proposition: Lemma KernelCompMonic2 {x y z : C} (f : x --> y) (M : Monic C y z) (K1 : Kernel Z (f · M)) (K2 : Kernel Z f) : is_iso (KernelCompMonic_mor2 f M K1 K2).
proof: Proof. use is_iso_qinv. - exact (KernelCompMonic_mor1 f M K1 K2). - split. + unfold KernelCompMonic_mor1. unfold KernelCompMonic_mor2. use KernelInsEq. rewrite <- assoc. rewrite KernelCommutes. rewrite KernelCommutes. apply pathsinv0. apply id_left. + unfold KernelCompMonic_mor1. unfold KernelCompMonic_mor2. use KernelInsEq. rewrite <- assoc. rewrite KernelCommutes. rewrite KernelCommutes. apply pathsinv0. apply id_left. 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