reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;

theorem
  (for x being Element of Trivial-addLoopStr holds x = {}) & (for x,y
  being Element of Trivial-addLoopStr holds x+y = {}) & (for x being Element of
  Trivial-addLoopStr holds -x = {}) & 0.Trivial-addLoopStr = {}
  by TARSKI:def 1;
