Parameter BASE : BT.Definition b := base BASE.Definition Digit := digit BASE.Definition Num := num BASE.Definition Val_bound := val_bound BASE.Definition Value := Val BASE.Definition Connection := connection order (inf b) (inf b) (R b).

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).