theorem Th14: :: PENCIL_4:14

for F being Field
for V being finite-dimensional VectSp of F
for W being Subspace of V
for v, u being Vector of V st v <> u & {v,u} is linearly-independent & W /\ (Lin {v,u}) = (0). V holds
dim (W + (Lin {v,u})) = (dim W) + 2