Lemma issubmodule_image {R : ring} {A B : module R} (f : modulefun A B) : issubmodule (abgr_image_hsubtype (modulefun_to_monoidfun f)). Proof. split. - apply abgr_image_issubgr. - intros r x. apply hinhfun. cbn. intro ap. induction ap as [a p]. split with (r * a). now rewrite (modulefun_to_islinear f), <- p. 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.