proposition: Lemma distr_lift_subst : forall M N n k, lift_rec n (subst N M) k = subst (lift_rec n N k) (lift_rec n M (S k)).
proof: Proof. intros; unfold subst in |- *. pattern k at 1 3 in |- *. replace k with (0 + k); auto with coc core arith sets. apply distr_lift_subst_rec. Qed.
imports: Arith Compare_dec Relations