intros n H; absurd (n < 0); auto with arith.
intros n H' n0; case n0; simpl in |- *; auto with arith.
Qed.

Theorem div_clean_dec2 :
forall (d : nat) (a b : mon d),
gb d (div_mon_clean d a b) = false -> mult_mon d (div_mon d a b) b <> a.