Proof using.
intros t1 t2 l1 l2 H; elim H; auto.
intros t0 t3 t4 t5 l0 l3 l4 l5 l6 l7 H0 H1 H2 H3; repeat rewrite length_app; auto.
Qed.

(* Specifications: *)
(* An ordered cover can  be completed in a substitution *)
Theorem ordered_cover_subst_pred :
forall (t1 : btree A) (l1 l2 : list (btree A)),
ordered_cover l1 t1 ->
length l1 = length l2 -> exists t2 : btree A, subst_pred l1 l2 t1 t2.