Empty proof means that if P is proved to be Q, if P can be proved to be false, the whole proof can be ended.

Trivial proof means that if you can prove that Q is correct, you can end the whole proof.

Empty evidence means that if the antecedent is wrong, it is meaningless to deduce the latter from the antecedent.

Ordinary proof means that if the latter is always true, there is no need for the former as a hypothesis.