
theorem
  for V be VectSp of F_Complex, f be diagReR+0valued hermitan-Form of V
for A,B be Vector of VectQuot(V,LKer(f)), v,w be Vector of V st A = v + LKer f
  & B = w + LKer f holds (ScalarForm(f)).(A,B) = f.(v,w)
proof
  let V be VectSp of F_Complex, f be diagReR+0valued hermitan-Form of V;
  set vq = VectQuot(V,LKer(f)), vr = VectQuot(V,RKer(f*'));
  let A,B be Vector of vq, v,w be Vector of V;
  reconsider W = B as Vector of vr by Th56;
  assume that
A1: A = v + LKer f and
A2: B = w + LKer f;
  W = w + RKer(f*') by A2,Th56;
  hence thesis by A1,Def12;
end;
