Lemma BinCoproductArrowZero {x y z: C} {BP : BinCoproduct x y} (f : x --> z) (g : y --> z) : f = ZeroArrow Z _ _ -> g = ZeroArrow Z _ _ -> BinCoproductArrow BP f g = ZeroArrow Z _ _ . Proof. intros X X0. apply pathsinv0. use BinCoproductArrowUnique. rewrite X. apply ZeroArrow_comp_right. rewrite X0. apply ZeroArrow_comp_right. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.ProductCategory.