proposition: Lemma AdditiveKernelToEqualizer_eq1 {x y : ob A} (f g : x --> y) (K : Kernel (to_Zero A) (to_binop _ _ f (to_inv g))) : KernelArrow K · f = KernelArrow K · g.
proof: Proof. use (to_rcan A (KernelArrow K · (to_inv g))). rewrite <- to_premor_linear'. rewrite <- to_premor_linear'. rewrite KernelCompZero. rewrite (@to_rinvax' A (to_Zero A)). rewrite ZeroArrow_comp_right. apply idpath. 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