Definition kleisli_ump_inv2cell {x : B} {g₁ g₂ : k --> x} (α : invertible_2cell (mor_of_kleisli_cocone k · g₁) (mor_of_kleisli_cocone k · g₂)) (p : lassociator _ _ _ • (cell_of_kleisli_cocone k ▹ _) • α = (_ ◃ α) • lassociator _ _ _ • (cell_of_kleisli_cocone k ▹ _)) : invertible_2cell g₁ g₂. Proof. use make_invertible_2cell. - exact (kleisli_ump_cell α p). - exact (kleisi_ump_cell_is_invertible α p). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax.