
theorem Th18: :: FinSubseq00
  for X being set, f being FinSequence of X, g being Subset of f
  st len Seq g = len f holds Seq g = f
proof
  let X be set, f be FinSequence of X, g be Subset of f such that
A1: len Seq g = len f;
A2: len Seq g = card g by GLIB_001:5;
  now
    assume g <> f;
    then g c< f;
    hence contradiction by A1,A2,CARD_2:48;
  end;
  hence thesis by FINSEQ_3:116;
end;
