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

Lemma bigfcupP x F P :
reflect (exists2 i : I, (i \in r) && P i & x \in F i)
(x \in \bigcup_(i <- r | P i) F i).