proposition: Lemma poset_disp_cat_locally_prop : locally_propositional poset_disp_cat.
proof: Proof. intro; intros; apply isaprop_is_monotone. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.DisplayedCats.Binproducts UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Categories.HSET.All