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].
Arguments reindex_onto [I J] h h' [P F].
Arguments reindex [I J] h [P F].

Lemma reindex_inj (I : finType) (h : I -> I) (P : pred I) F :
injective h -> \big[*%M/1]_(i | P i) F i = \big[*%M/1]_(j | P (h j)) F (h j).