proposition: Lemma issubmodule_kernel {R : ring} {A B : module R} (f : modulefun A B) : issubmodule (abgr_kernel_hsubtype (modulefun_to_monoidfun f)).
proof: Proof. split. - apply abgr_Kernel_subabgr_issubgr. - intros r x p. cbn. rewrite (modulefun_to_islinear f). rewrite <- (module_mult_1 r), <- p. reflexivity. Defined.
imports: UniMath.MoreFoundations.Subtypes UniMath.Algebra.RigsAndRings UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.Modules.Core