theorem
 for z being set holds z is Tuple of i,D iff z in i-tuples_on D
 proof let z be set;
  thus z is Tuple of i,D implies z in i-tuples_on D by Lm6;
  assume z in i-tuples_on D;
   then ex s being Element of D* st z = s & len s = i;
  hence z is Tuple of i,D by CARD_1:def 7;
 end;
