reserve X,X1 for set,
  r,s for Real,
  z for Complex,
  RNS for RealNormSpace,
  CNS, CNS1,CNS2 for ComplexNormSpace;

theorem
  for f be PartFunc of the carrier of CNS,REAL, Y be Subset of CNS st Y
<> {} & Y c= dom f & Y is compact & f is_uniformly_continuous_on Y ex x1,x2 be
  Point of CNS st x1 in Y & x2 in Y & f/.x1 = upper_bound (f.:Y) & f/.x2 =
  lower_bound (f.:Y) by Th23,NCFCONT1:96;
