
theorem
  for X being non empty compact TopSpace
  for F being Point of C_Normed_Algebra_of_ContinuousFunctions X holds
               0 <= ||.F.||
proof
  let X be non empty compact TopSpace;
  let F be Point of C_Normed_Algebra_of_ContinuousFunctions X;
  reconsider F1 = F as
       Point of C_Normed_Algebra_of_BoundedFunctions the carrier of X by Lm1;
  ||.F.|| = ||.F1.|| by FUNCT_1:49;
  hence 0 <= ||.F.|| by CC0SP1:20;
end;
