If the teacher gives you a theorem directly, you must prove it. If other problems need to use a theorem, you can directly use the existing theorem.

But we should also pay attention to the order of learning, and some should not be used indiscriminately. For example, if you want to prove Lagrange's mean value theorem, you should use Rolle's theorem instead of Cauchy's mean value theorem, because Cauchy's mean value theorem was learned after Lagrange's theorem.

For example, in our previous exam, if the process of proving a problem is long, even the exercises we have done before can be directly used in the process of proving. Sometimes the key depends on whether the thing you use directly is too simple. If it is too simple, I'm afraid it won't work.