End big_com.

(* Specifications: *)
Lemma sum_mset (X : {mset K}) (P : pred K) (F : K -> nat) :
\sum_(i <- X | P i) F i = \sum_(i <- finsupp X | P i) X i * F i.
Lemma prod_mset (X : {mset K}) (P : pred K) (F : K -> nat) :
\prod_(i <- X | P i) F i = \prod_(i <- finsupp X | P i) F i ^ X i.
Lemma msetME A B (u : K * K) : (A `*` B) u = A u.1 * B u.2.
Lemma mset1DE a A b : (a +` A) b = (b == a) + A b.
Lemma in_msetM A B (u : K * K) : (u \in A `*` B) = (u.1 \in A) && (u.2 \in B).
Section big.