fact: Definition BinDirectSum_from_BinProduct {X Y : A} (P : BinProduct A X Y) : BinDirectSum X Y := make_BinDirectSum A X Y (BinProductObject A P) (BinProductArrow A P (identity X) (ZeroArrow Z X Y)) (BinProductArrow A P (ZeroArrow Z Y X) (identity Y)) (BinProductPr1 A P) (BinProductPr2 A P) (make_isBinDirectSum _ _ _ _ _ _ _ _ (BinDirectSums_from_binproduct_bincoproducts_eq1 P) (BinDirectSums_from_binproduct_bincoproducts_eq4 P) (BinDirectSums_from_binproduct_bincoproducts_eq2 P) (BinDirectSums_from_binproduct_bincoproducts_eq3 P) (BinDirectSums_from_binproduct_bincoproducts_eq5 P)).
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