Class Monotone_exp :=
  monotone_exp : forall ex ey, (ex <= ey)%Z -> (fexp ex <= fexp ey)%Z.Class Monotone_exp :=
  monotone_exp : forall ex ey, (ex <= ey)%Z -> (fexp ex <= fexp ey)%Z.Global Instance monotone_exp_not_FTZ : Exp_not_FTZ.

Theorem ln_beta_round_ge : forall x, round rnd x <> 0%R -> (ln_beta beta x <= ln_beta beta (round rnd x))%Z.