
theorem
  for K be ZeroStr, V be non empty ModuleStr over K for f be Form of V,V
  holds leftker f c= diagker f & rightker f c= diagker f
proof
  let K be ZeroStr, V be non empty ModuleStr over K, f be Form of V,V;
  thus leftker f c= diagker f
  proof
    let x be object;
    assume x in leftker f;
    then consider v be Vector of V such that
A1: v=x and
A2: for w be Vector of V holds f.(v,w)=0.K;
    f.(v,v) = 0.K by A2;
    hence thesis by A1;
  end;
  let x be object;
  assume x in rightker f;
  then consider v be Vector of V such that
A3: v=x and
A4: for w be Vector of V holds f.(w,v)=0.K;
  f.(v,v) = 0.K by A4;
  hence thesis by A3;
end;
