Definition slice_parameterized_NNO : parameterized_NNO (codomain_fib_terminal x) (codomain_fib_binproducts PC x). Proof. use make_parameterized_NNO. - exact slice_parameterized_NNO_ob. - exact slice_parameterized_NNO_Z. - exact slice_parameterized_NNO_S. - intros b y zy sy. use iscontraprop1. + apply slice_parameterized_NNO_unique. + simple refine (_ ,, _ ,, _). * exact (slice_parameterized_NNO_mor zy sy). * apply slice_parameterized_NNO_mor_Z. * apply slice_parameterized_NNO_mor_S. Defined.
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.