Combining two Coq hypotheses

问题

So I have two hypotheses, one that is h : A -> B, and the other which is h2 : A. How can I get h3 : B to appear in my hypotheses?

回答1:

pose proof (h h2) as h3.

introduces h3 : B as a new hypothesis,

specialize (h h2).

modifies h : A -> B into h : B -- this can be useful if you won't need h later, and symmetrically,

apply h in h2.

converts h2 : A into h2 : B.

Another (not very convenient) way would be to

assert B as h3 by exact (h h2).

That's what the pose proof variant is equivalent to.

Also, in a simple case like the following, you can solve your goal without introducing a new hypothesis:

Goal forall (A B : Prop), (A -> B) -> A -> B.
  intros A B h h2.
  apply (h h2).
Qed.

来源：https://stackoverflow.com/questions/40448703/combining-two-coq-hypotheses