
theorem LMExtBit4:
  for K be non zero Nat,
  y be Tuple of K, BOOLEAN
  st y=0*K
  holds
  for n be non zero Nat st n <= K
  holds
  y /.n = 0
  proof
    let K be non zero Nat,
    y be Tuple of K, BOOLEAN;
    assume AS1: y=0*K;
    let n be non zero Nat;
    assume AS2: n <= K;
    A1: len y = K by CARD_1:def 7;
    0 < n; then
    1 + 0 <= n by NAT_1:13; then
    n in Seg K by FINSEQ_1:1,AS2; then
    n in dom y by A1,FINSEQ_1:def 3;
    hence y/.n = y.n by PARTFUN1:def 6
    .= 0 by AS1;
  end;
