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

(* It is very hard to use this lemma, because the unification fails to *)
(* defer the F j pattern (even though it's a Miller pattern!).         *)
Lemma bigcup_sup j P F : P j -> F j \subset \bigcup_(i | P i) F i.