Definition slice_coprod_ump_unique {q : slice_bicat b} {φ ψ : slice_coprod_cone --> q} (α : bincoprod_cocone_inl slice_coprod_cone · φ ==> bincoprod_cocone_inl slice_coprod_cone · ψ) (β : bincoprod_cocone_inr slice_coprod_cone · φ ==> bincoprod_cocone_inr slice_coprod_cone · ψ) : isaprop (∑ (γ : φ ==> ψ), bincoprod_cocone_inl slice_coprod_cone ◃ γ = α × bincoprod_cocone_inr slice_coprod_cone ◃ γ = β).
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.