proposition: Lemma AdditiveEqualizerToKernel_eq1 {x y : ob A} (f g : x --> y) (E : Equalizer f g) : EqualizerArrow E · to_binop x y f (to_inv g) = ZeroArrow (to_Zero A) E y.
proof: Proof. set (X:= @to_premor_linear' A). rewrite X. use (to_rcan A (EqualizerArrow E · g)). rewrite to_assoc. rewrite to_lunax''. rewrite <- to_premor_linear'. rewrite (@to_linvax' A (to_Zero A)). rewrite ZeroArrow_comp_right. rewrite to_runax''. apply (EqualizerEqAr E). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.MoreFoundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinDirectSums