Definition iso_twosided_disp_from_z_iso_disp {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} {x : C₁} {y : C₂} {xx yy : D x y} (ff : @z_iso_disp _ (twosided_disp_cat_to_disp_cat _ _ D) (x ,, y) (x ,, y) (identity_z_iso _) xx yy) : iso_twosided_disp (identity_z_iso x) (identity_z_iso y) xx yy. Proof. simple refine (_ ,, _ ,, _ ,, _). - exact (pr1 ff). - exact (inv_mor_disp_from_z_iso ff). - abstract (refine (inv_mor_after_z_iso_disp ff @ _) ; refine (_ @ !twosided_prod_transport _ _ _) ; unfold transportb ; apply maponpaths_2 ; apply isasetdirprod ; apply homset_property). - abstract (refine (z_iso_disp_after_inv_mor ff @ _) ; refine (_ @ !twosided_prod_transport _ _ _) ; unfold transportb ; apply maponpaths_2 ; apply isasetdirprod ; apply homset_property). 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat.