(****************************************************************************  IEEE754  :  Zenum  Laurent Thery  ***************************************************************************** Simple functions to enumerate relative numbers *)
Require Export Faux.
Require Export Omega.
Require Export List.
(* Returns the list of relative numbers from z to z+n *)
Fixpoint mZlist_aux (p : Z) (n : nat) {struct n} :
list Z :=
match n with
| O => p :: nil
| S n1 => p :: mZlist_aux (Z.succ p) n1
end.
intros n; elim n; clear n; auto.
intros p q; try rewrite <- Zplus_0_r_reverse.
intros H' H'0; simpl in |- *; left.
apply Zle_antisym; auto.
intros n H' p q H'0 H'1; case (Zle_lt_or_eq _ _ H'0); intros H'2.
simpl in |- *; right.
apply H'; auto with zarith.
rewrite Zplus_succ_comm.
rewrite <- inj_S; auto.
simpl in |- *; auto.
Qed.
intros n; elim n; clear n; simpl in |- *; auto.
intros p q H'; elim H'; auto with zarith.
intros n H' p q H'0; elim H'0; auto with zarith.
intros H'1; apply Zle_succ_le; auto with zarith.
Qed.

Theorem mZlist_aux_correct_rev2 :
forall (n : nat) (p q : Z),
In q (mZlist_aux p n) -> (q <= p + Z_of_nat n)%Z.