Definition iterated_slice_pb_nat_z_iso : nat_z_iso (cod_pb PB₁ h ∙ from_iterated_slice xf₁) (from_iterated_slice xf₂ ∙ cod_pb PB (dom_mor h)). Proof. use make_nat_z_iso. - exact iterated_slice_pb_nat_trans. - intro k. use is_z_iso_fiber_from_is_z_iso_disp. use is_z_iso_disp_codomain. cbn. apply is_z_isomorphism_identity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Limits.PreservationProperties. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodColimits.