
theorem Th6:
  for L being right_zeroed left_add-cancelable left-distributive
  non empty doubleLoopStr holds {0.L} is right-ideal
proof
  let L be right_zeroed left_add-cancelable left-distributive non empty
  doubleLoopStr;
  let p,x be Element of L;
  reconsider p9 = p as Element of L;
  assume x in {0.L};
  then x = 0.L by TARSKI:def 1;
  then x*p9 = 0.L by BINOM:1;
  hence thesis by TARSKI:def 1;
end;
