Section compare_num.
Variable BASE : BT.
Let Digit := digit BASE.
Let valB := val BASE.
Let ValB := Val BASE.
Let Num := num BASE.
Let Val_bound := val_bound BASE.
Let Cons := cons Digit.
Let Nil := nil Digit.

Lemma Comp_dif :
forall (n : nat) (x y : Digit) (X Y : Num n),
valB x < valB y ->
Compare_Nat.comparison (ValB (S n) (Cons n x X)) (ValB (S n) (Cons n y Y)) =
L.