proposition: Proposition local_equivalence_twocell_linvunitor {x y : B₁} (f : F x --> F y) : linvunitor (local_equivalence_inv_onecell f) = local_equivalence_inv_twocell (linvunitor f) • local_equivalence_inv_onecell_comp _ _ • (local_equivalence_inv_onecell_id x ▹ _).
proof: Proof. refine (!(id2_left _) @ _ @ id2_right _). rewrite <- lunitor_linvunitor. rewrite !vassocr. apply maponpaths_2. rewrite local_equivalence_twocell_lunitor. rewrite !vassocl. refine (!_). etrans. { do 2 apply maponpaths. rewrite !vassocr. rewrite rwhisker_vcomp. rewrite vcomp_rinv. rewrite id2_rwhisker. rewrite id2_left. apply idpath. } etrans. { apply maponpaths. rewrite !vassocr. rewrite vcomp_rinv. apply id2_left. } rewrite <- local_equivalence_inv_twocell_comp. rewrite linvunitor_lunitor. rewrite local_equivalence_inv_twocell_id. 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