simple induction 1; auto with arith pts.
intros.
inversion H1.
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.

Lemma nth_sub_item_inf :
forall (t : term) (d1 : decl) (n : nat) (g e f : env),
sub_in_env g d1 t n e f ->
forall v : nat,
n > v ->
forall u : term, item_lift u e v -> item_lift (subst_rec t u n) f v.