Section BigSetOps.
Variables T I : finType.
Implicit Types (U : {pred T}) (P : pred I) (A B : {set I}) (F :  I -> {set T}).

Lemma bigcup_disjoint U P F :
(forall i, P i -> [disjoint U & F i]) -> [disjoint U & \bigcup_(i | P i) F i].