proposition: Lemma full_pseudo_order_preserving `{!StrictlyOrderReflecting (f : A -> B)} : OrderPreserving f.
proof: Proof. intros x y E1. apply le_iff_not_lt_flip;apply le_iff_not_lt_flip in E1. intros E2. apply E1. apply (strictly_order_reflecting f). trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.orders HoTT.Classes.theory.apartness