  We are concerned with two separation theorems about analytic sets by Dyck and
Preiss, the former involves the positively-defined subsets of the Cantor space
and the latter the Borel-convex subsets of finite dimensional Banach spaces. We
show by introducing the corresponding separation trees that both of these
results admit a constructive proof. This enables us to give the uniform version
of the separation theorems, and derive as corollaries the results, which are
analogous to the fundamental fact "HYP is effectively bi-analytic" provided by
the Souslin-Kleene Theorem.
