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 Th40:
  S-bound C <= (LMP C)`2
proof
  LMP C in C by Th31;
  hence thesis by PSCOMP_1:24;
end;
