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.
Arguments big_enum_rank_cond [I A x] xA P F.

Lemma big_rev_mkord m n P F :
\big[op/idx]_(m <= k < n | P k) F k
= \big[op/idx]_(k < n - m | P (n - k.+1)) F (n - k.+1).