intros r1 r2 min max H' H'0 H'1 H'2; split.
case H'; auto.
split.
apply Rlt_le; auto.
intros f H'3 H'4.
case H'; auto.
intros H'5 H'6; elim H'6; intros H'7 H'8; apply H'8; clear H'6; auto.
case (Rle_or_lt (FtoR radix f) r1); auto; intros C1.
absurd (FtoR radix f < max)%R.
apply Rle_not_lt.
case H'0.
intros H'6 H'9; elim H'9; intros H'10 H'11; apply H'11; clear H'9; auto.
apply Rlt_le; auto.
apply Rle_lt_trans with (2 := H'2); auto.
Qed.

Theorem isMaxComp :
forall (r1 r2 : R) (min max : float),
isMin b radix r1 min ->
isMax b radix r1 max -> (min < r2)%R -> (r2 < max)%R -> isMax b radix r2 max.