intros fexp x; unfold generic_format.
exists (Float beta (Ztrunc (scaled_mantissa beta fexp x)) (canonic_exp beta fexp x)).
split; auto.
Qed.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Notation format := (generic_format beta (FLX_exp prec)).
Notation cexp := (canonic_exp beta (FLX_exp prec)).
Variable choice : Z -> bool.

(* Specifications: *)
(** Remainder of the division in FLX *)
Theorem div_error_FLX :
forall rnd { Zrnd : Valid_rnd rnd } x y,
format x -> format y ->
format (x - round beta (FLX_exp prec) rnd (x/y) * y)%R.
(** Remainder of the division in FLX *)
Theorem div_error_FLX :
forall rnd { Zrnd : Valid_rnd rnd } x y,
format x -> format y ->
format (x - round beta (FLX_exp prec) rnd (x/y) * y)%R.