Section BigFOpsSeq.
Variables (T : choiceType) (I : eqType) (r : seq I).
Implicit Types (P : pred I) (F :  I -> {fset T}).

Lemma bigfcupsP (U : {fset T}) P F :
reflect (forall i : I, i \in r -> P i -> F i `<=` U)
(\bigcup_(i <- r | P i) F i `<=` U).