
theorem
  for F being Field for V being VectSp of F for W1,W2,W3,W4 being
  Subspace of V st W1 is Subspace of W2 & W3 is Subspace of W4 & (Omega).W1=
(Omega).W3 & (Omega).W2=(Omega).W4 holds pencil(W1,W2) = pencil(W3,W4) by Th6;
