intros x y z; unfold Rmin.
destruct (Rle_dec y z);
destruct (Rle_dec x y);
destruct (Rle_dec x z);
destruct (Rle_dec y z) ; try intuition.
contradict n.
apply Rle_trans with y ; auto.
contradict r.
apply Rlt_not_le, Rlt_trans with y ; apply Rnot_le_lt ; auto.
Qed.

Lemma Rmax_assoc : forall x y z, Rmax x (Rmax y z) =
Rmax (Rmax x y) z.