(** Multiply all elements in list with a *)

Definition mapmult (a : Z) (l : Zlist) := map Z Z (fun x : Z => (a * x)%Z) l.

Lemma inlist_inj_abs_pos_list : forall (q : nat) (l : Zlist), allPos l -> inlist nat q (map Z nat Zabs_nat l) -> inlist Z (Z_of_nat q) l.