reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;
reserve s for Element of D*;

theorem
  for D9 being non empty Subset of D
  for z being Tuple of i,D9 holds z is Element of i-tuples_on D
proof let D9 be non empty Subset of D;
 let z being Tuple of i,D9;
  z is Tuple of i, D by Th22;
 hence thesis by Lm6;
end;
