
theorem Th4:
  for R being non empty Poset, s1,s2 being Element of R st s1 <= s2
  holds CComp(s1) = CComp(s2)
proof
  let R be non empty Poset, s1,s2 be Element of R;
  assume s1 <= s2;
  then [s1,s2] in Path_Rel R by Th2;
  hence thesis by EQREL_1:35;
end;
