Module MyNat.
End MyNat.
Open Scope R_scope.
(** * Integers *)
(** Integer part in Z *)
Definition floor x := proj1_sig (floor_ex x).
Definition floor1 x := proj1_sig (floor1_ex x).
(** Interger part in nat *)

Lemma nfloor_ex : forall x : R, 0 <= x -> {n : nat | INR n <= x < INR n + 1}.