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].
Arguments big_enum_val_cond [I A] P F.

Lemma big_enum_rank_cond (I : finType) (A : pred I) x (xA : x \in A) P F
(h := enum_rank_in xA) :
\big[op/idx]_(i < #|A| | P i) F i = \big[op/idx]_(s in A | P (h s)) F (h s).