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.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.

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