Proof with auto with typeclass_instances.
intros x.
destruct (Req_dec (round Zfloor x) x) as [Hx|Hx].
left.
rewrite <- Hx.
apply generic_format_round...
right.
intros H.
apply Hx.
apply round_generic...
Qed.
Section round_large.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.

(* Specifications: *)
Theorem round_large_pos_ge_pow :
forall x e,
(0 < round rnd x)%R ->
(bpow e <= x)%R ->
(bpow e <= round rnd x)%R.
Theorem round_large_pos_ge_pow :
forall x e,
(0 < round rnd x)%R ->
(bpow e <= x)%R ->
(bpow e <= round rnd x)%R.