intros w w' w'' H H0 H1 H2 H3.
apply Qpositive_plus_simpl with (Qpositive_sub w'' w).
rewrite (Qpositive_plus_sym w).
rewrite Qpositive_sub_correct2; auto.
rewrite (Qpositive_plus_sym w').
rewrite H3.
rewrite Qpositive_sub_correct2; auto with *.
Qed.

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