Definition bicat_of_enriched_cats_has_kleisli_ump_2 : has_kleisli_ump_2 EM bicat_of_enriched_cats_has_kleisli_cocone. Proof. intros C' G₁ G₂ α p. assert (p' : ∏ (x : C), # (pr11 G₁) (kleisli_nat_trans M x) · pr11 α x = pr11 α (M x) · # (pr11 G₂) (kleisli_nat_trans M x)). { intro x. pose (q := from_eq_enriched_nat_trans p x). cbn in q. rewrite !id_left, !id_right in q. exact q. } use iscontraprop1. - abstract (use invproofirrelevance ; intros β₁ β₂ ; use subtypePath ; [ intro ; apply cellset_property | ] ; use eq_enriched_nat_trans ; exact (enriched_nat_trans_from_univalent_kleisli_cat_unique HV EM' _ α (from_eq_enriched_nat_trans (pr2 β₁)) (from_eq_enriched_nat_trans (pr2 β₂)))). - simple refine (_ ,, _). + exact (enriched_nat_trans_from_univalent_kleisli_cat HV EM' _ α p'). + abstract (use eq_enriched_nat_trans ; exact (pre_whisker_enriched_nat_trans_from_univalent_kleisli_cat HV EM' _ α p')). 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.