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.
End FsetBigOps.
End FsetPartitions.

Lemma fset_bounded_coind (T : choiceType) (P : {fset T} -> Type) (U : {fset T}):
(forall X, (forall Y, Y `<=` U -> X `<` Y -> P Y) -> P X) ->
forall X, X `<=` U -> P X.