Section ListDenoteLems.
Context {A T : Type}.
Variables (f : A -> T) (g : T -> T -> T) (b : T).
Proof with auto.
induction l; simpl... rewrite IHl, listd_app; apply H.
Qed.

Lemma listd_compose h1 h2 l
(Hh1 : forall l, listd f g b l = listd f g b (h1 l))
(Hh2 : forall l, listd f g b l = listd f g b (h2 l)) :
listd f g b l = listd f g b ((h1 oo h2) l).