theorem
  ((for r,s,t holds (r * s) * t = r * (s * t)) &
    ex t st for s1 holds s1 * t = s1 & t * s1 = s1 &
    ex s2 st s1 * s2 = t & s2 * s1 = t) implies S is Group
  by Def2,Def3;
