Proposition comp_preserves_parameterized_NNO : preserves_parameterized_NNO N₁ N₃ (F ∙ G) (composition_preserves_terminal HF HG). Proof. use is_z_isomorphism_path. - exact (preserves_parameterized_NNO_mor N₂ N₃ G HG · #G (preserves_parameterized_NNO_mor N₁ N₂ F HF)). - exact comp_preserves_parameterized_NNO_eq. - use is_z_isomorphism_comp. + exact HGN. + use functor_on_is_z_isomorphism. exact HFN. 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.