Proposition local_equivalence_triangle1_inv {x y : B₁} (f : x --> y) : (local_equivalence_counit_inv2cell (#F f))^-1 • ##F ((local_equivalence_unit_inv2cell f)^-1) = id2 (#F f). Proof. use vcomp_move_R_pM. { is_iso. } rewrite id2_right. refine (!(id2_right _) @ _). use vcomp_move_R_pM. { exact (psfunctor_is_iso F (inv_of_invertible_2cell (local_equivalence_unit_inv2cell f))). } cbn. refine (!_). apply local_equivalence_triangle1. 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.