
theorem Th6:
  for X being non empty set for n be non zero Nat st
  n-tuples_on X is finite holds X is finite
  proof
    let X be non empty set;
    let n be non zero Nat;
    assume
A1: n-tuples_on X is finite;
    assume
A2: not X is finite;
    then card X = card (n-tuples_on X) by CARD_4:23;
    hence thesis by A1,A2;
  end;
