replace (Fabs f) with f; auto; unfold Fabs in |- *; apply floatEq;
simpl in |- *; auto with zarith real.
apply sym_eq; apply Zabs_eq; apply LeR0Fnum with radix; auto with zarith real.
replace (Fabs f) with (Fopp f);
[ rewrite Fnormalize_Fopp | apply floatEq; simpl in |- * ];
auto with arith.
apply sym_eq; apply Zabs_eq_opp; apply R0LeFnum with radix;
auto with zarith real.
Qed.

Theorem RoundedModeUlp :
forall P,
RoundedModeP b radix P ->
forall (p : R) (q : float), P p q -> (Rabs (p - q) < Fulp q)%R.