Section RND_FLT.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable emin prec : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Inductive FLT_format (x : R) : Prop :=
FLT_spec (f : float beta) :
x = F2R f -> (Z.abs (Fnum f) < Zpower beta prec)%Z ->
(emin <= Fexp f)%Z -> FLT_format x.
Definition FLT_exp e := Z.max (e - prec) emin.
(** Properties of the FLT format *)
Global Instance FLT_exp_valid : Valid_exp FLT_exp.
Proof with auto with typeclass_instances.
apply generic_inclusion_le...
intros e He.
unfold FIX_exp.
apply Z.max_lub.
omega.
apply Z.le_refl.
Qed.

Theorem ulp_FLT_small: forall x, (Rabs x < bpow (emin+prec))%R ->
ulp beta FLT_exp x = bpow emin.