Sound sleep presupposes a mind at ease.

充足睡心情轻松为先决条件。

It is a prerequisite of entry to the profession that you pass the exams.

做这一行的先决条件是要通过了有关的考试。

Success presupposes diligence.

勤勉是功的先决条件。

No preconditions should be imposed.

不应有[强加]先决条件。