
theorem
  for V be add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital
non empty ModuleStr over F_Complex for f be antilinear-Functional of V holds
  ker f is linearly-closed
proof
  let V be add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital non
  empty ModuleStr over F_Complex, f be antilinear-Functional of V;
  ker f = ker f*' by Th23;
  hence thesis by VECTSP10:33;
end;
