Definition indexed_cat_to_disp_cat_z_iso_weq_fiber : is_z_isomorphism f ≃ @is_z_iso_disp _ indexed_cat_to_disp_cat _ _ (identity_z_iso x) _ _ (indexed_cat_to_disp_cat_z_iso_weq_base xx₁ xx₂ f). Proof. use weqimplimpl. - exact indexed_cat_to_disp_cat_to_disp_iso. - exact indexed_cat_to_disp_cat_from_disp_iso. - apply isaprop_is_z_isomorphism. - apply isaprop_is_z_iso_disp. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategory.