**Proposition 11.2.4**: *Let F = F(t ^{a}, t, t^{b}) be a monomial semi-field type flock in PG(3,q) with q = p^{n} for some prime p, a = p^{i}, b = p^{j} with 0 < i < j < n. In the dual setting, the relation of parallelism on the lines containing at least two points of D_{F} is an equivalence relation.*

*Pf*: Let m_{1}, m_{2} and m_{3} be three lines of PG(3,q), each containing at least two points of D_{F}, with m_{1} || m_{2} and m_{2} || m_{3} in their respective affine planes. In the completion of the affine plane containing m_{1} and m_{2}, these lines meet at a point P of W'=0. In the completion of the affine plane containing m_{2} and m_{3}, these lines must also meet at a point of W'=0. Since this point is on m_{2}, it must also be P. Thus, m_{1} and m_{3} meet at P. In the affine plane determined by m_{1} and m_{3}, these lines are parallel since they meet at P on W'=0. Therefore, the relation of parallelism is transitive, and so, is an equivalence relation.