Section Abelian.
Variable op : Monoid.com_law 1.
Local Notation "'*%M'" := op (at level 0).
Local Notation "x * y" := (op x y).
Arguments bigID [I r].

Lemma bigU (I : finType) (A B : pred I) F :
[disjoint A & B] ->
\big[*%M/1]_(i in [predU A & B]) F i =
(\big[*%M/1]_(i in A) F i) * (\big[*%M/1]_(i in B) F i).