Lemma issubmodule_kernel {R : ring} {A B : module R} (f : modulefun A B) : issubmodule (abgr_kernel_hsubtype (modulefun_to_monoidfun f)). 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.
Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Modules.Core.