intros l t1 t2 H H0; apply cover_in_inb_inb with (1 := H) (2 := H0); auto.
Qed.
Let cover_inv_leaf_aux :
forall t l, cover l t -> forall a : A, t = leaf a -> l = leaf a :: nil.
Proof using.
intros t l H; elim H; simpl in |- *; auto.
intros t0 a H0; apply f_equal2 with (f := cons (A:=btree A)); auto.
intros.
generalize (H2 a H3); intros; discriminate.
Qed.

(* Specifications: *)
(* Covers of a leaf are singleton lists *)
Theorem cover_inv_leaf :
forall (a : A) l, cover l (leaf a) -> l = leaf a :: nil.