intros w w' w'' H H0 H1 H2 H3.
rewrite <- (Qpositive_sub_correct2 w w''); auto with *.
rewrite <- (Qpositive_sub_correct2 w' w''); auto with *.
rewrite H3; auto.
Qed.

Theorem Qpositive_sub_simpl_l :
forall w w' w'' : Qpositive,
w <> w'' :>Qpositive ->
w' <> w'' :>Qpositive ->
Qpositive_le w w'' ->
Qpositive_le w' w'' -> Qpositive_sub w'' w = Qpositive_sub w'' w' -> w = w'.