Proposition is_parameterized_NNO_prod_independent {C : univalent_category} {T : Terminal C} {BC₁ : BinProducts C} (BC₂ : BinProducts C) (N : parameterized_NNO T BC₁) : is_parameterized_NNO T BC₂ N (parameterized_NNO_Z N) (parameterized_NNO_S N). Proof. refine (transportf (λ z, is_parameterized_NNO _ z _ _ _) _ (pr222 N)). use funextsec ; intro x. use funextsec ; intro y. apply isaprop_BinProduct. apply univalent_category_is_univalent. 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.