proposition: Theorem add_sub_le1 : forall a b c : Qpositive, a <> b -> Qpositive_le b a -> Qpositive_le (Qpositive_sub a b) c -> Qpositive_le a (Qpositive_plus b c).
proof: Proof. 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.