do 5 intro.
cut (forall x : term, le_type e x U -> le_type e x V).
case t; simpl in |- *; intros.
apply H1 with s2; auto with arith pts.
apply H1 with x; auto with arith pts.
apply H1 with s U0; auto with arith pts.
apply H1 with Ur V0; auto with arith pts.
apply H1 with s1 s2 s3; auto with arith pts.
intros.
apply le_type_trans with U; auto with arith pts.
Qed.

Theorem inversion_lemma :
forall (e : env) (t T : term) (P : Prop),
inv_typ e t T P -> typ e t T -> P.