Hi, can someone prove this corollary about marginal dirichlet? And explain to me how it was done? Thank you so much

This problem is from Theory of Multivariate Statistics by Bilodeau and Brenner. It is so difficult to obtain solution manual on this. And the reference itself is very general and lacking of proofs.

with zi indep G(p;). i = 1, ..., n + 1, z = (21, . . ., Zn), and T = Zil zi. We find the following: Corollary 3.2 (Marginal Dirichlet) Ifx1 = (Xi, . .., lik ) denotes any subset of the coordinates, then x1 ~ Dr (P1; q) with p1 = (Pu , . . ., Pix) and p=q+>j=1Pi