proposition: Theorem Qpositive_le_sub_simpl_r : forall x y z : Qpositive, Qpositive_le z x -> Qpositive_le z y -> z <> x -> z <> y -> Qpositive_le (Qpositive_sub x z) (Qpositive_sub y z) -> Qpositive_le x y.
proof: Proof. 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.