Proposition local_equivalence_twocell_rassociator {w x y z : B₁} (f : F w --> F x) (g : F x --> F y) (h : F y --> F z) : local_equivalence_inv_onecell_comp (f · g) h • (local_equivalence_inv_onecell_comp f g ▹ _) • rassociator _ _ _ = local_equivalence_inv_twocell (rassociator _ _ _) • local_equivalence_inv_onecell_comp f (g · h) • (_ ◃ local_equivalence_inv_onecell_comp g h). Proof. refine (!(id2_left _) @ _). rewrite <- local_equivalence_inv_twocell_id. rewrite <- rassociator_lassociator. rewrite local_equivalence_inv_twocell_comp. rewrite !vassocl. apply maponpaths. rewrite !vassocr. rewrite local_equivalence_twocell_lassociator. rewrite !vassocl. rewrite lassociator_rassociator. 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.