Proof with auto with typeclass_instances.
intros x e Hx Fx.
apply FLX_format_generic.
apply generic_format_FIX in Fx.
revert Fx.
apply generic_inclusion with (e := e)...
apply Zle_refl.
Qed.
(** unbounded floating-point format with normal mantissas *)
Definition FLXN_format (x : R) :=
exists f : float beta,
x = F2R f /\ (x <> R0 ->
Zpower beta (prec - 1) <= Zabs (Fnum f) < Zpower beta prec)%Z.

Theorem FLXN_format_generic :
forall x, generic_format beta FLX_exp x -> FLXN_format x.