proposition: Lemma full_pseudo_order_reflecting `{!StrictlyOrderPreserving (f : A -> B)} : OrderReflecting 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_preserving f). trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.orders HoTT.Classes.theory.apartness