It's a corollary of the fact that
dim(W)+dim(annihilator(W))=
dim(V). All f_i's form a basis for the dual space of V and for i>k+1, f_i belongs to the annihilators. Literally can't figure this one out, I just can't wrap my head around the fact one needs precisely n-k hyperspaces of V to construct W, WHICH IS THE DIMENSION OF THE ANNIHILATOR