Lemma mor_eq_total_category_when_locally_prop {C : category} {D : disp_cat C} (loc : locally_propositional D) {xx yy : total_precategory D} {ff gg : xx --> yy} : pr1 ff = pr1 gg -> ff = gg. Proof. intro Hyp. use subtypePath. - red; intro; apply loc. - exact Hyp. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.