Definition R_fact (x y : Z) :=
  1 < x /\ 1 < y /\ exists q : Z, y = q * x /\ 1 < q.

(* Specifications: *)
Lemma R_fact_wf : well_founded R_fact.
Lemma ind_fact : forall P : Z -> Prop, (forall x : Z, (forall y : Z, (R_fact y x -> P y)) -> P x) -> forall x : Z, P x.
Lemma Zfact : forall a : Z, 1 < a -> exists b : Z, (b | a) /\ prime b.