 reserve
  S for non empty TopSpace,
  T for LinearTopSpace,
  X for non empty Subset of the carrier of S;
 reserve
    S,T for RealNormSpace,
    X for non empty Subset of the carrier of S;

theorem
  for S be non empty compact TopSpace,T be NormedLinearTopSpace
  for F be Point of R_NormSpace_of_ContinuousFunctions(S,T)
    holds 0 <= ||.F.||
proof
  let S be non empty compact TopSpace,T be NormedLinearTopSpace;
  let F be Point of R_NormSpace_of_ContinuousFunctions(S,T);
  reconsider F1=F as Point of
    R_NormSpace_of_BoundedFunctions(the carrier of S,T) by Th34;
  ||.F.|| =||.F1.|| by FUNCT_1:49;
  hence thesis;
end;
