proposition: Lemma KernelofZeroArrow_is_iso {x y : C} (K : Kernel (ZeroArrow Z x y)) : is_inverse_in_precat (KernelArrow K) (from_Kernel_to_Kernel (KernelofZeroArrow x y) K).
proof: Proof. use make_is_inverse_in_precat. - use KernelInsEq. rewrite <- assoc. unfold from_Kernel_to_Kernel. rewrite KernelCommutes. rewrite id_left. cbn. rewrite id_right. apply idpath. - unfold from_Kernel_to_Kernel. rewrite KernelCommutes. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Zero