intros w w' H H1; pattern w at 2 in |- *;
rewrite <- (Qpositive_sub_correct w w').
apply Qpositive_le_sub_r; auto.
apply sym_not_equal; rewrite Qpositive_plus_sym; apply Qpositive_plus_diff.
rewrite Qpositive_plus_sym; apply Qpositive_plus_le.
apply Qpositive_plus_le.
Qed.

(* Specifications: *)
Theorem Qpositive_sub_simpl_r :
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'.