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 Th46:
  inside_of_rectangle(a,b,c,d) c= closed_inside_of_rectangle(a,b,c,d)
proof
  let x be object;
  assume x in inside_of_rectangle(a,b,c,d);
  then ex p st x = p & a < p`1 & p`1 < b & c < p`2 & p`2 < d;
  hence thesis;
end;
