reserve L for non empty addLoopStr;
reserve a,b,c,x for Element of L;

theorem
  L is Abelian AddGroup iff (for a holds a + 0.L = a) & (for a ex x st a
  +x = 0.L) & (for a,b,c holds (a+b)+c = a+(b+c)) & for a,b holds a+b = b+a by
