Definition z_iso_disp_weq_op_disp_cat {C : category} {D : disp_cat C} {x : C} (xx yy : D x) : @z_iso_disp _ (op_disp_cat D) _ _ (@identity_z_iso C^op x) xx yy ≃ z_iso_disp (identity_z_iso x) xx yy. Proof. use make_weq. - exact z_iso_disp_from_op_disp_cat. - use isweq_iso. + exact z_iso_disp_to_op_disp_cat. + abstract (intro f ; use subtypePath ; [ intro ; apply isaprop_is_z_iso_disp | ] ; apply idpath). + abstract (intro f ; use subtypePath ; [ intro ; apply isaprop_is_z_iso_disp | ] ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.