simple induction 1; auto with arith pts.
intros.
inversion_clear H0.
simple destruct v; simpl in |- *; intros.
replace (n0 - 0) with n0; auto with arith pts.
inversion_clear H3; auto with arith pts.
inversion_clear H3; auto with arith pts.
Qed.

(* Specifications: *)
Lemma ins_item_lift_lt :
forall (d' : decl) (n : nat) (g e f : env),
ins_in_env g d' n e f ->
forall v : nat,
n > v ->
forall t : term, item_lift t e v -> item_lift (lift_rec 1 t n) f v.