
theorem Th27:
  for a being Complex
  for X being non empty compact TopSpace
  for F being Point of C_Normed_Algebra_of_ContinuousFunctions X holds
  ||.(a*F).|| = |.a.|*||.F.||
proof
  let a be Complex;
  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;
  thus ||.(a * F).|| = ||.(a * F1).|| by Lm5,Lm3
                 .= |.a.| * ||.F1.|| by CC0SP1:25
                 .= |.a.| * ||.F.|| by FUNCT_1:49;
end;
