Section AdditiveGroup.
Variable U : finZmodType.
Implicit Types x y : U.

Lemma zmod1gE : 1%g = 0 :> U.            Proof. by []. Qed.
Lemma zmodVgE x : x^-1%g = - x.          Proof. by []. Qed.
Lemma zmodMgE x y : (x * y)%g = x + y.   Proof. by []. Qed.
Lemma zmodXgE n x : (x ^+ n)%g = x *+ n. Proof. by []. Qed.
Lemma zmod_mulgC x y : commute x y.      Proof. exact: addrC. Qed.
Lemma zmod_abelian (A : {set U}) : abelian A.