
theorem Th5:
  for L being left_zeroed right_add-cancelable right-distributive
  non empty doubleLoopStr holds {0.L} is left-ideal
proof
  let L be left_zeroed right_add-cancelable right-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 p9*x = 0.L by BINOM:2;
  hence thesis by TARSKI:def 1;
end;
