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 z being Tuple of 3,D ex d1,d2,d3 st z = <*d1,d2,d3*>
proof
  let z be Tuple of 3,D;
A1: z is Element of D* by FINSEQ_1:def 11;
  len z = 3 by CARD_1:def 7;
  then z in 3-tuples_on D by A1;
  then z in the set of all  <*d1,d2,d3*> by Th100;
  hence thesis;
end;
