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 *)
Definition nfloor x pr := proj1_sig (nfloor_ex x pr).
Definition nfloor1 x pr := proj1_sig (nfloor1_ex x pr).
(** More theorems about INR *)

Lemma Rlt_nat (x : R) : (exists n : nat, x = INR (S n)) -> 0 < x.