CODEWITHSUNDEEP
coq
André Hincu
André Hincu

Reputation: 427

using an already proved lema/theorem/corollary in coq

I am trying to make a proof in Coq, and I would like to use a lemma already definded and proved by me. Is it possible for the following code?

Lemma conj_comm:
forall A B : Prop, A /\ B -> B /\ A.
Proof.
intros.
destruct H.
split.
exact H0.
exact H.
Qed.


Lemma not_conj_comm:
forall A B : Prop, ~(A /\ B) -> ~(B /\ A).
Proof.
intros.
intro.
unfold not in H.
apply H.
use H0.

In the above I want to use the fact that A /\B is the same as B /\ A in order to prove that ~(A /\ B) is the same as ~(B /\ A). Is it possible to use my proved lemma?

Upvotes: 2

Views: 417

Answers (1)

jspcal
jspcal

Reputation: 51894

you can use apply<lemma>.

there's an example here

http://blog.mikael.johanssons.org/archive/2007/08/coq-and-simple-group-theory/

see the line that says apply unit_uniq

Upvotes: 3

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