proposition: Lemma prodrMn (I : Type) (s : seq I) (P : pred I) (F : I -> R) (g : I -> nat) : \prod_(i <- s | P i) (F i *+ g i) = \prod_(i <- s | P i) (F i) *+ \prod_(i <- s | P i) g i.
proof: Proof. by elim/big_rec3: _ => // i y1 y2 y3 _ ->; rewrite mulrnAr mulrnAl -mulrnA. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)