reserve X for set;
reserve UN for Universe;

theorem
  for X being set st X in UN holds for n being Nat holds n-tuples_on X in UN
  proof
    let X be set;
    assume
A1: X in UN;
    let n be Nat;
    Seg n in UN by Th57;
    then Funcs(Seg n,X) in UN by A1,CLASSES2:61;
    hence thesis by FINSEQ_2:93;
  end;
