Definition op1_has_em_ump_2 (k : kleisli_cocone m) (Hk : has_kleisli_ump_2 _ k) : em_ump_2 m (to_op1_em_cone k). Proof. intros z g₁ g₂ α. use iscontraprop1. - exact (op1_has_em_ump_2_unique k Hk α). - simple refine (_ ,, _). + exact (op1_has_em_ump_2_cell k Hk α). + exact (op1_has_em_ump_2_eq k Hk α). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. 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. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.Colimits.KleisliObjects. Require Import UniMath.Bicategories.Monads.Examples.MonadsInOp1Bicat.