proposition: 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.
proof: Proof. 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.