Definition z_iso_cleaving_from_opcleaving_ob_disp_iso : z_iso_disp f z_iso_cleaving_from_opcleaving_ob d. Proof. use make_z_iso_disp. - exact z_iso_cleaving_from_opcleaving_ob_disp_iso_map. - simple refine (_ ,, _ ,, _). + exact ℓ. + abstract (apply opcartesian_factorisation_commutes). + abstract (apply (opcartesian_factorisation_unique ℓ_opcart) ; unfold transportb ; rewrite mor_disp_transportf_prewhisker ; rewrite assoc_disp ; unfold transportb ; etrans ; [ apply maponpaths ; apply maponpaths_2 ; apply (opcartesian_factorisation_commutes ℓ_opcart) | ] ; unfold transportb ; rewrite mor_disp_transportf_postwhisker ; rewrite id_left_disp, id_right_disp ; unfold transportb ; rewrite !transport_f_f ; apply maponpaths_2 ; apply homset_property). Defined.
Require Import UniMath.Foundations.Sets. 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.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Opposite. Section IsoCleavingFromOpcleaving. End IsoCleavingFromOpcleaving.