intros a b c H H0 H1.
rewrite <- (Qpositive_sub_correct2 a b); auto.
rewrite (Qpositive_plus_sym b).
apply Qpositive_le_add.
auto.
Qed.

(* Specifications: *)
Theorem add_sub_le2 :
forall a b c : Qpositive,
a <> b ->
Qpositive_le b a ->
Qpositive_le a (Qpositive_plus b c) -> Qpositive_le (Qpositive_sub a b) c.