Proof with auto with typeclass_instances.
intros x e Fx He.
exists (Ztrunc (scaled_mantissa beta fexp x)*Zpower beta (cexp x -e))%Z.
rewrite Fx at 1; unfold F2R; simpl.
rewrite Z2R_mult, Rmult_assoc.
f_equal.
rewrite Z2R_Zpower.
2: omega.
rewrite <- bpow_plus; f_equal; ring.
Qed.

(* Specifications: *)
Lemma ln_beta_minus1 :
forall z, z <> 0%R ->
(ln_beta beta z - 1)%Z = ln_beta beta (z / Z2R beta).
Theorem round_plus_mult_ulp :
forall x y, format x -> format y -> (x <> 0)%R ->
exists m, (round beta fexp rnd (x+y) = Z2R m * ulp beta fexp (x/Z2R beta))%R.