Notation Factorizable := (factorizable _) (only parsing).Notation Proper := (proper _) (only parsing).

Theorem factorization_for_realizer : factorizable _ R -> proper _ BASE R -> forall (n : nat) (a : A) (X Y : Num n), {a' : A | R (exp b n) a (Val_bound n X) (Val_bound n Y) a'}.