Definition double_round_mult_hyp fexp1 fexp2 :=
  (forall ex ey, (fexp2 (ex + ey) <= fexp1 ex + fexp1 ey)%Z)
  /\ (forall ex ey, (fexp2 (ex + ey - 1) <= fexp1 ex + fexp1 ey)%Z).

Lemma ln_beta_minus_disj : forall x y, 0 < x -> 0 < y -> (ln_beta y <= ln_beta x - 2)%Z -> ((ln_beta (x - y) = ln_beta x :> Z) \/ (ln_beta (x - y) = (ln_beta x - 1)%Z :> Z)).