Section FsetBigOps.
Variables (R : Type) (idx : R) (op : Monoid.com_law idx).
Let rhs_cond P K E :=
(\big[op/idx]_(A <- P) \big[op/idx]_(x <- A | K x) E x)%fset.
Let rhs P E := (\big[op/idx]_(A <- P) \big[op/idx]_(x <- A) E x)%fset.

Lemma partition_disjoint_bigfcup (f : T -> R) (F : I -> {fset T})
(K : {fset I}) :
(forall i j, i != j -> [disjoint F i & F j])%fset ->
\big[op/idx]_(i <- \big[fsetU/fset0]_(x <- K) (F x)) f i =
\big[op/idx]_(k <- K) (\big[op/idx]_(i <- F k) f i).