unfold lift in |- *.
intros.
apply typ_weak with e d e; auto with arith pts.
Qed.

(* Specifications: *)
Theorem thinning_n :
forall (n : nat) (e f : env),
trunc n e f ->
forall t T : term, typ f t T -> wf e -> typ e (lift n t) (lift n T).
Theorem thinning_n :
forall (n : nat) (e f : env),
trunc n e f ->
forall t T : term, typ f t T -> wf e -> typ e (lift n t) (lift n T).