists bcf_height_mkm_bindrop_target_point_choose_decoded_value. bcf_height_mkm_bindrop_target_point_choose_decoded_value + S (mkm_factor_bindrop_target_point) = S ((S (mkm_partial_bindrop_target_point)) * bcf_row_scale_mkm_bindrop_target_point_choose)) /\ exists bcf_quotient_mkm_bindrop_target_point_choose_decoded_value. bcf_row_code_mkm_bindrop_target_point_choose = bcf_quotient_mkm_bindrop_target_point_choose_decoded_value * S ((S (mkm_partial_bindrop_target_point)) * bcf_row_scale_mkm_bindrop_target_point_choose) + (mkm_factor_bindrop_target_point))))))))) /\ (((exists fs_h_mkm_bindrop_target_point_factor. fs_h_mkm_bindrop_target_point_factor + S (mkm_factor_bindrop_target_point) = S ((S (mkm_index_bindrop_target)) * cc)) /\ exists fs_q_mkm_bindrop_target_point_factor. cb = fs_q_mkm_bindrop_target_point_factor * S ((S (mkm_index_bindrop_target)) * cc) + (mkm_factor_bindrop_target_point)))))))Constructive proof overview
Generated structural guide
A complete binomial factor table restricts to the predecessor prefix.
The unchanged tactic script uses 1 declared prerequisite and contains 16 exact native proof lines.
Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
le_succ Stable theorem; checked-use authorizedDirect dependents
none
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.