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.
intros n x y X Y l.
apply comparisonL.
unfold ValB in |- *.
unfold Cons in |- *.
unfold Digit in |- *.
apply comp_dif.
auto.
Qed.
Hint Resolve Comp_dif.

Lemma Comp_eq :
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)) =
Compare_Nat.comparison (ValB n X) (ValB n Y).