intros x y z H H0 H1 H2 H3.
rewrite <- (Qpositive_sub_correct2 x z); auto.
rewrite <- (Qpositive_sub_correct2 y z); auto.
apply Qpositive_le_add.
auto.
Qed.

Theorem Qpositive_le_sub_simpl_l :
forall x y z : Qpositive,
Qpositive_le x z ->
Qpositive_le y z ->
z <> x ->
z <> y ->
Qpositive_le (Qpositive_sub z x) (Qpositive_sub z y) -> Qpositive_le y x.