Proof using.
intros t1 t2 l H; apply cover_inv_app_aux with (t := node t1 t2); auto.
Qed.

(* Covers of the direct subtrees generate a cover of the whole tree *)
Theorem cover_app :
forall t1 t2 l1 l2,
cover l1 t1 -> cover l2 t2 -> cover (l1 ++ l2) (node t1 t2).