intros a b c H H1 H2; rewrite <- (Qpositive_sub_correct c b).
apply Qpositive_le_sub_r; auto with *.
rewrite Qpositive_plus_sym; apply sym_not_equal; apply Qpositive_plus_diff.
rewrite Qpositive_plus_sym; apply Qpositive_plus_le.
rewrite Qpositive_plus_sym; auto.
Qed.

Theorem add_sub_eq1 :
forall a b c : Qpositive, a = Qpositive_plus b c -> Qpositive_sub a b = c.