proposition: Lemma isExact'_to_isExact {x y z : ob A} {f : x --> y} {g : y --> z} {H : f · g = ZeroArrow (to_Zero A) _ _} (iE : isExact' f g H) : isExact f g H.
proof: Proof. unfold isExact' in iE. unfold isExact. use make_isKernel. intros w0 h H'. use unique_exists. - use KernelIn. + exact h. + cbn. exact (isExact'_to_isExact_Eq iE h H'). - apply KernelCommutes. - intros y'. apply hs. - intros y' T. cbn in T. apply KernelInsEq. rewrite T. apply pathsinv0. apply KernelCommutes. 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