reserve n for Element of NAT,
  V for Subset of TOP-REAL n,
  s,s1,s2,t,t1,t2 for Point of TOP-REAL n,
  C for Simple_closed_curve,
  P for Subset of TOP-REAL 2,
  a,p ,p1,p2,q,q1,q2 for Point of TOP-REAL 2;

theorem Th21:
  for C being Subset of TOP-REAL 2 holds LSeg(North-Bound(p,C),
  South-Bound(p,C)) is vertical
proof
  let C be Subset of TOP-REAL 2;
  North-Bound(p,C)`1 = p`1 & South-Bound(p,C)`1 = p`1 by EUCLID:52;
  hence thesis by SPPOL_1:16;
end;
