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