proposition: Lemma BinCoproductArrowsEq (c d : C) (CC : BinCoproduct c d) (x : C) (k1 k2 : BinCoproductObject CC --> x) : BinCoproductIn1 CC · k1 = BinCoproductIn1 CC · k2 -> BinCoproductIn2 CC · k1 = BinCoproductIn2 CC · k2 -> k1 = k2.
proof: Proof. intros H1 H2. set (p1 := BinCoproductIn1 CC · k1). set (p2 := BinCoproductIn2 CC · k1). rewrite (BinCoproductArrowUnique _ _ CC _ p1 p2 k1). apply pathsinv0. apply BinCoproductArrowUnique. unfold p1. apply pathsinv0. apply H1. unfold p2. apply pathsinv0. apply H2. apply idpath. apply idpath. 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