Definition twosided_disp_cat_iso_to_z_iso (x : C₁) (y : C₂) {z₁ z₂ : D} (f : @iso_twosided_disp _ _ constant_twosided_disp_cat _ _ _ _ (identity_z_iso x) (identity_z_iso y) z₁ z₂) : z_iso z₁ z₂. Proof. use make_z_iso. - exact (pr1 f). - exact (pr12 f). - split. + abstract (pose (p := pr122 f) ; cbn in p ; unfold transportb_disp_mor2, transportf_disp_mor2 in p ; cbn in p ; rewrite !transportf_const in p ; exact p). + abstract (pose (p := pr222 f) ; cbn in p ; unfold transportb_disp_mor2, transportf_disp_mor2 in p ; cbn in p ; rewrite !transportf_const in p ; exact p). 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.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.