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

theorem Th1:
  for m,n be non zero Element of NAT, s be Element of n-tuples_on D
  st m <= n
  holds Op-Left(s,m) is Element of m-tuples_on D
  proof
    let m,n be non zero Element of NAT,
    s be Element of n-tuples_on D;
    assume A1: m <= n;
    len s = n by CARD_1:def 7;
    then len (Op-Left(s,m)) = m by A1,FINSEQ_1:59;
    then Op-Left(s,m) is Tuple of m,D by CARD_1:def 7;
    hence thesis by FINSEQ_2:131;
  end;
