Hint Rewrite @subst_lift0 (*@subst_lift0'*) @subst_lift0C : subst.

(* Specifications: *)
Lemma subst_lift1:
forall {A1 B} id v (f: A1 -> B) a,
subst id v (lift1 f a) = lift1 f (subst id v a).
Lemma subst_lift1':
forall {A1 B} id v (f: A1 -> B) a,
subst id v (fun rho => f (a rho)) = fun rho => f (subst id v a rho).
Lemma subst_lift1C:
forall {A1 B} id (v: environ -> val) (f: A1 -> B) (a: environ -> A1),
subst id v (`f a)  = `f (subst id v a).