Definition has_binprod_ump_2_op_cell : binprod_ump_2 op2_binprod_cone. Proof. intros q φ ψ α β. use iscontraprop1. - abstract (use invproofirrelevance ; intros φ₁ φ₂ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; exact (binprod_ump_2cell_unique_alt ump _ _ (pr12 φ₁ @ !(pr12 φ₂)) (pr22 φ₁ @ !(pr22 φ₂)))). - simple refine (_ ,, _ ,, _). + exact (binprod_ump_2cell ump α β). + exact (binprod_ump_2cell_pr1 ump α β). + exact (binprod_ump_2cell_pr2 ump α β). 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.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.CommaObjects. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.Limits.EilenbergMooreComonad. 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.