Definition bincoprod_ump_2cell_unique {a : B} {φ ψ : p --> a} (α : bincoprod_cocone_inl p · φ ==> bincoprod_cocone_inl p · ψ) (β : bincoprod_cocone_inr p · φ ==> bincoprod_cocone_inr p · ψ) (γ δ : φ ==> ψ) (γinl : bincoprod_cocone_inl p ◃ γ = α) (γinr : bincoprod_cocone_inr p ◃ γ = β) (δinl : bincoprod_cocone_inl p ◃ δ = α) (δinr : bincoprod_cocone_inr p ◃ δ = β) : γ = δ.
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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. 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.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Section UniversalFromUMP. End UniversalFromUMP.