
theorem Th19:
  for L be non empty RelStr for p be Element of L st p is
  completely-irreducible holds "/\"((uparrow p)\{p},L) <> p
proof
  let L be non empty RelStr;
  let p be Element of L;
  assume p is completely-irreducible;
  then ex_min_of (uparrow p)\{p},L;
  then "/\"((uparrow p)\{p},L) in (uparrow p)\{p} by WAYBEL_1:def 4;
  then not "/\"((uparrow p)\{p},L) in {p} by XBOOLE_0:def 5;
  hence thesis by TARSKI:def 1;
end;
