Lemma modulefun_unel {R : ring} {M N : module R} (f : R-mod(M, N)) : f (unel M) = unel N. Proof. rewrite <- (module_mult_0_to_0 (unel M)). rewrite ((modulefun_to_islinear f) ringunel1 (unel M)). rewrite (module_mult_0_to_0 _). reflexivity. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.