Definition codomain_functor_preserves_parameterized_NNO : preserves_parameterized_NNO (slice_parameterized_NNO N₁ PC₁ x) (slice_parameterized_NNO N₂ PC₂ (F x)) _ (preserves_terminal_fiber_disp_codomain_functor F x). Proof. unfold preserves_parameterized_NNO. use is_z_iso_fiber_from_is_z_iso_disp. use is_z_iso_disp_codomain. use is_z_isomorphism_path. - exact codomain_functor_preserves_parameterized_NNO_mor. - exact codomain_functor_preserves_parameterized_NNO_eq. - use is_z_isomorphism_comp. + exact codomain_functor_preserves_parameterized_NNO_iso. + apply is_z_iso_inv_from_z_iso. Defined.
Require Import UniMath.Foundations.All. 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.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Arithmetic.ParameterizedNNO. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor.