(** [Pos.to_nat] and other operations *)

(* Specifications: *)
Lemma inj_min p q :
to_nat (min p q) = Nat.min (to_nat p) (to_nat q).
Lemma inj_max p q :
to_nat (max p q) = Nat.max (to_nat p) (to_nat q).
Theorem inj_iter p {A} (f:A->A) (x:A) :
Pos.iter f x p = nat_rect _ x (fun _ => f) (to_nat p).
Theorem inj_pow p q : to_nat (p ^ q) = to_nat p ^ to_nat q.
End Pos2Nat.