proposition: Lemma Abeliain_precategory_homset_comm' {X Y : A} (f g : X --> Y) : Abelian_minus_op (Abelian_minus_op (AbelianPreCat_homset_zero X Y) f) g = Abelian_minus_op (Abelian_minus_op (AbelianPreCat_homset_zero X Y) g) f.
proof: Proof. rewrite <- (AbelianPreCat_homset_zero_right' g). rewrite AbelianPreCat_op_eq3. rewrite (AbelianPreCat_homset_zero_right' f). rewrite (AbelianPreCat_homset_zero_right' g). apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinDirectSums UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian