
theorem
  for F being Field for V being finite-dimensional VectSp of F for k
  being Nat 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,k) = pencil(W3,W4,k) by Th6;
