Definition LRB_associator {x y z w : B} (f : R (hom x y)) (g : R (hom y z)) (h : R (hom z w)) : z_iso (C := R (hom x w)) (LRB_composition _ _ _ (LRB_composition _ _ _ (f,g), h)) (LRB_composition _ _ _ (f, LRB_composition _ _ _ (g,h))). Proof. exists (pr1 (LRB_associator_nat_z_iso x y z w) (f,(g,h))). exists (pr1 (pr2 (LRB_associator_nat_z_iso x y z w) (f,(g,h)))). split ; apply (pr2 (LRB_associator_nat_z_iso x y z w) (f,(g,h))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.PrecompEquivalence. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.RezkCompletions.RezkCompletions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.YonedaLemma. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Properties. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition.