Proof with auto with typeclass_instances.
intros f Hf.
exists (Float beta (Ztrunc (scaled_mantissa beta fexp f)) (canonic_exp beta fexp f)).
assert (L:(f = F2R (Float beta (Ztrunc (scaled_mantissa beta fexp f)) (canonic_exp beta fexp f)))).
apply trans_eq with (round beta fexp Ztrunc f).
apply sym_eq, round_generic...
reflexivity.
split; trivial.
unfold canonic; rewrite <- L.
reflexivity.
Qed.

(* Specifications: *)
Theorem round_odd_prop: forall x,
round beta fexp (Znearest choice) (round beta fexpe Zrnd_odd x) =
round beta fexp (Znearest choice) x.
Theorem round_odd_prop: forall x,
round beta fexp (Znearest choice) (round beta fexpe Zrnd_odd x) =
round beta fexp (Znearest choice) x.