End not_FTZ.
Section monotone_exp.
Class Monotone_exp :=
monotone_exp : forall ex ey, (ex <= ey)%Z -> (fexp ex <= fexp ey)%Z.
Context { monotone_exp_ : Monotone_exp }.
Global Instance monotone_exp_not_FTZ : Exp_not_FTZ.

(* Specifications: *)
Lemma canonic_exp_le_bpow :
forall (x : R) (e : Z),
x <> 0%R ->
(Rabs x < bpow e)%R ->
(canonic_exp x <= fexp e)%Z.
Lemma canonic_exp_ge_bpow :
forall (x : R) (e : Z),
(bpow (e - 1) <= Rabs x)%R ->
(fexp e <= canonic_exp x)%Z.
Lemma canonic_exp_le_bpow :
forall (x : R) (e : Z),
x <> 0%R ->
(Rabs x < bpow e)%R ->
(canonic_exp x <= fexp e)%Z.
Lemma canonic_exp_ge_bpow :
forall (x : R) (e : Z),
(bpow (e - 1) <= Rabs x)%R ->
(fexp e <= canonic_exp x)%Z.