intuition.
eapply (@expected_poly_time_compose_simp _ _ _ _ (fun n a => fst a)); eauto.
eapply expected_poly_time_fst.
Qed.

(* Specifications: *)
Theorem expected_poly_time_snd_f :
forall (A B C : nat -> Type)(f : forall n, A n -> (B n * C n)),
efficient _ f ->
efficient _ (fun n (a : A n) => snd (f n a)).