(** All numbers in natlist are prime. *)

Definition allPrime : natlist -> Prop := alllist nat Prime.Definition allZPrime : Zlist -> Prop := alllist Z ZPrime.

(* Specifications: *)
Lemma allzprimeallpos : forall l : Zlist, allZPrime l -> allPos l.
Lemma allprimeallzprime : forall l : natlist, allPrime l -> allZPrime (map _ _ Z_of_nat l).
Lemma allzprimeallprime : forall l : Zlist, allZPrime l -> allPrime (map _ _ Zabs_nat l).