Definition to_iterated_slice_data : functor_data (C / x) (C / y / xf). Proof. use make_functor_data. - simple refine (λ h, make_cod_fib_ob _). + use make_cod_fib_ob. * exact (cod_dom h). * exact (cod_mor h · f). + use make_cod_fib_mor. * exact (cod_mor h). * abstract (cbn ; apply idpath). - simple refine (λ h₁ h₂ p, make_cod_fib_mor _ _). + use make_cod_fib_mor. * exact (dom_mor p). * abstract (cbn ; rewrite !assoc ; rewrite (mor_eq p) ; apply idpath). + abstract (use eq_mor_cod_fib ; rewrite comp_in_cod_fib ; cbn ; exact (mor_eq p)). 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.