Proposition is_NNO_parameterized_NNO_mor_Z : parameterized_NNO_Z N · is_NNO_parameterized_NNO_mor = zy. Proof. unfold is_NNO_parameterized_NNO_mor ; cbn. refine (_ @ parameterized_NNO_mor_Z N T y zy sy). rewrite !assoc. apply maponpaths_2. rewrite precompWithBinProductArrow. rewrite (TerminalEndo_is_identity (TerminalArrow T T)). rewrite id_left, id_right. apply maponpaths_2. apply TerminalArrowEq. Qed.
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.