Proof with eauto 10 with reg_renamings val_renamings.
intros.
unfold compare_floats32;
destruct v1; inversion Hval_obs; subst;
destruct v2; inversion Hval_obs'; subst...
Qed.

Lemma compare_floats_ren:
forall f rs rs' v1 v2 v1' v2'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2')
(Hrs_ren: regset_ren f rs rs'),
regset_ren f (compare_floats v1 v2 rs)
(compare_floats v1' v2' rs').