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

theorem Th64:
  for p1,p2 being Point of TOP-REAL 2
  st LE p1,p2,rectangle(-1,1,-1,1) & p1 in LSeg(|[-1,-1]|,|[-1,1]|)
  holds p2 in LSeg(|[-1,-1]|,|[-1,1]|)& p2`2>=p1`2 or
  p2 in LSeg(|[-1,1]|,|[1,1]|) or p2 in LSeg(|[1,1]|,|[1,-1]|)
  or p2 in LSeg(|[1,-1]|,|[-1,-1]|)& p2<>|[-1,-1]|
proof
  let p1,p2 be Point of TOP-REAL 2;
  set K = rectangle(-1,1,-1,1);
  assume that
A1: LE p1,p2,K and
A2: p1 in LSeg(|[-1,-1]|,|[-1,1]|);
  p2 in LSeg(|[-1,-1]|,|[-1,1]|) & p1`2<=p2`2
  or p2 in LSeg(|[-1,1]|,|[1,1]|) or p2 in LSeg(|[1,1]|,|[1,-1]|)
  or p2 in LSeg(|[1,-1]|,|[-1,-1]|) & p2<>W-min(K) by A1,A2,Th59;
  hence thesis by Th46;
end;
