proposition: Proposition local_equivalence_twocell_F_runitor {x y : B₁} (f : F x --> F y) : local_equivalence_inv_onecell_comp _ _ • (_ ◃ local_equivalence_inv_onecell_id y) • runitor (local_equivalence_inv_onecell f) = local_equivalence_inv_twocell (runitor f).
proof: Proof. rewrite local_equivalence_twocell_runitor. rewrite !vassocl. etrans. { apply maponpaths. rewrite !vassocr. rewrite lwhisker_vcomp. rewrite vcomp_rinv. rewrite lwhisker_id2. rewrite id2_left. apply idpath. } rewrite !vassocr. rewrite vcomp_rinv. apply id2_left. 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