intuition.
eapply constant_cost_le.
eapply (constant_cost_compose f1 (fun _ x => f3 x c)).
eauto.
eapply constant_cost_const.
intuition.
eauto.
omega.
Qed.

(* Specifications: *)
Theorem constant_cost_compose_binary_const_l :
forall (A B C D: Type)
(b : B)(f2 : A -> C)(f3 : B -> C -> D) c1 c2,
cost f2 c1 ->
cost (f3 b) c2 ->
cost (fun a => f3 b (f2 a)) (c1 + c2).