proposition: Lemma FromBinDirectSumsEq {c d : A} (DS : BinDirectSum c d) {x : A} (k1 k2 : DS --> x) : to_In1 DS · k1 = to_In1 DS · k2 -> to_In2 DS · k1 = to_In2 DS · k2 -> k1 = k2.
proof: Proof. intros H1 H2. rewrite (FromBinDirectSumUnique DS (to_In1 DS · k1) (to_In2 DS · k1) k1). apply pathsinv0. apply FromBinDirectSumUnique. - 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