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 Th49:
  closed_inside_of_rectangle(a,b,c,d) /\ inside_of_rectangle(a,b,c,d)
  = inside_of_rectangle(a,b,c,d)
proof
  set R = closed_inside_of_rectangle(a,b,c,d);
  set P1 = inside_of_rectangle(a,b,c,d);
  thus R /\ P1 c= P1 by XBOOLE_1:17;
  P1 /\ P1 c= P1 /\ R by Th46,XBOOLE_1:26;
  hence thesis;
end;
