proposition: Lemma moduleiso'_to_moduleiso {R} (M N : module R) : moduleiso' M N -> moduleiso M N.
proof: Proof. intro w. use tpair. - exact (pr1 w). - apply make_dirprod. + exact (pr1 (pr2 (pr1 w))). + exact (pr2 w). Defined.
imports: UniMath.MoreFoundations.Tactics UniMath.Algebra.RigsAndRings UniMath.Algebra.Groups UniMath.Algebra.Monoids