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