simple induction 1; intros.
apply wft_typed with s.
change (typ e (subst v T0) (subst v (Srt s))) in |- *.
apply substitution with V; auto with arith pts.
unfold subst in |- *.
simpl in |- *; auto with arith pts.
Qed.

(* Specifications: *)
Theorem type_correctness :
forall (e : env) (t T : term), typ e t T -> wf_type e T.
Theorem type_correctness :
forall (e : env) (t T : term), typ e t T -> wf_type e T.