
theorem Th11:
  for S be set,
  s be FinSequence of S,
  A be Subset of (dom s) holds
  len extract(s,A) = card A &
  for i be Nat st i in dom extract(s,A) holds
  (extract(s,A)).i=s.((canFS(A)).i)
  proof
    let S be set,
    s be FinSequence of S,
    A be Subset of (dom s);
    rng (canFS A) c= A by FINSEQ_1:def 4; then
    len (extract(s,A)) = len(canFS A) by FINSEQ_2:29,XBOOLE_1:1
    .= card A by FINSEQ_1:93;
    hence thesis by FUNCT_1:12;
  end;
