Definition is_NNO_parameterized_NNO : isNNO T N (parameterized_NNO_Z N) (parameterized_NNO_S N). Proof. intros y zy sy. use iscontraprop1. - exact (is_NNO_parameterized_NNO_isaprop y zy sy). - simple refine (_ ,, _ ,, _). + exact (is_NNO_parameterized_NNO_mor N y zy sy). + exact (is_NNO_parameterized_NNO_mor_Z N y zy sy). + exact (is_NNO_parameterized_NNO_mor_S N y zy sy). Defined.
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.Preservation. Require Import UniMath.CategoryTheory.Arithmetic.NNO.