Definition bicat_of_enriched_cats_has_kleisli_ump_1 : has_kleisli_ump_1 EM bicat_of_enriched_cats_has_kleisli_cocone. Proof. intro q. pose (F := mor_of_kleisli_cocone _ q). pose (γ := cell_of_kleisli_cocone _ q). pose (p₁ := from_eq_enriched_nat_trans (kleisli_cocone_unit _ q)). assert (p₂ : ∏ (x : C), pr11 γ (M x) · pr11 γ x = # (pr11 F) (μ M x) · pr11 γ x). { intro x. pose (p₂ := from_eq_enriched_nat_trans (kleisli_cocone_mult _ q) x). cbn in p₂. rewrite !id_left in p₂. exact p₂. } use make_kleisli_cocone_mor. - exact (enriched_functor_from_univalent_kleisli_cat HV EM' _ (enriched_functor_enrichment F) (enriched_nat_trans_enrichment _ γ) p₁ p₂). - exact (enriched_functor_from_univalent_kleisli_cat_nat_trans HV EM' _ (enriched_functor_enrichment F) (enriched_nat_trans_enrichment _ γ) p₁ p₂). - abstract (use eq_enriched_nat_trans ; intro x ; refine (_ @ maponpaths (λ z, z · _) (!(id_left _))) ; exact (enriched_functor_from_univalent_kleisli_cat_eq HV EM' _ (enriched_functor_enrichment F) (enriched_nat_trans_enrichment _ γ) p₁ p₂ x)). - use make_is_invertible_2cell_enriched. apply enriched_functor_from_univalent_kleisli_cat_nat_trans_is_z_iso. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.KleisliCategory. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentMonad. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnivalentKleisliEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnivalentKleisliMapping. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Monads.Examples.MonadsInBicatOfEnrichedCats. Require Import UniMath.Bicategories.Monads.Examples.MonadsInOp1Bicat. Require Import UniMath.Bicategories.Colimits.KleisliObjects.