Lemma 3.1: S is a blocking set in if and only if the intersection of any plane not containing V with the cone C(V,S) is a blocking set in that plane.
Pf: Suppose that the carrier S of a cone C(V,S) is a blocking set in its carrier plane . Let be any other plane of PG(3,q) not containing the point V. Let S' be the intersection of C(V,S) with . If l' is a line of which does not contain a point of S', then let the projection of l' from V into be denoted by l. Since S is a blocking set, there is a point P of S on l. The line VP lies in the plane determined by V and l', and so, it must intersect l' at a point P'. P' lies on a generator of the cone (i.e., VP) and in the plane , so it must be in S'. This contradiction shows that S' is a blocking set in .
On the other hand, S is the intersection of the cone with the plane , which does not contain V. Therefore, by assumption, S is a blocking set in .