
theorem Th9:
  for X being non empty set holds
    1_C_Algebra_of_BoundedFunctions X = X --> 1r
proof
  let X be non empty set;
A1:C_Algebra_of_BoundedFunctions X is ComplexSubAlgebra of CAlgebra X by Th2;
   1_CAlgebra X = X -->1r;
   hence thesis by A1,Th3;
end;
