proposition: Lemma preserves_nonpos `{!OrderPreserving f} x : x ≤ 0 -> f x ≤ 0.
proof: Proof. intros. rewrite <-(preserves_0 (f:=f)). apply (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