Merge of the reuse-temps branch:

- Reload temporaries are marked as destroyed (set to Vundef) across
  operations in the semantics of LTL, LTLin, Linear and Mach, 
  allowing Asmgen to reuse them.
- Added IA32 port.
- Cleaned up float conversions and axiomatization of floats.



git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@1499 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e

1 files changed, 503 insertions, 574 deletions

diff --git a/arm/Asmgenproof1.v b/arm/Asmgenproof1.v
index fc2ce7f..c10c9df 100644
--- a/arm/Asmgenproof1.v
+++ b/arm/Asmgenproof1.v
@@ -27,7 +27,7 @@ Require Import Machconcr.
 Require Import Machtyping.
 Require Import Asm.
 Require Import Asmgen.
-Require Conventions.
+Require Import Conventions.
 
 (** * Correspondence between Mach registers and PPC registers *)
 
@@ -41,91 +41,86 @@ Proof.
   destruct r1; destruct r2; simpl; intros; reflexivity || discriminate.
 Qed.
 
-(** Characterization of PPC registers that correspond to Mach registers. *)
-
-Definition is_data_reg (r: preg) : Prop :=
-  match r with
-  | IR IR14 => False
-  | CR _ => False
-  | PC => False
-  | _ => True
-  end.
-
-Lemma ireg_of_is_data_reg:
-  forall (r: mreg), is_data_reg (ireg_of r).
-Proof.
-  destruct r; exact I.
-Qed.
-
-Lemma freg_of_is_data_reg:
-  forall (r: mreg), is_data_reg (ireg_of r).
-Proof.
-  destruct r; exact I.
-Qed.
-
-Lemma preg_of_is_data_reg:
-  forall (r: mreg), is_data_reg (preg_of r).
-Proof.
-  destruct r; exact I.
-Qed.
-
 Lemma ireg_of_not_IR13:
   forall r, ireg_of r <> IR13.
 Proof.
-  intro. case r; discriminate.
+  destruct r; simpl; congruence.
 Qed.
+
 Lemma ireg_of_not_IR14:
   forall r, ireg_of r <> IR14.
 Proof.
-  intro. case r; discriminate.
+  destruct r; simpl; congruence.
 Qed.
 
-Hint Resolve ireg_of_not_IR13 ireg_of_not_IR14: ppcgen.
+Lemma preg_of_not_IR13:
+  forall r, preg_of r <> IR13.
+Proof.
+  unfold preg_of; intros. destruct (mreg_type r).
+  generalize (ireg_of_not_IR13 r); congruence.
+  congruence.
+Qed.
 
-Lemma preg_of_not:
-  forall r1 r2, ~(is_data_reg r2) -> preg_of r1 <> r2.
+Lemma preg_of_not_IR14:
+  forall r, preg_of r <> IR14.
 Proof.
-  intros; red; intro. subst r2. elim H. apply preg_of_is_data_reg.
+  unfold preg_of; intros. destruct (mreg_type r).
+  generalize (ireg_of_not_IR14 r); congruence.
+  congruence.
 Qed.
-Hint Resolve preg_of_not: ppcgen.
 
-Lemma preg_of_not_IR13:
-  forall r, preg_of r <> IR13.
+Lemma preg_of_not_PC:
+  forall r, preg_of r <> PC.
 Proof.
-  intro. case r; discriminate.
+  intros. unfold preg_of. destruct (mreg_type r); congruence.
 Qed.
-Hint Resolve preg_of_not_IR13: ppcgen.
 
-(** Agreement between Mach register sets and PPC register sets. *)
+Lemma ireg_diff:
+  forall r1 r2, r1 <> r2 -> IR r1 <> IR r2.
+Proof. intros; congruence. Qed.
+
+Hint Resolve ireg_of_not_IR13 ireg_of_not_IR14
+             preg_of_not_IR13 preg_of_not_IR14
+             preg_of_not_PC ireg_diff: ppcgen.
+
+(** Agreement between Mach register sets and ARM register sets. *)
 
-Definition agree (ms: Mach.regset) (sp: val) (rs: Asm.regset) :=
-  rs#IR13 = sp /\ forall r: mreg, ms r = rs#(preg_of r).
+Record agree (ms: Mach.regset) (sp: val) (rs: Asm.regset) : Prop := mkagree {
+  agree_sp: rs#IR13 = sp;
+  agree_sp_def: sp <> Vundef;
+  agree_mregs: forall r: mreg, Val.lessdef (ms r) (rs#(preg_of r))
+}.
 
 Lemma preg_val:
   forall ms sp rs r,
-  agree ms sp rs -> ms r = rs#(preg_of r).
+  agree ms sp rs -> Val.lessdef (ms r) rs#(preg_of r).
+Proof.
+  intros. destruct H. auto.
+Qed.
+
+Lemma preg_vals:
+  forall ms sp rs, agree ms sp rs ->
+  forall l, Val.lessdef_list (map ms l) (map rs (map preg_of l)).
 Proof.
-  intros. elim H. auto.
+  induction l; simpl. constructor. constructor. eapply preg_val; eauto. auto.
 Qed.
-  
+
 Lemma ireg_val:
   forall ms sp rs r,
   agree ms sp rs ->
   mreg_type r = Tint ->
-  ms r = rs#(ireg_of r).
+  Val.lessdef (ms r) rs#(ireg_of r).
 Proof.
-  intros. elim H; intros.
-  generalize (H2 r). unfold preg_of. rewrite H0. auto.
+  intros. generalize (preg_val _ _ _ r H). unfold preg_of. rewrite H0. auto.
 Qed.
 
 Lemma freg_val:
   forall ms sp rs r,
   agree ms sp rs ->
   mreg_type r = Tfloat ->
-  ms r = rs#(freg_of r).
+  Val.lessdef (ms r) rs#(freg_of r).
 Proof.
-  intros. elim H; intros.
-  generalize (H2 r). unfold preg_of. rewrite H0. auto.
+  intros. generalize (preg_val _ _ _ r H). unfold preg_of. rewrite H0. auto.
 Qed.
 
 Lemma sp_val:
@@ -133,76 +128,71 @@ Lemma sp_val:
   agree ms sp rs ->
   sp = rs#IR13.
 Proof.
-  intros. elim H; auto.
+  intros. destruct H; auto.
 Qed.
 
-Lemma agree_exten_1:
-  forall ms sp rs rs',
-  agree ms sp rs ->
-  (forall r, is_data_reg r -> rs'#r = rs#r) ->
-  agree ms sp rs'.
+Hint Resolve preg_val ireg_val freg_val sp_val: ppcgen.
+
+Definition important_preg (r: preg) : bool :=
+  match r with
+  | IR IR14 => false
+  | IR _ => true
+  | FR _ => true
+  | CR _ => false
+  | PC => false
+  end.
+
+Lemma preg_of_important:
+  forall r, important_preg (preg_of r) = true.
 Proof.
-  unfold agree; intros. elim H; intros.
-  split. rewrite H0. auto. exact I. 
-  intros. rewrite H0. auto. apply preg_of_is_data_reg.
+  intros. destruct r; reflexivity.
 Qed.
 
-Lemma agree_exten_2:
+Lemma important_diff:
+  forall r r',
+  important_preg r = true -> important_preg r' = false -> r <> r'.
+Proof.
+  congruence.
+Qed.
+Hint Resolve important_diff: ppcgen.
+
+Lemma agree_exten:
   forall ms sp rs rs',
   agree ms sp rs ->
-  (forall r, r <> PC -> r <> IR14 -> rs'#r = rs#r) ->
+  (forall r, important_preg r = true -> rs'#r = rs#r) ->
   agree ms sp rs'.
 Proof.
-  intros. eapply agree_exten_1; eauto. 
-  intros. apply H0; red; intro; subst r; elim H1.
+  intros. destruct H. split. 
+  rewrite H0; auto. auto.
+  intros. rewrite H0; auto. apply preg_of_important.
 Qed.
 
 (** Preservation of register agreement under various assignments. *)
 
 Lemma agree_set_mreg:
-  forall ms sp rs r v,
+  forall ms sp rs r v rs',
   agree ms sp rs ->
-  agree (Regmap.set r v ms) sp (rs#(preg_of r) <- v).
-Proof.
-  unfold agree; intros. elim H; intros; clear H.
-  split. rewrite Pregmap.gso. auto. apply sym_not_eq. apply preg_of_not_IR13.
-  intros. unfold Regmap.set. case (RegEq.eq r0 r); intro.
-  subst r0. rewrite Pregmap.gss. auto.
-  rewrite Pregmap.gso. auto. red; intro. 
-  elim n. apply preg_of_injective; auto.
-Qed.
-Hint Resolve agree_set_mreg: ppcgen.
-
-Lemma agree_set_mireg:
-  forall ms sp rs r v,
-  agree ms sp (rs#(preg_of r) <- v) ->
-  mreg_type r = Tint ->
-  agree ms sp (rs#(ireg_of r) <- v).
-Proof.
-  intros. unfold preg_of in H. rewrite H0 in H. auto.
-Qed.
-Hint Resolve agree_set_mireg: ppcgen.
-
-Lemma agree_set_mfreg:
-  forall ms sp rs r v,
-  agree ms sp (rs#(preg_of r) <- v) ->
-  mreg_type r = Tfloat ->
-  agree ms sp (rs#(freg_of r) <- v).
+  Val.lessdef v (rs'#(preg_of r)) ->
+  (forall r', important_preg r' = true -> r' <> preg_of r -> rs'#r' = rs#r') ->
+  agree (Regmap.set r v ms) sp rs'.
 Proof.
-  intros. unfold preg_of in H. rewrite H0 in H. auto.
+  intros. destruct H. split.
+  rewrite H1; auto. apply sym_not_equal. apply preg_of_not_IR13.
+  auto.
+  intros. unfold Regmap.set. destruct (RegEq.eq r0 r). congruence. 
+  rewrite H1. auto. apply preg_of_important.
+  red; intros; elim n. eapply preg_of_injective; eauto.
 Qed.
-Hint Resolve agree_set_mfreg: ppcgen.
 
 Lemma agree_set_other:
   forall ms sp rs r v,
   agree ms sp rs ->
-  ~(is_data_reg r) ->
+  important_preg r = false ->
   agree ms sp (rs#r <- v).
 Proof.
-  intros. apply agree_exten_1 with rs.
-  auto. intros. apply Pregmap.gso. red; intro; subst r0; contradiction.
+  intros. apply agree_exten with rs. auto.
+  intros. apply Pregmap.gso. congruence.
 Qed.
-Hint Resolve agree_set_other: ppcgen.
 
 Lemma agree_nextinstr:
   forall ms sp rs,
@@ -210,139 +200,159 @@ Lemma agree_nextinstr:
 Proof.
   intros. unfold nextinstr. apply agree_set_other. auto. auto.
 Qed.
-Hint Resolve agree_nextinstr: ppcgen.
 
-Lemma agree_set_mireg_twice:
-  forall ms sp rs r v v',
-  agree ms sp rs ->
-  mreg_type r = Tint ->
-  agree (Regmap.set r v ms) sp (rs #(ireg_of r) <- v' #(ireg_of r) <- v).
+Definition nontemp_preg (r: preg) : bool :=
+  match r with
+  | IR IR14 => false
+  | IR IR10 => false
+  | IR IR12 => false
+  | IR _ => true
+  | FR FR2 => false
+  | FR FR3 => false
+  | FR _ => true
+  | CR _ => false
+  | PC => false
+  end.
+
+Lemma nontemp_diff:
+  forall r r',
+  nontemp_preg r = true -> nontemp_preg r' = false -> r <> r'.
 Proof.
-  intros. replace (IR (ireg_of r)) with (preg_of r). elim H; intros.
-  split. repeat (rewrite Pregmap.gso; auto with ppcgen).
-  intros. case (mreg_eq r r0); intro.
-  subst r0. rewrite Regmap.gss. rewrite Pregmap.gss. auto.
-  assert (preg_of r <> preg_of r0). 
-    red; intro. elim n. apply preg_of_injective. auto.
-  rewrite Regmap.gso; auto.
-  repeat (rewrite Pregmap.gso; auto).
-  unfold preg_of. rewrite H0. auto.
+  congruence.
 Qed.
-Hint Resolve agree_set_mireg_twice: ppcgen.
 
-Lemma agree_set_twice_mireg:
-  forall ms sp rs r v v',
-  agree (Regmap.set r v' ms) sp rs ->
-  mreg_type r = Tint ->
-  agree (Regmap.set r v ms) sp (rs#(ireg_of r) <- v).
+Hint Resolve nontemp_diff: ppcgen.
+
+Lemma nontemp_important:
+  forall r, nontemp_preg r = true -> important_preg r = true.
 Proof.
-  intros. elim H; intros.
-  split. rewrite Pregmap.gso. auto. 
-  generalize (ireg_of_not_IR13 r); congruence.
-  intros. generalize (H2 r0). 
-  case (mreg_eq r0 r); intro.
-  subst r0. repeat rewrite Regmap.gss. unfold preg_of; rewrite H0.
-  rewrite Pregmap.gss. auto.
-  repeat rewrite Regmap.gso; auto.
-  rewrite Pregmap.gso. auto. 
-  replace (IR (ireg_of r)) with (preg_of r).
-  red; intros. elim n. apply preg_of_injective; auto.
-  unfold preg_of. rewrite H0. auto.
+  unfold nontemp_preg, important_preg; destruct r; auto. destruct i; auto.
 Qed.
-Hint Resolve agree_set_twice_mireg: ppcgen.
 
-Lemma agree_set_commut:
-  forall ms sp rs r1 r2 v1 v2,
-  r1 <> r2 ->
-  agree ms sp ((rs#r2 <- v2)#r1 <- v1) ->
-  agree ms sp ((rs#r1 <- v1)#r2 <- v2).
+Hint Resolve nontemp_important: ppcgen.
+
+Remark undef_regs_1:
+  forall l ms r, ms r = Vundef -> Mach.undef_regs l ms r = Vundef.
 Proof.
-  intros. apply agree_exten_1 with ((rs#r2 <- v2)#r1 <- v1). auto.
-  intros. 
-  case (preg_eq r r1); intro.
-  subst r1. rewrite Pregmap.gss. rewrite Pregmap.gso. rewrite Pregmap.gss.
-  auto. auto.
-  case (preg_eq r r2); intro.
-  subst r2. rewrite Pregmap.gss. rewrite Pregmap.gso. rewrite Pregmap.gss.
-  auto. auto.
-  repeat (rewrite Pregmap.gso; auto). 
-Qed. 
-Hint Resolve agree_set_commut: ppcgen.
-
-Lemma agree_nextinstr_commut:
-  forall ms sp rs r v,
-  agree ms sp (rs#r <- v) ->
-  r <> PC ->
-  agree ms sp ((nextinstr rs)#r <- v).
+  induction l; simpl; intros. auto. apply IHl. unfold Regmap.set.
+  destruct (RegEq.eq r a); congruence.
+Qed.
+
+Remark undef_regs_2:
+  forall l ms r, In r l -> Mach.undef_regs l ms r = Vundef.
+Proof.
+  induction l; simpl; intros. contradiction. 
+  destruct H. subst. apply undef_regs_1. apply Regmap.gss.
+  auto.
+Qed.
+
+Remark undef_regs_3:
+  forall l ms r, ~In r l -> Mach.undef_regs l ms r = ms r.
 Proof.
-  intros. unfold nextinstr. apply agree_set_commut. auto. 
-  apply agree_set_other. auto. auto. 
+  induction l; simpl; intros. auto.
+  rewrite IHl. apply Regmap.gso. intuition. intuition.
 Qed.
-Hint Resolve agree_nextinstr_commut: ppcgen.
 
-Lemma agree_set_mireg_exten:
-  forall ms sp rs r v (rs': regset),
+Lemma agree_exten_temps:
+  forall ms sp rs rs',
   agree ms sp rs ->
-  mreg_type r = Tint ->
-  rs'#(ireg_of r) = v ->
-  (forall r', r' <> PC -> r' <> ireg_of r -> r' <> IR14 -> rs'#r' = rs#r') ->
-  agree (Regmap.set r v ms) sp rs'.
+  (forall r, nontemp_preg r = true -> rs'#r = rs#r) ->
+  agree (undef_temps ms) sp rs'.
 Proof.
-  intros. apply agree_exten_2 with (rs#(ireg_of r) <- v).
-  auto with ppcgen.
-  intros. unfold Pregmap.set. case (PregEq.eq r0 (ireg_of r)); intro.
-  subst r0. auto. apply H2; auto.
+  intros. destruct H. split. 
+  rewrite H0; auto. auto. 
+  intros. unfold undef_temps. 
+  destruct (In_dec mreg_eq r (int_temporaries ++ float_temporaries)).
+  rewrite undef_regs_2; auto. 
+  rewrite undef_regs_3; auto. rewrite H0; auto.
+  simpl in n. destruct r; auto; intuition.
 Qed.
 
-(** Useful properties of the PC and GPR0 registers. *)
+Lemma agree_set_undef_mreg:
+  forall ms sp rs r v rs',
+  agree ms sp rs ->
+  Val.lessdef v (rs'#(preg_of r)) ->
+  (forall r', nontemp_preg r' = true -> r' <> preg_of r -> rs'#r' = rs#r') ->
+  agree (Regmap.set r v (undef_temps ms)) sp rs'.
+Proof.
+  intros. apply agree_set_mreg with (rs'#(preg_of r) <- (rs#(preg_of r))); auto.
+  eapply agree_exten_temps; eauto. 
+  intros. unfold Pregmap.set. destruct (PregEq.eq r0 (preg_of r)). 
+  congruence. auto. 
+  intros. rewrite Pregmap.gso; auto. 
+Qed.
+
+Lemma agree_undef_temps:
+  forall ms sp rs,
+  agree ms sp rs ->
+  agree (undef_temps ms) sp rs.
+Proof.
+  intros. eapply agree_exten_temps; eauto.
+Qed.
+
+(** Useful properties of the PC register. *)
 
 Lemma nextinstr_inv:
-  forall r rs, r <> PC -> (nextinstr rs)#r = rs#r.
+  forall r rs,
+  r <> PC ->
+  (nextinstr rs)#r = rs#r.
+Proof.
+  intros. unfold nextinstr. apply Pregmap.gso. red; intro; subst. auto.
+Qed.
+
+Lemma nextinstr_inv2:
+  forall r rs,
+  nontemp_preg r = true ->
+  (nextinstr rs)#r = rs#r.
 Proof.
-  intros. unfold nextinstr. apply Pregmap.gso. auto.
+  intros. apply nextinstr_inv. red; intro; subst; discriminate.
 Qed.
-Hint Resolve nextinstr_inv: ppcgen.
 
 Lemma nextinstr_set_preg:
   forall rs m v,
   (nextinstr (rs#(preg_of m) <- v))#PC = Val.add rs#PC Vone.
 Proof.
   intros. unfold nextinstr. rewrite Pregmap.gss. 
-  rewrite Pregmap.gso. auto. apply sym_not_eq. auto with ppcgen.
+  rewrite Pregmap.gso. auto. apply sym_not_eq. apply preg_of_not_PC. 
 Qed.
-Hint Resolve nextinstr_set_preg: ppcgen.
 
 (** Connection between Mach and Asm calling conventions for external
     functions. *)
 
 Lemma extcall_arg_match:
-  forall ms sp rs m l v,
+  forall ms sp rs m m' l v,
   agree ms sp rs ->
   Machconcr.extcall_arg ms m sp l v ->
-  Asm.extcall_arg rs m l v.
+  Mem.extends m m' ->
+  exists v', Asm.extcall_arg rs m' l v' /\ Val.lessdef v v'.
 Proof.
-  intros. inv H0. 
-  rewrite (preg_val _ _ _ r H). constructor.
-  rewrite (sp_val _ _ _ H) in H1.
-  destruct ty; unfold load_stack in H1.
-  econstructor. reflexivity. assumption.
-  econstructor. reflexivity. assumption.
+  intros. inv H0.
+  exists (rs#(preg_of r)); split. constructor. eauto with ppcgen.
+  unfold load_stack in H2. 
+  exploit Mem.loadv_extends; eauto. intros [v' [A B]].
+  rewrite (sp_val _ _ _ H) in A. 
+  exists v'; split; auto. destruct ty; econstructor; eauto.
 Qed.
 
 Lemma extcall_args_match:
-  forall ms sp rs m, agree ms sp rs ->
+  forall ms sp rs m m', agree ms sp rs -> Mem.extends m m' ->
   forall ll vl,
   Machconcr.extcall_args ms m sp ll vl ->
-  Asm.extcall_args rs m ll vl.
+  exists vl', Asm.extcall_args rs m' ll vl' /\ Val.lessdef_list vl vl'.
 Proof.
-  induction 2; constructor; auto. eapply extcall_arg_match; eauto.
+  induction 3.
+  exists (@nil val); split; constructor.
+  exploit extcall_arg_match; eauto. intros [v1' [A B]].
+  exploit IHextcall_args; eauto. intros [vl' [C D]].
+  exists(v1' :: vl'); split. constructor; auto. constructor; auto.
 Qed.
 
 Lemma extcall_arguments_match:
-  forall ms m sp rs sg args,
+  forall ms m sp rs sg args m',
   agree ms sp rs ->
   Machconcr.extcall_arguments ms m sp sg args ->
-  Asm.extcall_arguments rs m sg args.
+  Mem.extends m m' ->
+  exists args', Asm.extcall_arguments rs m' sg args' /\ Val.lessdef_list args args'.
 Proof.
   unfold Machconcr.extcall_arguments, Asm.extcall_arguments; intros.
   eapply extcall_args_match; eauto.
@@ -564,7 +574,7 @@ Proof.
   exploit loadimm_correct. intros [rs' [A [B C]]].
   exists (nextinstr (rs'#r1 <- (Val.and rs#r2 (Vint n)))).
   split. eapply exec_straight_trans. eauto. apply exec_straight_one.
-  simpl. rewrite B. rewrite C; auto with ppcgen. congruence.
+  simpl. rewrite B. rewrite C; auto with ppcgen. 
   auto.
   split. rewrite nextinstr_inv; auto with ppcgen. apply Pregmap.gss.
   intros. rewrite nextinstr_inv; auto. rewrite Pregmap.gso; auto.
@@ -756,20 +766,6 @@ Qed.
 
 (** Translation of conditions *)
 
-Ltac TypeInv :=
-  match goal with
-  | H: (List.map ?f ?x = nil) |- _ =>
-      destruct x; [clear H | simpl in H; discriminate]
-  | H: (List.map ?f ?x = ?hd :: ?tl) |- _ =>
-      destruct x; simpl in H;
-      [ discriminate |
-        injection H; clear H; let T := fresh "T" in (
-          intros H T; TypeInv) ]
-  | _ => idtac
-  end.
-
-(** Translation of conditions. *)
-
 Lemma compare_int_spec:
   forall rs v1 v2,
   let rs1 := nextinstr (compare_int rs v1 v2) in
@@ -783,11 +779,11 @@ Lemma compare_int_spec:
   /\ rs1#CRlt = (Val.cmp Clt v1 v2)
   /\ rs1#CRgt = (Val.cmp Cgt v1 v2)
   /\ rs1#CRle = (Val.cmp Cle v1 v2)
-  /\ forall r', is_data_reg r' -> rs1#r' = rs#r'.
+  /\ forall r', important_preg r' = true -> rs1#r' = rs#r'.
 Proof.
   intros. unfold rs1. intuition; try reflexivity. 
-  rewrite nextinstr_inv; [unfold compare_int; repeat rewrite Pregmap.gso; auto | idtac];
-  red; intro; subst r'; elim H.
+  rewrite nextinstr_inv; auto with ppcgen.
+  unfold compare_int. repeat rewrite Pregmap.gso; auto with ppcgen.
 Qed.
 
 Lemma compare_float_spec:
@@ -803,302 +799,237 @@ Lemma compare_float_spec:
   /\ rs'#CRlt = (Val.notbool (Val.cmpf Cge v1 v2))
   /\ rs'#CRgt = (Val.cmpf Cgt v1 v2)               
   /\ rs'#CRle = (Val.notbool (Val.cmpf Cgt v1 v2))
-  /\ forall r', is_data_reg r' -> rs'#r' = rs#r'.
+  /\ forall r', important_preg r' = true -> rs'#r' = rs#r'.
 Proof.
   intros. unfold rs'. intuition; try reflexivity. 
-  rewrite nextinstr_inv; [unfold compare_float; repeat rewrite Pregmap.gso; auto | idtac];
-  red; intro; subst r'; elim H.
+  rewrite nextinstr_inv; auto with ppcgen.
+  unfold compare_float. repeat rewrite Pregmap.gso; auto with ppcgen.
 Qed.
 
+Ltac TypeInv1 :=
+  match goal with
+  | H: (List.map ?f ?x = nil) |- _ =>
+      destruct x; inv H; TypeInv1
+  | H: (List.map ?f ?x = ?hd :: ?tl) |- _ =>
+      destruct x; simpl in H; simplify_eq H; clear H; intros; TypeInv1
+  | _ => idtac
+  end.
+
+Ltac TypeInv2 :=
+  match goal with
+  | H: (mreg_type _ = Tint) |- _ => try (rewrite H in *); clear H; TypeInv2
+  | H: (mreg_type _ = Tfloat) |- _ => try (rewrite H in *); clear H; TypeInv2
+  | _ => idtac
+  end.
+
+Ltac TypeInv := TypeInv1; simpl in *; unfold preg_of in *; TypeInv2.
+
 Lemma transl_cond_correct:
-  forall cond args k ms sp rs m b,
+  forall cond args k rs m b,
   map mreg_type args = type_of_condition cond ->
-  agree ms sp rs ->
-  eval_condition cond (map ms args) = Some b ->
+  eval_condition cond (map rs (map preg_of args)) = Some b ->
   exists rs',
      exec_straight (transl_cond cond args k) rs m k rs' m
   /\ rs'#(CR (crbit_for_cond cond)) = Val.of_bool b
-  /\ agree ms sp rs'.
+  /\ forall r, important_preg r = true -> rs'#r = rs r.
 Proof.
-  intros.
-  rewrite <- (eval_condition_weaken _ _ H1). clear H1. 
-  destruct cond; simpl in H; TypeInv; simpl.
+  intros until b; intros TY EV. rewrite <- (eval_condition_weaken _ _ EV). clear EV.  
+  destruct cond; simpl in TY; TypeInv.
   (* Ccomp *)
-  generalize (compare_int_spec rs ms#m0 ms#m1).
+  generalize (compare_int_spec rs (rs (ireg_of m0)) (rs (ireg_of m1))).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs ms#m0 ms#m1)).
-  split. apply exec_straight_one. simpl. 
-  repeat rewrite <- (ireg_val ms sp rs); trivial. 
-  reflexivity.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto.
+  split. case c; assumption.
+  auto.
   (* Ccompu *)
-  generalize (compare_int_spec rs ms#m0 ms#m1).
+  generalize (compare_int_spec rs (rs (ireg_of m0)) (rs (ireg_of m1))).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs ms#m0 ms#m1)).
-  split. apply exec_straight_one. simpl. 
-  repeat rewrite <- (ireg_val ms sp rs); trivial. 
-  reflexivity.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto.
+  split. case c; assumption.
+  auto.
   (* Ccompshift *)
-  generalize (compare_int_spec rs ms#m0 (eval_shift_total s ms#m1)).
+  generalize (compare_int_spec rs (rs (ireg_of m0)) (eval_shift_total s (rs (ireg_of m1)))).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs ms#m0 (eval_shift_total s ms#m1))).
-  split. apply exec_straight_one. simpl.
-  rewrite transl_shift_correct. 
-  repeat rewrite <- (ireg_val ms sp rs); trivial.
-  reflexivity.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto.
+  split. rewrite transl_shift_correct. case c; assumption.
+  rewrite transl_shift_correct. auto.
   (* Ccompushift *)
-  generalize (compare_int_spec rs ms#m0 (eval_shift_total s ms#m1)).
+  generalize (compare_int_spec rs (rs (ireg_of m0)) (eval_shift_total s (rs (ireg_of m1)))).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs ms#m0 (eval_shift_total s ms#m1))).
-  split. apply exec_straight_one. simpl.
-  rewrite transl_shift_correct. 
-  repeat rewrite <- (ireg_val ms sp rs); trivial.
-  reflexivity.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto.
+  split. rewrite transl_shift_correct. case c; assumption.
+  rewrite transl_shift_correct. auto.
   (* Ccompimm *)
   destruct (is_immed_arith i).
-  generalize (compare_int_spec rs ms#m0 (Vint i)).
+  generalize (compare_int_spec rs (rs (ireg_of m0)) (Vint i)).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs ms#m0 (Vint i))).
-  split. apply exec_straight_one. simpl. 
-  rewrite <- (ireg_val ms sp rs); trivial. auto.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto. 
+  split. case c; assumption.
+  auto.
   exploit (loadimm_correct IR14). intros [rs' [P [Q R]]].
-  assert (AG: agree ms sp rs'). apply agree_exten_2 with rs; auto. 
-  generalize (compare_int_spec rs' ms#m0 (Vint i)).
+  generalize (compare_int_spec rs' (rs (ireg_of m0)) (Vint i)).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs' ms#m0 (Vint i))).
+  econstructor.
   split. eapply exec_straight_trans. eexact P. apply exec_straight_one. simpl.
-  rewrite Q. rewrite <- (ireg_val ms sp rs'); trivial. auto.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs'; auto.
+  rewrite Q. rewrite R; eauto with ppcgen. auto.
+  split. case c; assumption.
+  intros. rewrite K; auto with ppcgen.
   (* Ccompuimm *)
   destruct (is_immed_arith i).
-  generalize (compare_int_spec rs ms#m0 (Vint i)).
+  generalize (compare_int_spec rs (rs (ireg_of m0)) (Vint i)).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs ms#m0 (Vint i))).
-  split. apply exec_straight_one. simpl. 
-  rewrite <- (ireg_val ms sp rs); trivial. auto.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto. 
+  split. case c; assumption.
+  auto.
   exploit (loadimm_correct IR14). intros [rs' [P [Q R]]].
-  assert (AG: agree ms sp rs'). apply agree_exten_2 with rs; auto. 
-  generalize (compare_int_spec rs' ms#m0 (Vint i)).
+  generalize (compare_int_spec rs' (rs (ireg_of m0)) (Vint i)).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_int rs' ms#m0 (Vint i))).
+  econstructor.
   split. eapply exec_straight_trans. eexact P. apply exec_straight_one. simpl.
-  rewrite Q. rewrite <- (ireg_val ms sp rs'); trivial. auto.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs'; auto.
+  rewrite Q. rewrite R; eauto with ppcgen. auto.
+  split. case c; assumption.
+  intros. rewrite K; auto with ppcgen.
   (* Ccompf *)
-  generalize (compare_float_spec rs ms#m0 ms#m1).
+  generalize (compare_float_spec rs (rs (freg_of m0)) (rs (freg_of m1))).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_float rs ms#m0 ms#m1)).
-  split. apply exec_straight_one. simpl. 
-  repeat rewrite <- (freg_val ms sp rs); trivial. auto.
-  split. 
-  case c; simpl; auto.
-  apply agree_exten_1 with rs; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto.
+  split. case c; assumption.
+  auto.
   (* Cnotcompf *)
-  generalize (compare_float_spec rs ms#m0 ms#m1).
+  generalize (compare_float_spec rs (rs (freg_of m0)) (rs (freg_of m1))).
   intros [A [B [C [D [E [F [G [H [I [J K]]]]]]]]]].
-  exists (nextinstr (compare_float rs ms#m0 ms#m1)).
-  split. apply exec_straight_one. simpl. 
-  repeat rewrite <- (freg_val ms sp rs); trivial. auto.
-  split. 
-  case c; simpl; auto.
+  econstructor.
+  split. apply exec_straight_one. simpl. eauto. auto.
+  split. case c; try assumption.
     rewrite Val.negate_cmpf_ne. auto.
     rewrite Val.negate_cmpf_eq. auto.
-  apply agree_exten_1 with rs; auto.
+  auto.
 Qed.
 
 (** Translation of arithmetic operations. *)
 
-Ltac TranslOpSimpl :=
+Ltac Simpl :=
   match goal with
-  | |- exists rs' : regset,
-         exec_straight ?c ?rs ?m ?k rs' ?m /\
-         agree (Regmap.set ?res ?v ?ms) ?sp rs'  =>
-    (exists (nextinstr (rs#(ireg_of res) <- v));
-     split; 
-     [ apply exec_straight_one;
-       [ repeat (rewrite (ireg_val ms sp rs); auto);
-         simpl; try rewrite transl_shift_correct; reflexivity
-       | reflexivity ]
-     | auto with ppcgen ])
-  ||
-    (exists (nextinstr (rs#(freg_of res) <- v));
-     split; 
-     [ apply exec_straight_one;
-       [ repeat (rewrite (freg_val ms sp rs); auto); reflexivity
-       | reflexivity ]
-     | auto with ppcgen ])
+  | [ |- nextinstr _ _ = _ ] => rewrite nextinstr_inv; [auto | auto with ppcgen]
+  | [ |- Pregmap.get ?x (Pregmap.set ?x _ _) = _ ] => rewrite Pregmap.gss; auto
+  | [ |- Pregmap.set ?x _ _ ?x = _ ] => rewrite Pregmap.gss; auto
+  | [ |- Pregmap.get _ (Pregmap.set _ _ _) = _ ] => rewrite Pregmap.gso; [auto | auto with ppcgen]
+  | [ |- Pregmap.set _ _ _ _ = _ ] => rewrite Pregmap.gso; [auto | auto with ppcgen]
   end.
 
+Ltac TranslOpSimpl :=
+  econstructor; split;
+  [ apply exec_straight_one; [simpl; eauto | reflexivity ]
+  | split; [try rewrite transl_shift_correct; repeat Simpl | intros; repeat Simpl] ].
+
 Lemma transl_op_correct:
-  forall op args res k ms sp rs m v,
+  forall op args res k (rs: regset) m v,
   wt_instr (Mop op args res) ->
-  agree ms sp rs ->
-  eval_operation ge sp op (map ms args) = Some v ->
+  eval_operation ge rs#IR13 op (map rs (map preg_of args)) = Some v ->
   exists rs',
      exec_straight (transl_op op args res k) rs m k rs' m
-  /\ agree (Regmap.set res v ms) sp rs'.
+  /\ rs'#(preg_of res) = v
+  /\ forall r, important_preg r = true -> r <> preg_of res -> rs'#r = rs#r.
 Proof.
-  intros. rewrite <- (eval_operation_weaken _ _ _ _ H1). (*clear H1; clear v.*)
-  inversion H.
+  intros. rewrite <- (eval_operation_weaken _ _ _ _ H0). inv H.
   (* Omove *)
-  simpl. exists (nextinstr (rs#(preg_of res) <- (ms r1))).
-  split. caseEq (mreg_type r1); intro.
-  apply exec_straight_one. simpl. rewrite (ireg_val ms sp rs); auto.
-  simpl. unfold preg_of. rewrite <- H3. rewrite H6. reflexivity.
-  auto with ppcgen.
-  apply exec_straight_one. simpl. rewrite (freg_val ms sp rs); auto.
-  simpl. unfold preg_of. rewrite <- H3. rewrite H6. reflexivity.
-  auto with ppcgen.
-  auto with ppcgen.
+  simpl.
+  exists (nextinstr (rs#(preg_of res) <- (rs#(preg_of r1)))).
+  split. unfold preg_of; rewrite <- H2.
+  destruct (mreg_type r1); apply exec_straight_one; auto.
+  split. Simpl. Simpl.
+  intros. Simpl. Simpl.
   (* Other instructions *)
-  clear H2 H3 H5. 
-  destruct op; simpl in H6; injection H6; clear H6; intros;
-  TypeInv; simpl; try (TranslOpSimpl).
+  destruct op; simpl in H5; inv H5; TypeInv; try (TranslOpSimpl; fail).
   (* Omove again *)
   congruence.
   (* Ointconst *)
-  generalize (loadimm_correct (ireg_of res) i k rs m).
-  intros [rs' [A [B C]]]. 
-  exists rs'. split. auto. 
-  apply agree_set_mireg_exten with rs; auto. 
+  generalize (loadimm_correct (ireg_of res) i k rs m). intros [rs' [A [B C]]]. 
+  exists rs'. split. auto. split. auto. intros. auto with ppcgen.
   (* Oaddrstack *)
   generalize (addimm_correct (ireg_of res) IR13 i k rs m). 
   intros [rs' [EX [RES OTH]]].
-  exists rs'. split. auto. 
-  apply agree_set_mireg_exten with rs; auto.
-  rewrite (sp_val ms sp rs). auto. auto.
+  exists rs'. split. auto. split. auto. auto with ppcgen.
   (* Ocast8signed *)
-  set (rs1 := nextinstr (rs#(ireg_of res) <- (Val.shl (ms m0) (Vint (Int.repr 24))))).
-  set (rs2 := nextinstr (rs1#(ireg_of res) <- (Val.shr (rs1 (ireg_of res)) (Vint (Int.repr 24))))).
-  exists rs2. split.
-  apply exec_straight_two with rs1 m; auto.
-  simpl. rewrite <- (ireg_val ms sp rs); auto.
-  unfold rs2. 
-  replace (Val.shr (rs1 (ireg_of res)) (Vint (Int.repr 24))) with (Val.sign_ext 8 (ms m0)).
-  apply agree_nextinstr. unfold rs1. apply agree_nextinstr_commut.
-  apply agree_set_mireg_twice; auto with ppcgen. auto with ppcgen. 
-  unfold rs1. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
-  destruct (ms m0); simpl; auto. rewrite Int.sign_ext_shr_shl. reflexivity.
-  vm_compute; auto. 
+  econstructor; split.
+  eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. 
+  split. Simpl. Simpl. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
+  destruct (rs (ireg_of m0)); simpl; auto. rewrite Int.sign_ext_shr_shl. reflexivity.
+  compute; auto.
+  intros. repeat Simpl. 
   (* Ocast8unsigned *)
-  exists (nextinstr (rs#(ireg_of res) <- (Val.and (ms m0) (Vint (Int.repr 255))))).
-  split. apply exec_straight_one. repeat (rewrite (ireg_val ms sp rs)); auto. reflexivity.
-  replace (Val.zero_ext 8 (ms m0))
-      with (Val.and (ms m0) (Vint (Int.repr 255))).
-  auto with ppcgen. 
-  destruct (ms m0); simpl; auto. rewrite Int.zero_ext_and. reflexivity. 
-  vm_compute; auto.
+  econstructor; split.
+  eapply exec_straight_one. simpl; eauto. auto. 
+  split. Simpl. Simpl.
+  destruct (rs (ireg_of m0)); simpl; auto. rewrite Int.zero_ext_and. reflexivity.
+  compute; auto.
+  intros. repeat Simpl.
   (* Ocast16signed *)
-  set (rs1 := nextinstr (rs#(ireg_of res) <- (Val.shl (ms m0) (Vint (Int.repr 16))))).
-  set (rs2 := nextinstr (rs1#(ireg_of res) <- (Val.shr (rs1 (ireg_of res)) (Vint (Int.repr 16))))).
-  exists rs2. split.
-  apply exec_straight_two with rs1 m; auto.
-  simpl. rewrite <- (ireg_val ms sp rs); auto. 
-  unfold rs2. 
-  replace (Val.shr (rs1 (ireg_of res)) (Vint (Int.repr 16))) with (Val.sign_ext 16 (ms m0)).
-  apply agree_nextinstr. unfold rs1. apply agree_nextinstr_commut.
-  apply agree_set_mireg_twice; auto with ppcgen. auto with ppcgen. 
-  unfold rs1. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
-  destruct (ms m0); simpl; auto. rewrite Int.sign_ext_shr_shl. reflexivity.
-  vm_compute; auto. 
+  econstructor; split.
+  eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. 
+  split. Simpl. Simpl. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
+  destruct (rs (ireg_of m0)); simpl; auto. rewrite Int.sign_ext_shr_shl. reflexivity.
+  compute; auto.
+  intros. repeat Simpl. 
   (* Ocast16unsigned *)
-  set (rs1 := nextinstr (rs#(ireg_of res) <- (Val.shl (ms m0) (Vint (Int.repr 16))))).
-  set (rs2 := nextinstr (rs1#(ireg_of res) <- (Val.shru (rs1 (ireg_of res)) (Vint (Int.repr 16))))).
-  exists rs2. split.
-  apply exec_straight_two with rs1 m; auto.
-  simpl. rewrite <- (ireg_val ms sp rs); auto. 
-  unfold rs2. 
-  replace (Val.shru (rs1 (ireg_of res)) (Vint (Int.repr 16))) with (Val.zero_ext 16 (ms m0)).
-  apply agree_nextinstr. unfold rs1. apply agree_nextinstr_commut.
-  apply agree_set_mireg_twice; auto with ppcgen. auto with ppcgen. 
-  unfold rs1. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
-  destruct (ms m0); simpl; auto. rewrite Int.zero_ext_shru_shl. reflexivity.
-  vm_compute; auto. 
+  econstructor; split.
+  eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto. 
+  split. Simpl. Simpl. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
+  destruct (rs (ireg_of m0)); simpl; auto. rewrite Int.zero_ext_shru_shl. reflexivity.
+  compute; auto.
+  intros. repeat Simpl.
   (* Oaddimm *)
   generalize (addimm_correct (ireg_of res) (ireg_of m0) i k rs m).
   intros [rs' [A [B C]]]. 
-  exists rs'. split. auto.
-  apply agree_set_mireg_exten with rs; auto.
-  rewrite (ireg_val ms sp rs); auto. 
+  exists rs'. split. auto. split. auto. auto with ppcgen.
   (* Orsbimm *)
   exploit (makeimm_correct Prsb (fun v1 v2 => Val.sub v2 v1) (ireg_of res) (ireg_of m0));
   auto with ppcgen.
   intros [rs' [A [B C]]].
   exists rs'.
-  split. eauto.
-  apply agree_set_mireg_exten with rs; auto. rewrite B. 
-  rewrite <- (ireg_val ms sp rs); auto. 
+  split. eauto. split. rewrite B. auto. auto with ppcgen. 
   (* Omul *)
   destruct (ireg_eq (ireg_of res) (ireg_of m0) || ireg_eq (ireg_of res) (ireg_of m1)).
-  set (rs1 := nextinstr (rs#IR14 <- (Val.mul (ms m0) (ms m1)))).
-  set (rs2 := nextinstr (rs1#(ireg_of res) <- (rs1#IR14))).
-  exists rs2; split.
-  apply exec_straight_two with rs1 m; auto.
-  simpl. repeat rewrite <- (ireg_val ms sp rs); auto.
-  unfold rs2. unfold rs1. rewrite nextinstr_inv. rewrite Pregmap.gss. 
-  apply agree_nextinstr. apply agree_nextinstr_commut. 
-  apply agree_set_mireg; auto.  apply agree_set_mreg. apply agree_set_other. auto.
-  simpl; auto. auto with ppcgen. discriminate.
+  econstructor; split.
+  eapply exec_straight_two. simpl; eauto. simpl; eauto. auto. auto.
+  split. repeat Simpl.
+  intros. repeat Simpl.
   TranslOpSimpl.
   (* Oandimm *)
   generalize (andimm_correct (ireg_of res) (ireg_of m0) i k rs m
                             (ireg_of_not_IR14 m0)).
   intros [rs' [A [B C]]]. 
-  exists rs'. split. auto.
-  apply agree_set_mireg_exten with rs; auto.
-  rewrite (ireg_val ms sp rs); auto. 
+  exists rs'. split. auto. split. auto. auto with ppcgen.
   (* Oorimm *)
   exploit (makeimm_correct Porr Val.or (ireg_of res) (ireg_of m0));
   auto with ppcgen.
-  intros [rs' [A [B C]]].
-  exists rs'.
-  split. eauto.
-  apply agree_set_mireg_exten with rs; auto. rewrite B. 
-  rewrite <- (ireg_val ms sp rs); auto. 
+  intros [rs' [A [B C]]]. 
+  exists rs'. split. eauto. split. auto. auto with ppcgen.
   (* Oxorimm *)
   exploit (makeimm_correct Peor Val.xor (ireg_of res) (ireg_of m0));
   auto with ppcgen.
-  intros [rs' [A [B C]]].
-  exists rs'.
-  split. eauto.
-  apply agree_set_mireg_exten with rs; auto. rewrite B. 
-  rewrite <- (ireg_val ms sp rs); auto.
+  intros [rs' [A [B C]]]. 
+  exists rs'. split. eauto. split. auto. auto with ppcgen.
   (* Oshrximm *)
-  assert (exists n, ms m0 = Vint n /\ Int.ltu i (Int.repr 31) = true).
-    simpl in H1. destruct (ms m0); try discriminate.
+  assert (exists n, rs (ireg_of m0) = Vint n /\ Int.ltu i (Int.repr 31) = true).
+    destruct (rs (ireg_of m0)); try discriminate.
     exists i0; split; auto. destruct (Int.ltu i (Int.repr 31)); discriminate || auto.
-  destruct H3 as [n [ARG1 LTU]].
+  destruct H as [n [ARG1 LTU]]. clear H0.
   assert (LTU': Int.ltu i Int.iwordsize = true).
     exploit Int.ltu_inv. eexact LTU. intro.
     unfold Int.ltu. apply zlt_true.
-    assert (Int.unsigned (Int.repr 31) < Int.unsigned Int.iwordsize). vm_compute; auto.
+    assert (Int.unsigned (Int.repr 31) < Int.unsigned Int.iwordsize). compute; auto.
     omega.
-  assert (RSm0: rs (ireg_of m0) = Vint n).
-    rewrite <- ARG1. symmetry. eapply ireg_val; eauto. 
   set (islt := Int.lt n Int.zero).
   set (rs1 := nextinstr (compare_int rs (Vint n) (Vint Int.zero))).
-  assert (OTH1: forall r', is_data_reg r' -> rs1#r' = rs#r').
+  assert (OTH1: forall r', important_preg r' = true -> rs1#r' = rs#r').
     generalize (compare_int_spec rs (Vint n) (Vint Int.zero)).
     fold rs1. intros [A B]. intuition.
   exploit (addimm_correct IR14 (ireg_of m0) (Int.sub (Int.shl Int.one i) Int.one)).
@@ -1107,83 +1038,47 @@ Proof.
   set (rs4 := nextinstr (rs3#(ireg_of res) <- (Val.shr rs3#IR14 (Vint i)))).
   exists rs4; split.
   apply exec_straight_step with rs1 m.
-  simpl. rewrite RSm0. auto. auto.
+  simpl. rewrite ARG1. auto. auto.
   eapply exec_straight_trans. eexact EXEC2.
   apply exec_straight_two with rs3 m.
   simpl. rewrite OTH2. change (rs1 CRge) with (Val.cmp Cge (Vint n) (Vint Int.zero)).
     unfold Val.cmp. change (Int.cmp Cge n Int.zero) with (negb islt).
-    rewrite OTH2. rewrite OTH1. rewrite RSm0. 
+    rewrite OTH2. rewrite OTH1. rewrite ARG1. 
     unfold rs3. case islt; reflexivity.
-    apply ireg_of_is_data_reg. decEq; auto with ppcgen. auto with ppcgen. congruence. congruence.
+    destruct m0; reflexivity. auto with ppcgen. auto with ppcgen. discriminate. discriminate.
   simpl. auto. 
   auto. unfold rs3. case islt; auto. auto.
-  (* agreement *)
-  assert (RES4: rs4#(ireg_of res) = Vint(Int.shrx n i)).
-    unfold rs4. rewrite nextinstr_inv; auto. rewrite Pregmap.gss.
-    rewrite Int.shrx_shr. fold islt. unfold rs3.
-    repeat rewrite nextinstr_inv; auto. 
-    case islt. rewrite RES2. rewrite OTH1. rewrite RSm0. 
-    simpl. rewrite LTU'. auto.
-    apply ireg_of_is_data_reg. 
-    rewrite Pregmap.gss. simpl. rewrite LTU'. auto. congruence.
-    exact LTU. auto with ppcgen. 
-  assert (OTH4: forall r, is_data_reg r -> r <> ireg_of res -> rs4#r = rs#r).
-    intros. 
-    assert (r <> PC). red; intro; subst r; elim H3.
-    assert (r <> IR14). red; intro; subst r; elim H3.
-    unfold rs4. rewrite nextinstr_inv; auto. rewrite Pregmap.gso; auto.
-    unfold rs3. rewrite nextinstr_inv; auto.
-    transitivity (rs2 r).
-    case islt. auto. apply Pregmap.gso; auto.
-    rewrite OTH2; auto. 
-  apply agree_exten_1 with (rs#(ireg_of res) <- (Val.shrx (ms m0) (Vint i))).
-  auto with ppcgen.
-  intros. unfold Pregmap.set. destruct (PregEq.eq r (ireg_of res)).
-  subst r. rewrite ARG1. simpl. rewrite LTU'. auto.
-  auto.
-  (* Ointoffloat *)
-  exists (nextinstr (rs#(ireg_of res) <- (Val.intoffloat (ms m0)))).
-  split. apply exec_straight_one. 
-  repeat (rewrite (freg_val ms sp rs); auto).
-  reflexivity. auto with ppcgen.
-  (* Ointuoffloat *)
-  exists (nextinstr (rs#(ireg_of res) <- (Val.intuoffloat (ms m0)))).
-  split. apply exec_straight_one. 
-  repeat (rewrite (freg_val ms sp rs); auto).
-  reflexivity. auto with ppcgen.
-  (* Ofloatofint *)
-  exists (nextinstr (rs#(freg_of res) <- (Val.floatofint (ms m0)))).
-  split. apply exec_straight_one. 
-  repeat (rewrite (ireg_val ms sp rs); auto).
-  reflexivity. auto 10 with ppcgen.
-  (* Ofloatofintu *)
-  exists (nextinstr (rs#(freg_of res) <- (Val.floatofintu (ms m0)))).
-  split. apply exec_straight_one. 
-  repeat (rewrite (ireg_val ms sp rs); auto).
-  reflexivity. auto 10 with ppcgen.
+  split. unfold rs4. repeat Simpl. rewrite ARG1. simpl. rewrite LTU'. rewrite Int.shrx_shr.
+  fold islt. unfold rs3. rewrite nextinstr_inv; auto with ppcgen. 
+  destruct islt. rewrite RES2. change (rs1 (IR (ireg_of m0))) with (rs (IR (ireg_of m0))). 
+  rewrite ARG1. simpl. rewrite LTU'. auto.
+  rewrite Pregmap.gss. simpl. rewrite LTU'. auto. 
+  assumption.
+  intros. unfold rs4; repeat Simpl. unfold rs3; repeat Simpl. 
+  transitivity (rs2 r). destruct islt; auto. Simpl. 
+  rewrite OTH2; auto with ppcgen.
   (* Ocmp *)
-  assert (exists b, eval_condition c ms##args = Some b /\ v = Val.of_bool b).
-    simpl in H1. destruct (eval_condition c ms##args). 
-    destruct b; inv H1. exists true; auto. exists false; auto.
-    discriminate.
-  destruct H5 as [b [EVC EQ]].
-  exploit transl_cond_correct; eauto. intros [rs' [A [B C]]].
-  rewrite (eval_condition_weaken _ _ EVC).
-  set (rs1 := nextinstr (rs'#(ireg_of res) <- (Vint Int.zero))).
-  set (rs2 := nextinstr (if b then (rs1#(ireg_of res) <- Vtrue) else rs1)).
-  exists rs2; split.
-  eapply exec_straight_trans. eauto. 
-  apply exec_straight_two with rs1 m; auto.
-  simpl. replace (rs1 (crbit_for_cond c)) with (Val.of_bool b).
-  unfold rs2. destruct b; auto. 
-  unfold rs2. destruct b; auto.
-  apply agree_set_mireg_exten with rs'; auto.
-  unfold rs2. rewrite nextinstr_inv; auto with ppcgen. 
-  destruct b. apply Pregmap.gss.
-  unfold rs1. rewrite nextinstr_inv; auto with ppcgen. apply Pregmap.gss.
-  intros. unfold rs2. rewrite nextinstr_inv; auto. 
-  transitivity (rs1 r'). destruct b; auto. rewrite Pregmap.gso; auto.
-  unfold rs1. rewrite nextinstr_inv; auto. apply Pregmap.gso; auto.
+  fold preg_of in *.
+  assert (exists b, eval_condition c rs ## (preg_of ## args) = Some b /\ v = Val.of_bool b).
+    fold preg_of in H0. destruct (eval_condition c rs ## (preg_of ## args)).
+    exists b; split; auto. destruct b; inv H0; auto. congruence.
+  clear H0. destruct H as [b [EVC VBO]]. rewrite (eval_condition_weaken _ _ EVC).
+  destruct (transl_cond_correct c args 
+             (Pmov (ireg_of res) (SOimm Int.zero)
+              :: Pmovc (crbit_for_cond c) (ireg_of res) (SOimm Int.one) :: k)
+             rs m b H1 EVC)
+  as [rs1 [A [B C]]].
+  set (rs2 := nextinstr (rs1#(ireg_of res) <- (Vint Int.zero))).
+  set (rs3 := nextinstr (if b then (rs2#(ireg_of res) <- Vtrue) else rs2)).
+  exists rs3.
+  split. eapply exec_straight_trans. eauto. 
+  apply exec_straight_two with rs2 m; auto.
+  simpl. replace (rs2 (crbit_for_cond c)) with (Val.of_bool b).
+  unfold rs3. destruct b; auto.
+  unfold rs3. destruct b; auto.
+  split. unfold rs3. Simpl. destruct b. Simpl. unfold rs2. repeat Simpl.
+  intros. unfold rs3. Simpl. transitivity (rs2 r). 
+  destruct b; auto; Simpl. unfold rs2. repeat Simpl. 
 Qed.
 
 Remark val_add_add_zero:
@@ -1191,15 +1086,15 @@ Remark val_add_add_zero:
 Proof.
   intros. destruct v1; destruct v2; simpl; auto; rewrite Int.add_zero; auto.
 Qed.
- 
+
 Lemma transl_load_store_correct:
   forall (mk_instr_imm: ireg -> int -> instruction)
          (mk_instr_gen: option (ireg -> shift_addr -> instruction))
          (is_immed: int -> bool)
          addr args k ms sp rs m ms' m',
   (forall (r1: ireg) (rs1: regset) n k,
-    eval_addressing_total sp addr (map ms args) = Val.add rs1#r1 (Vint n) ->
-    agree ms sp rs1 ->
+    eval_addressing_total sp addr (map rs (map preg_of args)) = Val.add rs1#r1 (Vint n) ->
+    (forall (r: preg), r <> PC -> r <> IR14 -> rs1 r = rs r) ->
     exists rs',
     exec_straight (mk_instr_imm r1 n :: k) rs1 m k rs' m' /\
     agree ms' sp rs') ->
@@ -1207,8 +1102,8 @@ Lemma transl_load_store_correct:
   | None => True
   | Some mk =>
       (forall (r1: ireg) (sa: shift_addr) (rs1: regset) k,
-      eval_addressing_total sp addr (map ms args) = Val.add rs1#r1 (eval_shift_addr sa rs1) ->
-      agree ms sp rs1 ->
+      eval_addressing_total sp addr (map rs (map preg_of args)) = Val.add rs1#r1 (eval_shift_addr sa rs1) ->
+      (forall (r: preg), r <> PC -> r <> IR14 -> rs1 r = rs r) ->
       exists rs',
       exec_straight (mk r1 sa :: k) rs1 m k rs' m' /\
       agree ms' sp rs')
@@ -1224,62 +1119,53 @@ Proof.
   (* Aindexed *)
   case (is_immed i).
   (* Aindexed, small displacement *)
-  apply H; eauto. simpl. rewrite (ireg_val ms sp rs); auto.
+  apply H; auto.
   (* Aindexed, large displacement *)
-  exploit (addimm_correct IR14 (ireg_of t)); eauto with ppcgen. 
-  intros [rs' [A [B C]]].
-  exploit (H IR14 rs' Int.zero); eauto.
-  simpl. rewrite (ireg_val ms sp rs); auto. rewrite B.
-  rewrite Val.add_assoc. simpl Val.add. rewrite Int.add_zero. reflexivity.
-  apply agree_exten_2 with rs; auto. 
+  destruct (addimm_correct IR14 (ireg_of m0) i (mk_instr_imm IR14 Int.zero :: k) rs m)
+  as [rs' [A [B C]]].
+  exploit (H IR14 rs' Int.zero); eauto. 
+  rewrite B. rewrite Val.add_assoc. simpl Val.add. rewrite Int.add_zero. reflexivity.
   intros [rs'' [D E]].
   exists rs''; split.
   eapply exec_straight_trans. eexact A. eexact D. auto.
   (* Aindexed2 *)
   destruct mk_instr_gen as [mk | ]. 
   (* binary form available *)
-  apply H0; auto. simpl. repeat rewrite (ireg_val ms sp rs); auto. 
+  apply H0; auto.
   (* binary form not available *)
-  set (rs' := nextinstr (rs#IR14 <- (Val.add (ms t) (ms t0)))).
+  set (rs' := nextinstr (rs#IR14 <- (Val.add (rs (ireg_of m0)) (rs (ireg_of m1))))).
   exploit (H IR14 rs' Int.zero); eauto.
-  simpl. repeat rewrite (ireg_val ms sp rs); auto.
   unfold rs'. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
-  repeat rewrite (ireg_val ms sp rs); auto. apply val_add_add_zero. 
-  unfold rs'; auto with ppcgen.
+  apply val_add_add_zero. 
+  unfold rs'. intros. repeat Simpl. 
   intros [rs'' [A B]].
   exists rs''; split.
   eapply exec_straight_step with (rs2 := rs'); eauto.
-  simpl. repeat rewrite <- (ireg_val ms sp rs); auto.
-  auto.
+  simpl. auto. auto.
   (* Aindexed2shift *)
   destruct mk_instr_gen as [mk | ]. 
   (* binary form available *)
-  apply H0; auto. simpl. repeat rewrite (ireg_val ms sp rs); auto.
-  rewrite transl_shift_addr_correct. auto.
+  apply H0; auto. rewrite transl_shift_addr_correct. auto.
   (* binary form not available *)
-  set (rs' := nextinstr (rs#IR14 <- (Val.add (ms t) (eval_shift_total s (ms t0))))).
+  set (rs' := nextinstr (rs#IR14 <- (Val.add (rs (ireg_of m0)) (eval_shift_total s (rs (ireg_of m1)))))).
   exploit (H IR14 rs' Int.zero); eauto.
-  simpl. repeat rewrite (ireg_val ms sp rs); auto.
   unfold rs'. rewrite nextinstr_inv; auto with ppcgen. rewrite Pregmap.gss. 
-  repeat rewrite (ireg_val ms sp rs); auto. apply val_add_add_zero. 
-  unfold rs'; auto with ppcgen.
+  apply val_add_add_zero.
+  unfold rs'; intros; repeat Simpl.
   intros [rs'' [A B]].
   exists rs''; split.
   eapply exec_straight_step with (rs2 := rs'); eauto.
-  simpl. rewrite transl_shift_correct. 
-  repeat rewrite <- (ireg_val ms sp rs); auto.
+  simpl. rewrite transl_shift_correct. auto. 
   auto.
   (* Ainstack *)
   destruct (is_immed i).
   (* Ainstack, short displacement *)
-  apply H. simpl.  rewrite (sp_val ms sp rs); auto. auto. 
+  apply H; auto. rewrite (sp_val _ _ _ H1). auto.
   (* Ainstack, large displacement *)
-  exploit (addimm_correct IR14 IR13); eauto with ppcgen. 
-  intros [rs' [A [B C]]].
+  destruct (addimm_correct IR14 IR13 i (mk_instr_imm IR14 Int.zero :: k) rs m)
+  as [rs' [A [B C]]].
   exploit (H IR14 rs' Int.zero); eauto.
-  simpl. rewrite (sp_val ms sp rs); auto. rewrite B.
-  rewrite Val.add_assoc. simpl Val.add. rewrite Int.add_zero. reflexivity.
-  apply agree_exten_2 with rs; auto. 
+  rewrite (sp_val _ _ _ H1). rewrite B. rewrite Val.add_assoc. simpl Val.add. rewrite Int.add_zero. auto.
   intros [rs'' [D E]].
   exists rs''; split.
   eapply exec_straight_trans. eexact A. eexact D. auto.
@@ -1288,116 +1174,159 @@ Qed.
 Lemma transl_load_int_correct:
   forall (mk_instr: ireg -> ireg -> shift_addr -> instruction)
          (is_immed: int -> bool)
-         (rd: mreg) addr args k ms sp rs m chunk a v,
+         (rd: mreg) addr args k ms sp rs m m' chunk a v,
   (forall (c: code) (r1 r2: ireg) (sa: shift_addr) (rs1: regset),
-    exec_instr ge c (mk_instr r1 r2 sa) rs1 m =
-    exec_load chunk (Val.add rs1#r2 (eval_shift_addr sa rs1)) r1 rs1 m) ->
+    exec_instr ge c (mk_instr r1 r2 sa) rs1 m' =
+    exec_load chunk (Val.add rs1#r2 (eval_shift_addr sa rs1)) r1 rs1 m') ->
   agree ms sp rs ->
   map mreg_type args = type_of_addressing addr ->
   mreg_type rd = Tint ->
   eval_addressing ge sp addr (map ms args) = Some a ->
   Mem.loadv chunk m a = Some v ->
+  Mem.extends m m' ->
   exists rs',
-    exec_straight (transl_load_store_int mk_instr is_immed rd addr args k) rs m
-                        k rs' m
-  /\ agree (Regmap.set rd v ms) sp rs'.
+    exec_straight (transl_load_store_int mk_instr is_immed rd addr args k) rs m'
+                        k rs' m'
+  /\ agree (Regmap.set rd v (undef_temps ms)) sp rs'.
 Proof.
   intros. unfold transl_load_store_int.
-  exploit eval_addressing_weaken. eauto. intros. 
+  exploit eval_addressing_lessdef. eapply preg_vals; eauto. eauto. 
+  intros [a' [A B]].
+  exploit Mem.loadv_extends; eauto. intros [v' [C D]]. 
+  exploit eval_addressing_weaken. eexact A. intros E.
   apply transl_load_store_correct with ms; auto.
-  intros. exists (nextinstr (rs1#(ireg_of rd) <- v)); split.
-  apply exec_straight_one. rewrite H. simpl. rewrite <- H6. rewrite H5. 
-  unfold exec_load. rewrite H4. auto. auto.
-  auto with ppcgen.
-  intros. exists (nextinstr (rs1#(ireg_of rd) <- v)); split.
-  apply exec_straight_one. rewrite H. simpl. rewrite <- H6. rewrite H5. 
-  unfold exec_load. rewrite H4. auto. auto.
-  auto with ppcgen.
+  intros.
+  assert (Val.add (rs1 r1) (Vint n) = a') by congruence.
+  exists (nextinstr (rs1#(ireg_of rd) <- v')); split.
+  apply exec_straight_one. rewrite H. unfold exec_load. 
+  simpl. rewrite H8. rewrite C. auto. auto.
+  apply agree_nextinstr. eapply agree_set_undef_mreg; eauto. 
+  unfold preg_of. rewrite H2. rewrite Pregmap.gss. auto. 
+  unfold preg_of. rewrite H2. intros. rewrite Pregmap.gso; auto. apply H7; auto with ppcgen.
+  intros.
+  assert (Val.add (rs1 r1) (eval_shift_addr sa rs1) = a') by congruence.
+  exists (nextinstr (rs1#(ireg_of rd) <- v')); split.
+  apply exec_straight_one. rewrite H. unfold exec_load. 
+  simpl. rewrite H8. rewrite C. auto. auto.
+  apply agree_nextinstr. eapply agree_set_undef_mreg; eauto. 
+  unfold preg_of. rewrite H2. rewrite Pregmap.gss. auto. 
+  unfold preg_of. rewrite H2. intros. rewrite Pregmap.gso; auto. apply H7; auto with ppcgen.
 Qed.
 
 Lemma transl_load_float_correct:
   forall (mk_instr: freg -> ireg -> int -> instruction)
          (is_immed: int -> bool)
-         (rd: mreg) addr args k ms sp rs m chunk a v,
+         (rd: mreg) addr args k ms sp rs m m' chunk a v,
   (forall (c: code) (r1: freg) (r2: ireg) (n: int) (rs1: regset),
-    exec_instr ge c (mk_instr r1 r2 n) rs1 m =
-    exec_load chunk (Val.add rs1#r2 (Vint n)) r1 rs1 m) ->
+    exec_instr ge c (mk_instr r1 r2 n) rs1 m' =
+    exec_load chunk (Val.add rs1#r2 (Vint n)) r1 rs1 m') ->
   agree ms sp rs ->
   map mreg_type args = type_of_addressing addr ->
   mreg_type rd = Tfloat ->
   eval_addressing ge sp addr (map ms args) = Some a ->
   Mem.loadv chunk m a = Some v ->
+  Mem.extends m m' ->
   exists rs',
-    exec_straight (transl_load_store_float mk_instr is_immed rd addr args k) rs m
-                        k rs' m
-  /\ agree (Regmap.set rd v ms) sp rs'.
+    exec_straight (transl_load_store_float mk_instr is_immed rd addr args k) rs m'
+                        k rs' m'
+  /\ agree (Regmap.set rd v (undef_temps ms)) sp rs'.
 Proof.
-  intros. unfold transl_load_store_float.
-  exploit eval_addressing_weaken. eauto. intros. 
+  intros. unfold transl_load_store_int.
+  exploit eval_addressing_lessdef. eapply preg_vals; eauto. eauto. 
+  intros [a' [A B]].
+  exploit Mem.loadv_extends; eauto. intros [v' [C D]]. 
+  exploit eval_addressing_weaken. eexact A. intros E.
   apply transl_load_store_correct with ms; auto.
-  intros. exists (nextinstr (rs1#(freg_of rd) <- v)); split.
-  apply exec_straight_one. rewrite H. rewrite <- H6. rewrite H5. 
-  unfold exec_load. rewrite H4. auto. auto.
-  auto with ppcgen.
+  intros.
+  assert (Val.add (rs1 r1) (Vint n) = a') by congruence.
+  exists (nextinstr (rs1#(freg_of rd) <- v')); split.
+  apply exec_straight_one. rewrite H. unfold exec_load. 
+  simpl. rewrite H8. rewrite C. auto. auto.
+  apply agree_nextinstr. eapply agree_set_undef_mreg; eauto. 
+  unfold preg_of. rewrite H2. rewrite Pregmap.gss. auto. 
+  unfold preg_of. rewrite H2. intros. rewrite Pregmap.gso; auto. apply H7; auto with ppcgen.
 Qed.
 
 Lemma transl_store_int_correct:
   forall (mk_instr: ireg -> ireg -> shift_addr -> instruction)
          (is_immed: int -> bool)
-         (rd: mreg) addr args k ms sp rs m chunk a m',
+         (rd: mreg) addr args k ms sp rs m1 chunk a m2 m1',
   (forall (c: code) (r1 r2: ireg) (sa: shift_addr) (rs1: regset),
-    exec_instr ge c (mk_instr r1 r2 sa) rs1 m =
-    exec_store chunk (Val.add rs1#r2 (eval_shift_addr sa rs1)) r1 rs1 m) ->
+    exec_instr ge c (mk_instr r1 r2 sa) rs1 m1' =
+    exec_store chunk (Val.add rs1#r2 (eval_shift_addr sa rs1)) r1 rs1 m1') ->
   agree ms sp rs ->
   map mreg_type args = type_of_addressing addr ->
   mreg_type rd = Tint ->
   eval_addressing ge sp addr (map ms args) = Some a ->
-  Mem.storev chunk m a (ms rd) = Some m' ->
-  exists rs',
-    exec_straight (transl_load_store_int mk_instr is_immed rd addr args k) rs m
-                        k rs' m'
-  /\ agree ms sp rs'.
+  Mem.storev chunk m1 a (ms rd) = Some m2 ->
+  Mem.extends m1 m1' ->
+  exists m2',
+    Mem.extends m2 m2' /\
+    exists rs',
+    exec_straight (transl_load_store_int mk_instr is_immed rd addr args k) rs m1'
+                        k rs' m2'
+    /\ agree (undef_temps ms) sp rs'.
 Proof.
   intros. unfold transl_load_store_int.
-  exploit eval_addressing_weaken. eauto. intros. 
+  exploit eval_addressing_lessdef. eapply preg_vals; eauto. eauto. 
+  intros [a' [A B]].
+  exploit preg_val; eauto. instantiate (1 := rd). intros C.
+  exploit Mem.storev_extends; eauto. unfold preg_of; rewrite H2. intros [m2' [D E]].
+  exploit eval_addressing_weaken. eexact A. intros F.
+  exists m2'; split; auto.
   apply transl_load_store_correct with ms; auto.
-  intros. exists (nextinstr rs1); split.
-  apply exec_straight_one. rewrite H. simpl. rewrite <- H6. rewrite H5.
-  unfold exec_store. rewrite <- (ireg_val ms sp rs1); auto.
-  rewrite H4. auto. auto.
-  auto with ppcgen.
-  intros. exists (nextinstr rs1); split.
-  apply exec_straight_one. rewrite H. simpl. rewrite <- H6. rewrite H5.
-  unfold exec_store. rewrite <- (ireg_val ms sp rs1); auto.
-  rewrite H4. auto. auto.
-  auto with ppcgen.
+  intros.
+  assert (Val.add (rs1 r1) (Vint n) = a') by congruence.
+  exists (nextinstr rs1); split.
+  apply exec_straight_one. rewrite H. simpl. rewrite H8. 
+  unfold exec_store. rewrite H7; auto with ppcgen. rewrite D. auto. auto.
+  apply agree_nextinstr. apply agree_exten_temps with rs; auto with ppcgen.
+  intros.
+  assert (Val.add (rs1 r1) (eval_shift_addr sa rs1) = a') by congruence.
+  exists (nextinstr rs1); split.
+  apply exec_straight_one. rewrite H. simpl. rewrite H8. 
+  unfold exec_store. rewrite H7; auto with ppcgen. rewrite D. auto. auto.
+  apply agree_nextinstr. apply agree_exten_temps with rs; auto with ppcgen.
 Qed.
 
 Lemma transl_store_float_correct:
   forall (mk_instr: freg -> ireg -> int -> instruction)
          (is_immed: int -> bool)
-         (rd: mreg) addr args k ms sp rs m chunk a m',
-  (forall (c: code) (r1: freg) (r2: ireg) (n: int) (rs1: regset),
-    exec_instr ge c (mk_instr r1 r2 n) rs1 m =
-    exec_store chunk (Val.add rs1#r2 (Vint n)) r1 rs1 m) ->
+         (rd: mreg) addr args k ms sp rs m1 chunk a m2 m1',
+  (forall (c: code) (r1: freg) (r2: ireg) (n: int) (rs1: regset) m2',
+   exec_store chunk (Val.add rs1#r2 (Vint n)) r1 rs1 m1' = OK (nextinstr rs1) m2' ->
+   exists rs2,
+   exec_instr ge c (mk_instr r1 r2 n) rs1 m1' = OK rs2 m2'
+   /\ (forall (r: preg), r <> FR3 -> rs2 r = nextinstr rs1 r)) ->
   agree ms sp rs ->
   map mreg_type args = type_of_addressing addr ->
   mreg_type rd = Tfloat ->
   eval_addressing ge sp addr (map ms args) = Some a ->
-  Mem.storev chunk m a (ms rd) = Some m' ->
-  exists rs',
-    exec_straight (transl_load_store_float mk_instr is_immed rd addr args k) rs m
-                        k rs' m'
-  /\ agree ms sp rs'.
+  Mem.storev chunk m1 a (ms rd) = Some m2 ->
+  Mem.extends m1 m1' ->
+  exists m2',
+    Mem.extends m2 m2' /\
+    exists rs',
+    exec_straight (transl_load_store_float mk_instr is_immed rd addr args k) rs m1'
+                        k rs' m2'
+    /\ agree (undef_temps ms) sp rs'.
 Proof.
   intros. unfold transl_load_store_float.
-  exploit eval_addressing_weaken. eauto. intros. 
+  exploit eval_addressing_lessdef. eapply preg_vals; eauto. eauto. 
+  intros [a' [A B]].
+  exploit preg_val; eauto. instantiate (1 := rd). intros C.
+  exploit Mem.storev_extends; eauto. unfold preg_of; rewrite H2. intros [m2' [D E]].
+  exploit eval_addressing_weaken. eexact A. intros F.
+  exists m2'; split; auto.
   apply transl_load_store_correct with ms; auto.
-  intros. exists (nextinstr rs1); split.
-  apply exec_straight_one. rewrite H. simpl. rewrite <- H6. rewrite H5.
-  unfold exec_store. rewrite <- (freg_val ms sp rs1); auto.
-  rewrite H4. auto. auto.
-  auto with ppcgen.
+  intros.
+  assert (Val.add (rs1 r1) (Vint n) = a') by congruence.
+  exploit (H fn (freg_of rd) r1 n rs1 m2').
+  unfold exec_store. rewrite H8. rewrite H7; auto with ppcgen. rewrite D. auto.
+  intros [rs2 [P Q]].
+  exists rs2; split. apply exec_straight_one. auto. rewrite Q; auto with ppcgen.
+  apply agree_exten_temps with rs; auto.
+  intros. rewrite Q; auto with ppcgen. Simpl. apply H7; auto with ppcgen.
 Qed.
 
 End STRAIGHTLINE.