Applying hypotesis to a variable

Question

Let's say I'm in the middle of a proof and I have hypotheses like these:

a : nat
b : nat
c : nat
H : somePred a b

and the definition of somePred says:

Definition somePred (p:nat) (q:nat) : Prop := forall (x : nat), P(x, p, q).

How do I apply H to c and to get P(c, a, b)?

How would you get a variable `H : somePred a b`? Shouldn't it be `H : Prop`? — Aadit M Shah, Mar 28 '15 at 10:43
@AaditMShah , I'm trying to prove something like forall (a:nat) (b:nat) (c:nat), (somePred a b) -> ..., so I used intros a b c H. — poe123, Mar 28 '15 at 10:45
won't you get ``P(c, b, c)`` instead of ``P(c, a, b)`` ? The ``p`` in ``somePred``'s definition doesn't to be used at all. — Vinz, Mar 30 '15 at 07:50

score 1 · Accepted Answer · answered Mar 28 '15 at 14:37

1

The answer is:

specialize H with c.

answered Mar 28 '15 at 14:37

poe123

You might need to ``unfold somePred in H.`` before specializing. Alternatively, if you need to keep ``H`` as it is, you can assert a new statement, with ``assert (foo := H c).`` or ``assert (foo: P(c, a, b)) by apply H.`` . – Vinz Mar 30 '15 at 08:49

1 Answers1