Definition submodule_smul {R : ring} {M : module R} {A : submodule M} (r : R) (m : A) : A. Proof. use tpair. - exact (r * pr1 m). - exact (submodule_to_issubsetwithsmul A r (pr1 m) (pr2 m)). 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.