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].
Arguments bigD1 [I] j [P F].
Arguments cardD1x [I A].
Arguments partition_big [I s J P] p Q [F].

Lemma big_image_cond I (J : finType) (h : J -> I) (A : pred J) (P : pred I) F :
\big[*%M/1]_(i <- [seq h j | j in A] | P i) F i
= \big[*%M/1]_(j in A | P (h j)) F (h j).