reserve C for Simple_closed_curve,
  P for Subset of TOP-REAL 2,
  p for Point of TOP-REAL 2,
  n for Element of NAT;
reserve D for compact with_the_max_arc Subset of TOP-REAL 2;

theorem Th39:
  (UMP C)`2 <= N-bound C
proof
  UMP C in C by Th30;
  hence thesis by PSCOMP_1:24;
end;
