intros a b c H; rewrite H; rewrite Qpositive_plus_sym;
rewrite Qpositive_sub_correct; auto.
Qed.

Theorem add_sub_eq2 :
forall a b c : Qpositive,
a <> b ->
Qpositive_le b a -> c = Qpositive_sub a b -> Qpositive_plus b c = a.