I wrote:

On Tuesday 21 December 2010 19:34:11, Felipe Almeida Lessa wrote:

...

Theorem mirror_mirror : forall A (x : Tree A), mirror (mirror x) = x. induction x; simpl; auto. rewrite IHx1; rewrite IHx2; trivial. Qed.

Since mirror (mirror x) = x doesn't hold in Haskell, I take it that Coq doesn't allow infinite structures?

Oops, mirroring infinite binary trees should work. Ignore above.