case MaxEx with (r := r) (3 := pGivesBound); auto with arith.
intros x H'; exists x; red in |- *; auto.
case MinEx with (r := r) (3 := pGivesBound); auto with arith.
intros x H'; exists x; red in |- *; left; split; auto.
apply Rlt_le; auto.
Qed.

Theorem ToZeroCompatible : CompatibleP ToZeroP.
red in |- *.