Definition disp_iso_weq_iso : (∑ (h : z_iso y z), f = h · g) ≃ z_iso_disp (identity_z_iso x) fy gz. Proof. use weq_iso. - exact (λ h, iso_to_disp_iso (pr1 h) (pr2 h)). - exact disp_iso_to_iso. - abstract (intro ff ; use subtypePath ; [ intro ; apply homset_property | ] ; use z_iso_eq ; cbn ; apply idpath). - abstract (intro ff ; use subtypePath ; [ intro ; apply isaprop_is_z_iso_disp | ] ; use eq_cod_mor ; cbn ; 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.