proposition: Lemma preserves_neg `{!StrictlyOrderPreserving f} x : x < 0 -> f x < 0.
proof: Proof. intros. rewrite <-(preserves_0 (f:=f)). apply (strictly_order_preserving f);trivial. Qed.
imports: HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.orders HoTT.Classes.orders.maps