induction a;
simpl in *; try apply le_s; auto.
Qed.
Definition nat_to_pos (n : nat) : (n <> 0) -> positive :=
fun _ => (P_of_succ_nat (pred n)).

(* Specifications: *)
Lemma double_nat_nz : forall(a : nat)(pf : a <> 0),
((2 * a) <> 0).