Definition eq := zeq.Module ZMap := IMap(ZIndexed).Definition t := N.Definition index (n: N): positive :=
    match n with
    | N0 => xH
    | Npos p => xO p
    end.

(* Specifications: *)
Lemma index_inj: forall (x y: N), index x = index y -> x = y.
Lemma eq: forall (x y: N), {x = y} + {x <> y}.