Proposition local_equivalence_twocell_rassociator_inv {w x y z : B₁} (f : F w --> F x) (g : F x --> F y) (h : F y --> F z) : rassociator _ _ _ • (_ ◃ (local_equivalence_inv_onecell_comp g h)^-1) • (local_equivalence_inv_onecell_comp f (g · h))^-1 = ((local_equivalence_inv_onecell_comp f g)^-1 ▹ _) • (local_equivalence_inv_onecell_comp (f · g) h)^-1 • local_equivalence_inv_twocell (rassociator _ _ _). Proof. use vcomp_move_L_pM ; [ is_iso | ]. rewrite !vassocr. do 2 (use vcomp_move_R_Mp ; [ is_iso | ]). exact (local_equivalence_twocell_rassociator f g h). 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.