reserve a, b, c, d, r, s for Real,
  n for Element of NAT,
  p, p1, p2 for Point of TOP-REAL 2,
  x, y for Point of TOP-REAL n,
  C for Simple_closed_curve,
  A, B, P for Subset of TOP-REAL 2,
  U, V for Subset of (TOP-REAL 2)|C`,
  D for compact with_the_max_arc Subset of TOP-REAL 2;

theorem Th48:
  closed_inside_of_rectangle(a,b,c,d) misses outside_of_rectangle(a,b,c,d)
proof
  set R = closed_inside_of_rectangle(a,b,c,d);
  set P2 = outside_of_rectangle(a,b,c,d);
  assume R meets P2;
  then consider x being object such that
A1: x in R and
A2: x in P2 by XBOOLE_0:3;
A3: ex p st x = p & a <= p`1 & p`1 <= b & c <= p`2 & p`2 <= d by A1;
  ex p st x = p & not (a <= p`1 & p`1 <= b & c <= p`2 & p`2 <= d) by A2;
  hence thesis by A3;
end;
