
theorem Th21: :: THEOREM 4.19 (ii)
  for L be upper-bounded non empty Poset holds not Top L in Irr L
proof
  let L be upper-bounded non empty Poset;
  assume Top L in Irr L;
  then Top L is completely-irreducible by Def4;
  then "/\" ((uparrow Top L)\{Top L},L) <> Top L by Th19;
  then "/\" ({Top L}\{Top L},L) <> Top L by WAYBEL_4:24;
  then "/\" ({},L) <> Top L by XBOOLE_1:37;
  hence contradiction by YELLOW_0:def 12;
end;
