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 Th22:
  for A being OSSubset of OU0, s being SortSymbol of S1 holds
  OSSubSort(A,s) c= SubSort(A,s)
proof
  let A be OSSubset of OU0, s be SortSymbol of S1;
  let x be object;
  assume x in OSSubSort(A,s);
  then
A1: ex B being OSSubset of OU0 st B in OSSubSort(A) & x = B.s by Def10;
  OSSubSort(A) c= SubSort(A) by Th16;
  hence thesis by A1,MSUALG_2:def 13;
end;
