proposition: Lemma sum_nat_seq_eq0 I r (P : pred I) F : (\sum_(i <- r | P i) F i == 0)%N = all (fun i => P i ==> (F i == 0%N)) r.
proof: Proof. by rewrite (big_morph _ (id1:=true) addn_eq0)// big_all_cond. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)