theorem
  multMagma (# REAL, addreal #) is commutative Group
proof
  reconsider G = multMagma (# REAL, addreal #) as Group by Th3;
  G is commutative
  proof
    let h,g be Element of G;
    reconsider A = h, B = g as Real;
    thus h * g = B + A by BINOP_2:def 9
      .= g * h by BINOP_2:def 9;
  end;
  hence thesis;
end;
