proposition: Lemma lift_type_by_app : forall {a} t {b c} (p : scope_le b c) (q : scope_le a b), lift_type_by p (lift_type_by q t) = lift_type_by (scope_le_app q p) t.
proof: Proof. depind t; intros b c p; depind p; intros q; repeat (autorewrite with scope_le_app lift_var_by lift_type_by; rewrite ?IHt1, ?IHt2; auto). Qed.
imports: Program Equations(Equations) Coq.Classes.EquivDec Arith