reserve p,p1,p2,p3,q,q1,q2 for Point of TOP-REAL 2,
  i for Nat,
  lambda for Real;

theorem
  for p1,p2,p3,p4 being Point of TOP-REAL 2,
  P being non empty compact Subset of TOP-REAL 2 st
  P is being_simple_closed_curve & p1 in P & p2 in P & p3 in P & p4 in P &
  LE p2,p3,P & LE p3,p4,P holds
  LE p1,p2,P or LE p2,p1,P & LE p1,p3,P or LE p3,p1,P & LE p1,p4,P or
  LE p4,p1,P by Th73;
