
theorem Th8:
  for X being non empty set holds
    0.C_Algebra_of_BoundedFunctions X = X -->0
proof
  let X be non empty set;
A1:C_Algebra_of_BoundedFunctions X is ComplexSubAlgebra of CAlgebra X by Th2;
  0.CAlgebra X = X -->0;
  hence thesis by A1,Th3;
end;
