proposition: Lemma BinProductArrowsEq (c d : C) (P : BinProduct c d) (x : C) (k1 k2 : x --> BinProductObject P) : k1 · BinProductPr1 P = k2 · BinProductPr1 P -> k1 · BinProductPr2 P = k2 · BinProductPr2 P -> k1 = k2.
proof: Proof. intros H1 H2. set (p1 := k1 · BinProductPr1 P). set (p2 := k1 · BinProductPr2 P). rewrite (BinProductArrowUnique _ _ P _ p1 p2 k1). apply pathsinv0. apply BinProductArrowUnique. 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.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