∀ {G : Type u_1} [inst : Group G] (x : AddSubgroup (Additive G)),
  (fun S =>
        let __src := Submonoid.toAddSubmonoid S.toSubmonoid;
        { toAddSubmonoid := __src, neg_mem' := ⋯ })
      ((fun S =>
          let __src := AddSubmonoid.toSubmonoid S.toAddSubmonoid;
          { toSubmonoid := __src, inv_mem' := ⋯ })
        x) =
    x