intros P p r H' H'0 H'1.
case H'.
intros H'2 H'3; Elimc H'3; intros H'3 H'4; Elimc H'4; intros H'4 H'5;
case (H'4 r p); auto; intros H'6.
apply RleMinR0 with (r := r); auto.
apply Rle_trans with r; auto; apply isMax_inv1 with (1 := H'6).
Qed.

Theorem RleMaxR0 :
forall (r : R) (max : float),
(r <= 0)%R -> isMax b radix r max -> (max <= 0)%R.