reserve x for set,
  R for non empty Poset;
reserve S1 for OrderSortedSign,
  OU0 for OSAlgebra of S1;
reserve s,s1,s2,s3,s4 for SortSymbol of S1;

theorem Th7:
  for M being ManySortedSet of the carrier of S1 holds M c= OSCl M
proof
  let M be ManySortedSet of the carrier of S1;
  let i be object;
  assume i in the carrier of S1;
  then reconsider s = i as SortSymbol of S1;
  M.s in {M.s1: s1 <= s};
  then M.s c= union { M.s1: s1 <= s} by ZFMISC_1:74;
  hence thesis by Def4;
end;
