
theorem Th5:
  for R being non empty Poset, A being ManySortedSet of the carrier
  of R, s being (Element of R), x being set st x in A.s holds x in A-carrier_of
  CComp(s)
proof
  let R be non empty Poset;
  let A be ManySortedSet of the carrier of R, s be (Element of R), x be set
  such that
A1: x in A.s;
  s in CComp(s) by EQREL_1:20;
  then A.s in {A.s1 where s1 is Element of R: s1 in CComp(s)};
  hence thesis by A1,TARSKI:def 4;
end;
