Proof with eauto 15 with reg_renamings val_renamings.
intros.
assert (Hinjective := injective (weak_obs_eq Hmem_obs_eq)).
unfold compare_ints...
Qed.

(* Specifications: *)
Lemma compare_longs_ren:
forall f v1 v2 v1' v2' rs rs' m m'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2')
(Hrs_ren: regset_ren f rs rs')
(Hmem_obs_eq: mem_obs_eq f m m'),
regset_ren f (compare_longs v1 v2 rs m)
(compare_longs v1' v2' rs' m').