intros w w' w'' H.
rewrite <- (Qpositive_sub_correct w' w'').
rewrite <- (Qpositive_sub_correct w w'').
rewrite H.
auto.
Qed.

Theorem Qpositive_sub_correct2 :
forall w w' : Qpositive,
w <> w' -> Qpositive_le w' w -> Qpositive_plus (Qpositive_sub w w') w' = w.