
theorem Th22:
  for V be non empty ModuleStr over F_Complex, f be Functional of
  V for v be Vector of V holds f.v = 0.F_Complex iff f*'.v = 0.F_Complex
proof
  let V be non empty ModuleStr over F_Complex, f be Functional of V;
  let v be Vector of V;
  thus f.v = 0.F_Complex implies f*'.v = 0.F_Complex by Def2,COMPLFLD:47;
  assume f*'.v = 0.F_Complex;
  then (f.v)*'*' = 0.F_Complex by Def2,COMPLFLD:47;
  hence thesis;
end;
