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 Rle_trans with r; auto; apply isMin_inv1 with (1 := H'6).
apply RleMaxR0 with (r := r); auto.
Qed.

Theorem PminPos :
forall p min : float,
(0 <= p)%R ->
Fbounded b p ->
isMin b radix (/ 2%nat * p) min ->
exists c : float, Fbounded b c /\ c = (p - min)%R :>R.