proposition: Lemma prodn_cond_gt0 I r (P : pred I) F : (forall i, P i -> 0 < F i) -> 0 < \prod_(i <- r | P i) F i.
proof: Proof. by move=> Fpos; elim/big_ind: _ => // n1 n2; rewrite muln_gt0 => ->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)