Proposition slice_parameterized_NNO_mor_eq : slice_parameterized_NNO_mor_mor · cod_mor y = cod_mor d. Proof. unfold slice_parameterized_NNO_mor_mor ; cbn. use parameterized_NNO_mor_unique. - exact (cod_mor b). - apply identity. - rewrite !assoc. rewrite parameterized_NNO_mor_Z. apply (mor_eq zy). - rewrite !assoc. rewrite parameterized_NNO_mor_S. rewrite id_right. rewrite !assoc'. apply maponpaths. apply (mor_eq sy). - rewrite !assoc. rewrite BinProductPr1Commutes. apply id_left. - rewrite !assoc. rewrite BinProductOfArrowsPr1. rewrite !id_right. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Arithmetic.ParameterizedNNO. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor.