Definition all_disp_mor_iso_from_prop {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} (HD₁ : isaprop_disp_twosided_mor D) (HD₂ : sym_mor_twosided_disp_cat D) : all_disp_mor_iso D. Proof. intros x₁ x₂ y₁ y₂ xy₁ xy₂ f g Hf Hg fg. simple refine (_ ,, _ ,, _). - apply HD₂. exact fg. - apply HD₁. - apply HD₁. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Profunctors.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.