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 Th52:
  a < b & c < d implies
  Fr closed_inside_of_rectangle(a,b,c,d) = rectangle(a,b,c,d)
proof
  assume that
A1: a < b and
A2: c < d;
  set P = closed_inside_of_rectangle(a,b,c,d);
  thus Fr P = P \ Int P by TOPS_1:43
    .= P \ inside_of_rectangle(a,b,c,d) by A1,A2,Th50
    .= rectangle(a,b,c,d) by A1,A2,Th51;
end;
