Definition disp_locally_groupoid_kleisli_help (a b : univalent_category) (f g : bicat_of_univ_cats ⟦ a , b ⟧) (x : invertible_2cell f g) (aa : kleisli_triple a) (bb : kleisli_triple b) (ff : kleisli_triple_on_functor aa bb f) (gg : kleisli_triple_on_functor aa bb g) (xx : kleisli_triple_nat_trans (pr1 x) ff gg) (X : a) : pr1 (pr1 gg X) = (bind_kt bb (pr1 (x ^-1) X · unit_kt bb (pr1 f X))) · pr1 ff X · (pr11 x (pr1 aa X)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.