Definition total_em_cone : em_cone m. Proof. use make_em_cone. - exact (pr1 cone ,, pr1 (HD m)). - exact (mor_of_mnd_mor (mor_of_em_cone _ cone) ,, pr12 (HD m)). - refine (mnd_mor_endo (mor_of_em_cone _ cone) ,, _). cbn. apply (pr2 (HD m)). - abstract (use subtypePath ; [ intro ; apply HD₁ | ] ; refine (_ @ mnd_mor_unit (mor_of_em_cone _ cone)) ; cbn ; rewrite id2_rwhisker ; rewrite id2_right ; apply idpath). - abstract (use subtypePath ; [ intro ; apply HD₁ | ] ; refine (_ @ mnd_mor_mu (mor_of_em_cone _ cone)) ; cbn ; rewrite !vassocl ; do 2 apply maponpaths ; use vcomp_move_L_pM ; [ is_iso | ] ; cbn ; rewrite !vassocr ; rewrite lunitor_triangle ; rewrite <- vcomp_lunitor ; rewrite !vassocl ; rewrite lunitor_triangle ; apply idpath). 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.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EndoMap. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.Monads.Examples.MonadsInTotalBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion.