proposition: Lemma ToBinDirectSumsEq {c d : A} (DS : BinDirectSum c d) {x : A} (k1 k2 : x --> DS) : k1 · to_Pr1 DS = k2 · to_Pr1 DS -> k1 · to_Pr2 DS = k2 · to_Pr2 DS -> k1 = k2.
proof: Proof. intros H1 H2. rewrite (ToBinDirectSumUnique DS (k1 · to_Pr1 DS) (k1 · to_Pr2 DS) k1). apply pathsinv0. apply ToBinDirectSumUnique. - apply pathsinv0. apply H1. - apply pathsinv0. apply H2. - apply idpath. - apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.Algebra.BinaryOperations UniMath.Algebra.Groups UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis