Proposition local_equivalence_twocell_F_lunitor {x y : B₁} (f : F x --> F y) : local_equivalence_inv_onecell_comp _ _ • ((local_equivalence_inv_onecell_id x) ▹ _) • lunitor (local_equivalence_inv_onecell f) = local_equivalence_inv_twocell (lunitor f). Proof. rewrite local_equivalence_twocell_lunitor. rewrite !vassocl. etrans. { apply maponpaths. rewrite !vassocr. rewrite rwhisker_vcomp. rewrite vcomp_rinv. rewrite id2_rwhisker. rewrite id2_left. apply idpath. } rewrite !vassocr. rewrite vcomp_rinv. apply id2_left. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Properties.