proposition: Lemma KernelsIn_is_iso {x y : C} {f : x --> y} (K1 K2 : Kernel f) : is_iso (KernelIn K1 K2 (KernelArrow K2) (KernelCompZero K2)).
proof: Proof. use is_iso_qinv. - use KernelIn. + use KernelArrow. + use KernelCompZero. - split. + use KernelInsEq. rewrite <- assoc. rewrite KernelCommutes. rewrite KernelCommutes. rewrite id_left. apply idpath. + use KernelInsEq. rewrite <- assoc. rewrite KernelCommutes. rewrite KernelCommutes. rewrite id_left. 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