simple destruct 1; try constructor; intros.
apply typ_free_db with (1 := H0).
Qed.
Hint Resolve wft_free_db: pts.

(* Specifications: *)
(* Thinning lemma *)
Theorem typ_weak :
forall (g : env) (d : decl) (e : env) (t T : term),
typ e t T ->
forall (n : nat) (f : env),
ins_in_env g d n e f -> wf f -> typ f (lift_rec 1 t n) (lift_rec 1 T n).
(* Thinning lemma *)
Theorem typ_weak :
forall (g : env) (d : decl) (e : env) (t T : term),
typ e t T ->
forall (n : nat) (f : env),
ins_in_env g d n e f -> wf f -> typ f (lift_rec 1 t n) (lift_rec 1 T n).