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 Th25:
  for C being non vertical compact Subset of TOP-REAL 2 holds UMP C <> E-max C
proof
  let C being non vertical compact Subset of TOP-REAL 2;
A1: (E-max C)`1 = E-bound C & (UMP C)`1 = (W-bound C + E-bound C)/2 by
EUCLID:52;
  assume UMP C = E-max C;
  hence thesis by A1,SPRECT_1:31;
end;
