如果一个主键有auto_increment，删除该主键之前为什么需要先去掉auto_increment

mysql> SHOW COLUMNS FROM tb;
+----------+----------------------+------+-----+---------+----------------+
| Field    | Type                 | Null | Key | Default | Extra          |
+----------+----------------------+------+-----+---------+----------------+
| id       | smallint(6)          | NO   | PRI | NULL    | auto_increment |
| username | varchar(20)          | NO   | UNI | NULL    |                |
| age      | smallint(6)          | NO   |     | NULL    |                |
| score    | smallint(5) unsigned | YES  |     | 0       |                |
+----------+----------------------+------+-----+---------+----------------+
4 rows in set (0.00 sec)

mysql> ALTER TABLE tb DROP PRIMARY KEY;
ERROR 1075 (42000): Incorrect table definition; there can be only one auto column and it must be defined as a key
mysql> ALTER TABLE tb MODIFY id SMALLINT NOT NULL;
Query OK, 0 rows affected (0.01 sec)
Records: 0  Duplicates: 0  Warnings: 0

mysql> SHOW COLUMNS FROM tb;
+----------+----------------------+------+-----+---------+-------+
| Field    | Type                 | Null | Key | Default | Extra |
+----------+----------------------+------+-----+---------+-------+
| id       | smallint(6)          | NO   | PRI | NULL    |       |
| username | varchar(20)          | NO   | UNI | NULL    |       |
| age      | smallint(6)          | NO   |     | NULL    |       |
| score    | smallint(5) unsigned | YES  |     | 0       |       |
+----------+----------------------+------+-----+---------+-------+
4 rows in set (0.00 sec)

mysql> ALTER TABLE tb DROP PRIMARY KEY;
Query OK, 0 rows affected (0.01 sec)
Records: 0  Duplicates: 0  Warnings: 0

mysql> SHOW COLUMNS FROM tb;
+----------+----------------------+------+-----+---------+-------+
| Field    | Type                 | Null | Key | Default | Extra |
+----------+----------------------+------+-----+---------+-------+
| id       | smallint(6)          | NO   |     | NULL    |       |
| username | varchar(20)          | NO   | PRI | NULL    |       |
| age      | smallint(6)          | NO   |     | NULL    |       |
| score    | smallint(5) unsigned | YES  |     | 0       |       |
+----------+----------------------+------+-----+---------+-------+
4 rows in set (0.00 sec)

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好像是这样的，自增字段必须是主键。删除主键但对应字段是自增的话，抛错。