theorem Th11: :: PENCIL_4:11

for F being Field
for V being finite-dimensional VectSp of F
for W1, W2, P, Q being Subspace of V
for k being Nat st (dim W1) + 1 = k & dim W2 = k + 1 & P in pencil (W1,W2,k) & Q in pencil (W1,W2,k) & P <> Q holds
( P /\ Q = (Omega). W1 & P + Q = (Omega). W2 )