Module X86Inj.
(** Injections on registers *)
Definition reg_ren f (r:PregEq.t) (rs rs' : regset) : Prop :=
val_obs f (Pregmap.get r rs) (Pregmap.get r rs').
Definition regset_ren f rs rs' : Prop :=
forall r, reg_ren f r rs rs'.
Definition core_inj f c c' :=
match c, c' with State rs _, State rs' _ => regset_ren f rs rs' end.
Include X86WD.
(* Lemma decode_longs_val_obs_list: forall f (vals vals' : seq val) tys (Hobs_eq: val_obs_list f vals vals'), val_obs_list f (val_casted.decode_longs tys vals) (val_casted.decode_longs tys vals'). *)
(** ** Proof that related states take related steps*)
Proof with eauto with renamings.
intros.
destruct Hge_wd as (? & ?).
unfold Senv.symbol_address in *.
specialize (H0 id ofs _ ltac:(reflexivity)).
destruct (Senv.find_symbol g id) eqn:Hsymb; constructor.
destruct H0 as [b' Hfg'].
assert (Heq := Hfg _ _ Hfg'); subst...
Qed.

Lemma eval_builtin_arg_ren:
forall (g : genv) (rs rs' : regset) (f fg: memren) (m m' : mem)
(arg : builtin_arg preg) (varg : val)
(Hmem_obs_eq: mem_obs_eq f m m')
(Hrs_ren: regset_ren f rs rs')
(Hfg: forall b1 b2, fg b1 = Some b2 -> b1 = b2)
(Hge_wd: ge_wd fg g)
(Hincr: ren_incr fg f)
(Heval: eval_builtin_arg g rs (rs RSP) m arg varg),
exists varg',
eval_builtin_arg g rs' (rs' RSP) m' arg varg' /\
val_obs f varg varg'.