Section BigFsetDep.
Variables (R : Type) (idx : R) (op : Monoid.com_law idx)
(I : choiceType) (J : choiceType) (K : choiceType).

Lemma pair_big_dep_cond (A : {fset I}) (B : I -> {fset J})
(P : pred I) (Q : I -> pred J) (F : I -> J -> R) :
\big[op/idx]_(i <- A | P i) \big[op/idx]_(j <- B i | Q i j) F i j =
\big[op/idx]_(p <- [fset ((i, j) : I * J) | i in [fset i in A | P i],
j in [fset j in B i | Q i j]]) F p.1 p.2.