reserve D for non empty set;
reserve s for FinSequence of D;
reserve m,n for Element of NAT;

theorem
  for n be non zero Element of NAT,
  s be Element of n-tuples_on D
  holds (Op-LeftShift(s)) is Element of n-tuples_on D
  proof
    let n be non zero Element of NAT,
    s be Element of n-tuples_on D;
    A1: len s = n by CARD_1:def 7;
    1 <= len s by NAT_1:14;
    then (Op-LeftShift(s)) is FinSequence of D &
    len (Op-LeftShift(s)) = len s by Th5;
    then Op-LeftShift(s) is Tuple of n,D by A1,CARD_1:def 7;
    hence thesis by FINSEQ_2:131;
  end;
