intros r p H' H'0 H'1.
split; auto.
split; auto.
intros f H'2 H'3.
case (Rle_or_lt f p); auto; intros H'5.
Contradict H'3.
(* If we are between a bound and its successor, it is our minimum *)
apply Rlt_not_le.
apply Rlt_le_trans with (1 := H'1); auto with real.
replace (FtoRradix f) with (FtoRradix (Fnormalize radix b precision f)).
unfold FtoRradix in |- *; apply FNSuccProp; auto; try apply FnormalizeCanonic;
auto.
unfold FtoRradix in |- *; repeat rewrite FnormalizeCorrect; auto with real.
apply FcanonicBound with (radix := radix); auto.
apply FnormalizeCanonic; auto.
unfold FtoRradix in |- *; rewrite FnormalizeCorrect; auto with real.
unfold FtoRradix in |- *; rewrite FnormalizeCorrect; auto with real.
Qed.

Theorem FminRep :
forall p q : float,
isMin p q -> exists m : Z, q = Float m (Fexp p) :>R.