Definition slice_coprod_ump_1_map_inv2cell : invertible_2cell (bincoprod_ump_1cell ump h₁ h₂) (slice_coprod_ump_1_map_mor · pr21 q). Proof. use make_invertible_2cell. - use (bincoprod_ump_2cell ump). + exact (bincoprod_ump_1cell_inl _ _ _ _ • pr1 (pr2 (bincoprod_cocone_inl q)) • ((bincoprod_ump_1cell_inl _ _ _ _)^-1 ▹ _) • rassociator _ _ _). + exact (bincoprod_ump_1cell_inr _ _ _ _ • pr1 (pr2 (bincoprod_cocone_inr q)) • ((bincoprod_ump_1cell_inr _ _ _ _)^-1 ▹ _) • rassociator _ _ _). - use bincoprod_ump_2cell_invertible. + is_iso ; apply property_from_invertible_2cell. + is_iso ; apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. 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.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts.