Definition procedure_family(A : nat -> Type) := forall n, A n.Definition efficiency_predicate := forall (A : nat -> Type), procedure_family A -> Prop.

Theorem expected_poly_time_compose_0_binary : forall (A B C : nat -> Type)(f1 : forall n, A n)(f2 : forall n, B n)(f3 : forall n, A n -> B n -> C n) , efficient _ f1 -> efficient _ f2 -> efficient _ f3 -> efficient _ (fun n => f3 n (f1 n) (f2 n)).