(* Truncated real log. *)

(* Specifications: *)
Lemma trunc_log_bounds p n :
1 < p -> 0 < n -> let k := trunc_log p n in p ^ k <= n < p ^ k.+1.
Lemma trunc_log_ltn p n : 1 < p -> n < p ^ (trunc_log p n).+1.
Lemma trunc_logP p n : 1 < p -> 0 < n -> p ^ trunc_log p n <= n.
Canonical nat_pred_pred := Eval hnf in [predType of nat_pred].