Proposition local_equivalence_twocell_rwhisker_alt {x y z : B₁} {f₁ f₂ : F x --> F y} (τ : f₁ ==> f₂) (g : F y --> F z) : local_equivalence_inv_twocell (τ ▹ g) = local_equivalence_inv_onecell_comp f₁ g • (local_equivalence_inv_twocell τ ▹ _) • (local_equivalence_inv_onecell_comp f₂ g)^-1. Proof. rewrite <- local_equivalence_twocell_rwhisker. rewrite !vassocl. rewrite vcomp_rinv. rewrite id2_right. apply idpath. 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.