intros.
inversion_clear H1.
inversion_clear H3.
apply type_prod with x x0; trivial with arith pts.
apply type_conv_srt with (Srt s1); auto with arith pts.
apply type_conv_srt with (Srt s2); auto with arith pts.
Qed.

Theorem typ_wf : forall (e : env) (t T : term), typ e t T -> wf e.
simple induction 1; auto with arith pts.