theorem
  for f holds {LSeg(f,i): 1<=i & i<=len f} is Subset-Family of TOP-REAL 2
proof
  let f;
  set F = {LSeg(f,i): 1<=i & i<=len f};
  F c= bool (REAL 2)
  proof
    let x be object;
    assume x in F;
    then ex i st LSeg(f,i)=x & 1<=i & i<=len f;
    then x is Subset of REAL 2 by EUCLID:22;
    hence thesis;
  end;
  hence thesis by EUCLID:22;
end;
