case H; intros.
- red; left.
apply Rlt_mult_inv_pos; auto with real.
- rewrite <- H1.
red; right; ring.
Qed.

Lemma sqrt_cauchy :
forall a b c d:R,
a * c + b * d <= sqrt (Rsqr a + Rsqr b) * sqrt (Rsqr c + Rsqr d).