Definition from_z_iso_disp_codomain {C : category} {x y : C} {f : z_iso x y} {h₁ : disp_codomain C x} {h₂ : disp_codomain C y} (ff : z_iso_disp f h₁ h₂) : z_iso (pr1 h₁) (pr1 h₂). Proof. use make_z_iso. - exact (pr11 ff). - exact (pr112 ff). - split. + abstract (refine (maponpaths pr1 (pr222 ff) @ _) ; rewrite transportb_cod_disp ; apply idpath). + abstract (refine (maponpaths pr1 (pr122 ff) @ _) ; rewrite transportb_cod_disp ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations.