intros n X Y o o' C.
unfold b in |- *.
apply factorization_for_verification with (A := order) (BASE := BASE).
exact is_factorizable.
exact (is_proper BASE).
try trivial.
Qed.

Theorem correctness :
forall (n : nat) (X Y : Num n) (o : order),
Connection n E X Y o -> o = Compare_Nat.comparison (Value n X) (Value n Y).