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
  for S being all-with_const_op OrderSortedSign, OU0 being non-empty
OSAlgebra of S, OU1 being non-empty OSSubAlgebra of OU0 holds OSConstants(OU0)
  is non-empty OSSubset of OU1
proof
  let S be all-with_const_op OrderSortedSign, OU0 be non-empty OSAlgebra of S,
  OU1 be non-empty OSSubAlgebra of OU0;
  Constants(OU0) c= OSConstants(OU0) by Th10;
  hence thesis by Th13,PBOOLE:131;
end;
