Lemma moduleiso_to_moduleiso' {R} (M N : module R) : moduleiso M N -> moduleiso' M N. Proof. intro w. use tpair. - use tpair. + exact w. + use tpair. * exact (modulefun_to_isbinopfun w). * apply (modulefun_unel w). - exact (modulefun_to_islinear w). Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.