End Double_round_mult_FTZ.
End Double_round_mult.
Section Double_round_plus.

Lemma ln_beta_plus_separated :
forall fexp : Z -> Z,
forall x y,
0 < x -> 0 <= y ->
generic_format beta fexp x ->
(ln_beta y <= fexp (ln_beta x))%Z ->
(ln_beta (x + y) = ln_beta x :> Z).