Proposition is_NNO_parameterized_NNO_mor_S : parameterized_NNO_S N · is_NNO_parameterized_NNO_mor = is_NNO_parameterized_NNO_mor · sy. Proof. unfold is_NNO_parameterized_NNO_mor. rewrite !assoc'. rewrite <- parameterized_NNO_mor_S. rewrite !assoc. apply maponpaths_2. rewrite precompWithBinProductArrow. rewrite postcompWithBinProductArrow. 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.