Section Double_round_mult.

Lemma ln_beta_mult_disj :
forall x y,
x <> 0 -> y <> 0 ->
((ln_beta (x * y) = (ln_beta x + ln_beta y - 1)%Z :> Z)
\/ (ln_beta (x * y) = (ln_beta x + ln_beta y)%Z :> Z)).