Definition slice_local_iso_cleaving : local_iso_cleaving (slice_disp_bicat a). Proof. intros c₁ c₂ t₁ t₂ s₁ s₂ α β ; cbn in *. simple refine (_ ,, _ ,, _). - exact (comp_of_invertible_2cell α (rwhisker_of_invertible_2cell _ (inv_of_invertible_2cell β))). - abstract (cbn ; rewrite !vassocl ; rewrite rwhisker_vcomp ; rewrite vcomp_linv ; rewrite id2_rwhisker ; apply id2_right). - apply disp_locally_groupoid_slice_disp_bicat. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.LaxSlice. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice.