proposition: Lemma LRB_associator_comm (x y z w : B) : pre_whisker (pair_functor (η_{x,y}) (pair_functor (η_{y,z}) (η (hom z w)))) (lift_nat_trans_along (R (hom x w)) (pair_functor (η_{x,y}) (pair_functor (η_{y,z}) (η (hom z w)))) (eso3 _ _ _) (ff3 _ _ _) (LRB_associator_nat_z_iso_pre x y z w) ) = LRB_associator_nat_z_iso_pre x y z w.
proof: Proof. apply (lift_nat_trans_along_comm _ _ _ _ (LRB_associator_nat_z_iso_pre x y z w)). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.RezkCompletion UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.YonedaLemma UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties UniMath.Bicategories.PseudoFunctors.Examples.Composition