
theorem Th4:
  for L being right_zeroed non empty addLoopStr holds {0.L} is add-closed
proof
  let L be right_zeroed non empty addLoopStr;
  let x,y be Element of L;
  assume x in {0.L} & y in {0.L};
  then x = 0.L & y= 0.L by TARSKI:def 1;
  then x + y = 0.L by RLVECT_1:def 4;
  hence thesis by TARSKI:def 1;
end;
