case (le_lt_or_eq _ _ H'1); intros H'2.
apply Rlt_dichotomy_converse; auto with real.
Contradict H'; auto.
apply Compare.not_eq_sym; apply Rlt_dichotomy_converse; auto with real.
Qed.
Hint Resolve NEq_INR: real.

Theorem NEq_INRO : forall n : nat, n <> 0 -> INR n <> 0%R.
replace 0%R with (INR 0); auto with real.