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.

Lemma cexp_ge_bpow :
forall (x : R) (e : Z),
(bpow (e - 1) <= Rabs x)%R ->
(fexp e <= cexp x)%Z.