Combining two Coq hypotheses
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?
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.
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