intros w w' H H0.
pattern w at 1 in |- *; rewrite <- (Qpositive_sub_correct w w').
red in |- *; intros H1.
elim (Qpositive_plus_diff w w').
symmetry  in |- *.
apply Qpositive_sub_simpl_r with w'; auto.
apply sym_not_equal; rewrite Qpositive_plus_sym; apply Qpositive_plus_diff.
rewrite Qpositive_plus_sym; apply Qpositive_plus_le.
Qed.

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