Section ListDenoteSeparate.
Context {X Y B : Type}.
Variables (f : X -> pred B) (g : Y -> pred B) (b : pred B) (l1 : list X)
(l2 : list Y).

Lemma listd_separate :
listd f inter (listd g inter b l2) l1 =
andp (listd f inter TT l1) (andp (listd g inter TT l2) b).