Fixpoint pow2 (n : nat) : nat :=
  match n with
    | O => 1%nat
    | S n => (2 * pow2 n)%nat
  end.

Lemma Rdiv_lt_0_compat : forall r1 r2 : R, 0 < r1 -> 0 < r2 -> 0 < r1 / r2.