proposition: Lemma BinProductArrowZero {x y z: C} {BP : BinProduct C x y} (f : z --> x) (g : z --> y) : f = ZeroArrow Z _ _ -> g = ZeroArrow Z _ _ -> BinProductArrow C BP f g = ZeroArrow Z _ _ .
proof: Proof. intros X X0. apply pathsinv0. use BinProductArrowUnique. rewrite X. apply ZeroArrow_comp_left. rewrite X0. apply ZeroArrow_comp_left. 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.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets