intros p1 H'; Contradict H'; auto with real zarith.
intros p1 H'; absurd (INR (nat_of_P p1) = 0%R); auto with real zarith.
rewrite <- (Ropp_involutive (INR (nat_of_P p1))).
unfold IZR in H'; rewrite <- INR_IPR in H'.
rewrite H'; auto with real.
Qed.

(* Specifications: *)
Theorem INR_lt_nm : forall n m : nat, n < m -> (INR n < INR m)%R.
intros n m H'; elim H'; auto.