proposition: 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: Proof. intros X X0. apply pathsinv0. use BinCoproductArrowUnique. rewrite X. apply ZeroArrow_comp_right. rewrite X0. apply ZeroArrow_comp_right. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.ProductCategory