Proposition local_equivalence_twocell_lwhisker_inv {x y z : B₁} (f : F x --> F y) {g₁ g₂ : F y --> F z} (τ : g₁ ==> g₂) : (local_equivalence_inv_onecell_comp f g₁)^-1 • local_equivalence_inv_twocell (f ◃ τ) = (_ ◃ local_equivalence_inv_twocell τ) • (local_equivalence_inv_onecell_comp f g₂)^-1. Proof. use vcomp_move_R_pM ; [ is_iso | ]. rewrite !vassocr. apply local_equivalence_twocell_lwhisker_alt. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Properties.