(** Interger part in nat *)

(* Specifications: *)
Lemma nfloor_ex : forall x : R, 0 <= x -> {n : nat | INR n <= x < INR n + 1}.
Definition nfloor x pr := proj1_sig (nfloor_ex x pr).
Lemma nfloor1_ex : forall x : R, 0 < x -> {n : nat | INR n < x <= INR n + 1}.
Definition nfloor1 x pr := proj1_sig (nfloor1_ex x pr).