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 addGroup
  by Def2,RLVECT_1:def 3;
