  We say that a finite set S of points in R^d is in "strong general position"
if for any collection {F_1,..., F_r} of r pairwise disjoint subsets of S (1 <=
r <= |S|) we have: d-dim (the intersection of aff F_1,aff F_2,...,aff F_r) =
min{d+1, (d-dim aff F_1)+(d-dim aff F_2)+...+(d-dim aff F_r)}. In this paper we
reduce the set of conditions that one has to check in order to determine if S
is in "strong general position".
