Lemma ispartialorder_pointwiseorder {X:UU} (P : X -> Poset) : isPartialOrder (pointwiseorder P). Proof. repeat split. - repeat intro. eapply istrans_posetRelation; auto. - repeat intro. apply isrefl_posetRelation. - intros f g le_f_g le_g_f. use funextsec; intro. apply isantisymm_posetRelation; auto. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.