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.
Definition fixset := iterF n.
Hint Resolve fixsetK : core.

Lemma in_iter (x : T) k : x \in fixset -> fix_order x <= k -> x \in iterF k.