Definition Connection := connection A Digit Digit (R b).Notation Factorizable := (factorizable _) (only parsing).Notation Proper := (proper _) (only parsing).

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