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 CNS1,CNS2, Y be Subset of CNS1 st Y c= dom f & Y
  is compact & f is_uniformly_continuous_on Y holds f.:Y is compact by Th19,
