intros H1; Contradict H; apply Zle_not_lt.
apply le_IZR; auto.
Qed.
Hint Resolve Rlt_IZR: real.

(* Specifications: *)
Theorem Rle_IZR : forall x y : Z, (x <= y)%Z -> (IZR x <= IZR y)%R.
intros x y H'.