intros t; split; auto.
intros t2 H; inversion H; auto.
generalize (permutation_length _ _ _ H0); simpl in |- *; intros; discriminate.
Qed.
Hint Resolve cover_min_one : core.

(* Minimum trees are preserved by permutation *)
Theorem cover_min_permutation :
forall (t : btree A) (l1 l2 : list (btree A)),
cover_min l1 t -> permutation l1 l2 -> cover_min l2 t.