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].
Arguments reindex_omap [I J] h h' [P F].

Lemma reindex_onto (I J : finType) (h : J -> I) h' (P : pred I) F :
(forall i, P i -> h (h' i) = i) ->
\big[*%M/1]_(i | P i) F i =
\big[*%M/1]_(j | P (h j) && (h' (h j) == j)) F (h j).