proposition: Proposition local_equivalence_unit_natural_alt {x y : B₁} {f g : x --> y} (τ : f ==> g) : (local_equivalence_unit_inv2cell f)^-1 • τ = local_equivalence_inv_twocell (##F τ) • (local_equivalence_unit_inv2cell g)^-1.
proof: Proof. rewrite local_equivalence_inv_twocell_psfunctor. rewrite !vassocl. rewrite vcomp_rinv. rewrite id2_right. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties