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

theorem Th4:
  for a,b being Element of Trivial-addLoopStr holds a = b
proof
  let a,b be Element of Trivial-addLoopStr;
  thus a = {} by TARSKI:def 1
    .= b by TARSKI:def 1;
end;
