Lemma isbinopfuninvmap {R} {M N : module R} (f : moduleiso M N) : isbinopfun (invmap f). Proof. intros x y. apply (invmaponpathsweq f). rewrite (homotweqinvweq f (op x y)). apply pathsinv0. transitivity (op ((moduleiso_to_weq f) (invmap f x)) ((moduleiso_to_weq f) (invmap f y))). apply (modulefun_to_isbinopfun f (invmap f x) (invmap f y)). rewrite 2 (homotweqinvweq f). apply idpath. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.