Definition functor_from_oplax_slice_cleaving_nat_z_iso : nat_z_iso (functor_from_cleaving (oplax_slice_disp_bicat B a) (oplax_slice_disp_2cells_isaprop B a) (oplax_slice_disp_univalent_2_1 B a) (oplax_slice_global_cleaving a) (oplax_slice_local_iso_cleaving a) f) (oplax_slice_fib_to_hom _ _ ∙ functor_opp (pre_comp a f) ∙ hom_to_oplax_slice_fib _ _). Proof. use make_nat_z_iso. - exact functor_from_oplax_slice_cleaving_nat_trans. - intro g. apply is_z_iso_discrete_fiber. apply oplax_slice_invertible_2cell_is_left_disp_adj_equiv. cbn. is_iso. 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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.LaxSlice. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.DisplayedBicats.FiberBicategory. Require Import UniMath.Bicategories.DisplayedBicats.FiberCategory. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.SliceCleaving. Require Import UniMath.Bicategories.DisplayedBicats.FiberBicategory.FunctorFromCleaving.