apply Rmult_lt_reg_l with (r := INR 2); auto with real.
rewrite <- Rmult_assoc; rewrite Rinv_r.
apply Rmult_lt_compat_r; replace 1%R with (INR 1); auto with real arith.
replace 0%R with (INR 0); auto with real arith.
Qed.
Hint Resolve Rledouble: real.

Theorem Rle_Rinv : forall x y : R, (0 < x)%R -> (x <= y)%R -> (/ y <= / x)%R.
intros x y H H1; case H1; intros H2.