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 bigD1 (I : finType) j (P : pred I) F :
P j -> \big[*%M/1]_(i | P i) F i
= F j * \big[*%M/1]_(i | P i && (i != j)) F i.