
theorem
  for V be non empty ModuleStr over F_Complex, f be Form of V,V holds
  diagker f = diagker f*'
proof
  let V be non empty ModuleStr over F_Complex, f be Form of V,V;
  set K = F_Complex;
  thus diagker f c= diagker f*'
  proof
    let x be object;
    assume x in diagker f;
    then consider v be Vector of V such that
A1: x=v and
A2: f.(v,v)= 0.K;
    (f*').(v,v) = 0.K by A2,Def8,COMPLFLD:47;
    hence thesis by A1;
  end;
  let x be object;
  assume x in diagker f*';
  then consider v be Vector of V such that
A3: x=v and
A4: f*'.(v,v)= 0.K;
  (f.(v,v))*'*' = 0.K by A4,Def8,COMPLFLD:47;
  hence thesis by A3;
end;
