proposition: Lemma preserves_lt_1 `{!StrictlyOrderPreserving f} x : x < 1 -> f x < 1.
proof: Proof. intros. rewrite <-(preserves_1 (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