proposition: Lemma isExact_opp_Eq {A : AbelianPreCat} {x y z : ob A} {f : x --> y} {g : y --> z} (H : f · g = ZeroArrow (to_Zero A) _ _) : (g : (Abelian_opp A)⟦_, _⟧) · (f : (Abelian_opp A)⟦_, _⟧) = @ZeroArrow (Abelian_opp A) (Zero_opp A (to_Zero A)) _ _.
proof: Proof. cbn. use (pathscomp0 H). use ZeroArrow_opp. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian UniMath.CategoryTheory.AbelianToAdditive UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinDirectSums