elim (le_or_lt z y).
intros H;
generalize ((fun m n p : nat => mult_le_compat_l p n m) (S x) _ _ H).
intros H1 H2; elim (le_not_gt _ _ H1); auto.
auto.
Qed.

Theorem Qpositive_sub_correct :
forall w w' : Qpositive, Qpositive_sub (Qpositive_plus w w') w' = w.