reserve x,z for set;
reserve k for Element of NAT;
reserve D for non empty set;
reserve X for set;
reserve p,r for relation;
reserve a,a1,a2,b for FinSequence;
reserve a,b for FinSequence of D;
reserve p,r for Element of relations_on D;
reserve u,v,w for boolean object;
reserve A,z for set,
  x,y for FinSequence of A,
  h for PartFunc of A*,A,
  n,m for Nat;
reserve A for non empty set,
  h for PartFunc of A*,A,
  a for Element of A;

theorem
  for n be Nat, D be non empty set, D1 be non empty Subset of D
  holds n-tuples_on D /\ n-tuples_on D1 = n-tuples_on D1
proof
  let n be Nat,D be non empty set, D1 be non empty Subset of D;
  n-tuples_on D1 c= n-tuples_on D
  proof
    let z be object;
    assume z in n-tuples_on D1;
    then z is Tuple of n,D1 by FINSEQ_2:131;
    then z is Element of n-tuples_on D by FINSEQ_2:109;
    hence thesis;
  end;
  hence thesis by XBOOLE_1:28;
end;
