(* If [v] is [k]-closed and [t] is [k+1]-closed, then [subst v 0 t] is [k]-closed. *)

Lemma subst_preserves_closed:
forall `{Lift V, Lift T, Subst V T},
@LiftSubst2 V _ T _ _ ->
forall k (v : V) (t : T),
closed k v ->
closed (S k) t ->
closed k (subst v 0 t).