proposition: Lemma prod_nat_seq_neq0 I r (P : pred I) F : (\prod_(i <- r | P i) F i != 0)%N = all (fun i => P i ==> (F i != 0%N)) r.
proof: Proof. by rewrite prod_nat_seq_eq0 -all_predC; apply: eq_all => i /=; case: (P i). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)