intros w w' w'' H H0 H1 H2.
apply Qpositive_plus_simpl with w'.
rewrite Qpositive_sub_correct2; auto.
apply Qpositive_plus_simpl with (Qpositive_sub w' w'').
rewrite <- (Qpositive_plus_sym w').
rewrite Qpositive_plus_assoc.
rewrite Qpositive_sub_correct2; auto.
rewrite Qpositive_plus_assoc.
rewrite (Qpositive_plus_sym w'').
rewrite Qpositive_sub_correct2; auto.
apply Qpositive_plus_sym.
red in |- *; intros H3; try exact H3.
elim H1; try assumption.
rewrite <- H3; rewrite Qpositive_sub_correct; auto.
rewrite <- (Qpositive_sub_correct2 w' w''); auto with *.
apply Qpositive_le_add.
auto.
Qed.

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