Proof using.
intros t1 t2 l1 l2 H; elim H; auto.
Qed.

(* Specifications: *)
(* The second cover of the substitution is an ordered cover *)
Theorem subst_pred_ordered_cover_r :
forall (t1 t2 : btree A) (l1 l2 : list (btree A)),
subst_pred l1 l2 t1 t2 -> ordered_cover l2 t2.
(* The two covers have same length *)
Theorem subst_pred_length :
forall (t1 t2 : btree A) (l1 l2 : list (btree A)),
subst_pred l1 l2 t1 t2 -> length l1 = length l2.