Definition from_iso_twosided_disp_cat_on_disp_cat {x : E₁} {y : E₂} {xy₁ xy₂ : twosided_disp_cat_on_disp_cat x y} (fg : iso_twosided_disp (identity_z_iso x) (identity_z_iso y) xy₁ xy₂) : iso_twosided_disp (identity_z_iso (pr1 x)) (identity_z_iso (pr1 y)) xy₁ xy₂. Proof. simple refine (_ ,, _). - exact fg. - use from_is_iso_twosided_disp_cat_on_disp_cat_id. apply fg. 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.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total.