1 files changed, 459 insertions, 459 deletions

diff --git a/src/translation/HTLgenspec.v b/src/translation/HTLgenspec.v
index a9626c4..4662cf4 100644
--- a/src/translation/HTLgenspec.v
+++ b/src/translation/HTLgenspec.v
@@ -148,462 +148,462 @@ Inductive tr_instr (fin rtrn st stk : reg) : RTL.instruction -> stmnt -> stmnt -
     tr_instr fin rtrn st stk (RTL.Ijumptable r tbl) (Vskip) (Vcase (Vvar r) cexpr (Some Vskip)).
 Hint Constructors tr_instr : htlspec.
 
-Inductive tr_code (c : RTL.code) (pc : RTL.node) (i : RTL.instruction) (stmnts trans : PTree.t stmnt)
-          (fin rtrn st stk : reg) : Prop :=
-  tr_code_intro :
-    forall s t,
-      c!pc = Some i ->
-      stmnts!pc = Some s ->
-      trans!pc = Some t ->
-      tr_instr fin rtrn st stk i s t ->
-      tr_code c pc i stmnts trans fin rtrn st stk.
-Hint Constructors tr_code : htlspec.
-
-Inductive tr_module (f : RTL.function) : module -> Prop :=
-  tr_module_intro :
-    forall data control fin rtrn st stk stk_len m start rst clk scldecls arrdecls wf,
-      m = (mkmodule f.(RTL.fn_params)
-                        data
-                        control
-                        f.(RTL.fn_entrypoint)
-                        st stk stk_len fin rtrn start rst clk scldecls arrdecls wf) ->
-      (forall pc i, Maps.PTree.get pc f.(RTL.fn_code) = Some i ->
-               tr_code f.(RTL.fn_code) pc i data control fin rtrn st stk) ->
-      stk_len = Z.to_nat (f.(RTL.fn_stacksize) / 4) ->
-      Z.modulo (f.(RTL.fn_stacksize)) 4 = 0 ->
-      0 <= f.(RTL.fn_stacksize) < Integers.Ptrofs.modulus ->
-      st = ((RTL.max_reg_function f) + 1)%positive ->
-      fin = ((RTL.max_reg_function f) + 2)%positive ->
-      rtrn = ((RTL.max_reg_function f) + 3)%positive ->
-      stk = ((RTL.max_reg_function f) + 4)%positive ->
-      start = ((RTL.max_reg_function f) + 5)%positive ->
-      rst = ((RTL.max_reg_function f) + 6)%positive ->
-      clk = ((RTL.max_reg_function f) + 7)%positive ->
-      tr_module f m.
-Hint Constructors tr_module : htlspec.
-
-Lemma create_reg_datapath_trans :
-  forall sz s s' x i iop,
-    create_reg iop sz s = OK x s' i ->
-    s.(st_datapath) = s'.(st_datapath).
-Proof. intros. monadInv H. trivial. Qed.
-Hint Resolve create_reg_datapath_trans : htlspec.
-
-Lemma create_reg_controllogic_trans :
-  forall sz s s' x i iop,
-    create_reg iop sz s = OK x s' i ->
-    s.(st_controllogic) = s'.(st_controllogic).
-Proof. intros. monadInv H. trivial. Qed.
-Hint Resolve create_reg_controllogic_trans : htlspec.
-
-Lemma declare_reg_datapath_trans :
-  forall sz s s' x i iop r,
-    declare_reg iop r sz s = OK x s' i ->
-    s.(st_datapath) = s'.(st_datapath).
-Proof. intros. monadInv H. trivial. Qed.
-Hint Resolve create_reg_datapath_trans : htlspec.
-
-Lemma declare_reg_controllogic_trans :
-  forall sz s s' x i iop r,
-    declare_reg iop r sz s = OK x s' i ->
-    s.(st_controllogic) = s'.(st_controllogic).
-Proof. intros. monadInv H. trivial. Qed.
-Hint Resolve create_reg_controllogic_trans : htlspec.
-
-Lemma declare_reg_freshreg_trans :
-  forall sz s s' x i iop r,
-    declare_reg iop r sz s = OK x s' i ->
-    s.(st_freshreg) = s'.(st_freshreg).
-Proof. inversion 1; auto. Qed.
-Hint Resolve declare_reg_freshreg_trans : htlspec.
-
-Lemma create_arr_datapath_trans :
-  forall sz ln s s' x i iop,
-    create_arr iop sz ln s = OK x s' i ->
-    s.(st_datapath) = s'.(st_datapath).
-Proof. intros. monadInv H. trivial. Qed.
-Hint Resolve create_arr_datapath_trans : htlspec.
-
-Lemma create_arr_controllogic_trans :
-  forall sz ln s s' x i iop,
-    create_arr iop sz ln s = OK x s' i ->
-    s.(st_controllogic) = s'.(st_controllogic).
-Proof. intros. monadInv H. trivial. Qed.
-Hint Resolve create_arr_controllogic_trans : htlspec.
-
-Lemma get_refl_x :
-  forall s s' x i,
-    get s = OK x s' i ->
-    s = x.
-Proof. inversion 1. trivial. Qed.
-Hint Resolve get_refl_x : htlspec.
-
-Lemma get_refl_s :
-  forall s s' x i,
-    get s = OK x s' i ->
-    s = s'.
-Proof. inversion 1. trivial. Qed.
-Hint Resolve get_refl_s : htlspec.
-
-Ltac inv_incr :=
-  repeat match goal with
-  | [ H: create_reg _ _ ?s = OK _ ?s' _ |- _ ] =>
-    let H1 := fresh "H" in
-    assert (H1 := H); eapply create_reg_datapath_trans in H;
-    eapply create_reg_controllogic_trans in H1
-  | [ H: create_arr _ _ _ ?s = OK _ ?s' _ |- _ ] =>
-    let H1 := fresh "H" in
-    assert (H1 := H); eapply create_arr_datapath_trans in H;
-    eapply create_arr_controllogic_trans in H1
-  | [ H: get ?s = OK _ _ _ |- _ ] =>
-    let H1 := fresh "H" in
-    assert (H1 := H); apply get_refl_x in H; apply get_refl_s in H1;
-    subst
-  | [ H: st_prop _ _ |- _ ] => unfold st_prop in H; destruct H
-  | [ H: st_incr _ _ |- _ ] => destruct st_incr
-  end.
-
-Lemma collect_controllogic_trans :
-  forall A f l cs cs' ci,
-  (forall s s' x i y, f y s = OK x s' i -> s.(st_controllogic) = s'.(st_controllogic)) ->
-  @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_controllogic) = cs'.(st_controllogic).
-Proof.
-  induction l; intros; monadInv H0.
-  - trivial.
-  - apply H in EQ. rewrite EQ. eauto.
-Qed.
-
-Lemma collect_datapath_trans :
-  forall A f l cs cs' ci,
-  (forall s s' x i y, f y s = OK x s' i -> s.(st_datapath) = s'.(st_datapath)) ->
-  @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_datapath) = cs'.(st_datapath).
-Proof.
-  induction l; intros; monadInv H0.
-  - trivial.
-  - apply H in EQ. rewrite EQ. eauto.
-Qed.
-
-Lemma collect_freshreg_trans :
-  forall A f l cs cs' ci,
-  (forall s s' x i y, f y s = OK x s' i -> s.(st_freshreg) = s'.(st_freshreg)) ->
-  @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_freshreg) = cs'.(st_freshreg).
-Proof.
-  induction l; intros; monadInv H0.
-  - trivial.
-  - apply H in EQ. rewrite EQ. eauto.
-Qed.
-
-Lemma collect_declare_controllogic_trans :
-  forall io n l s s' i,
-  HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i ->
-  s.(st_controllogic) = s'.(st_controllogic).
-Proof.
-  intros. eapply collect_controllogic_trans; try eassumption.
-  intros. eapply declare_reg_controllogic_trans. simpl in H0. eassumption.
-Qed.
-
-Lemma collect_declare_datapath_trans :
-  forall io n l s s' i,
-  HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i ->
-  s.(st_datapath) = s'.(st_datapath).
-Proof.
-  intros. eapply collect_datapath_trans; try eassumption.
-  intros. eapply declare_reg_datapath_trans. simpl in H0. eassumption.
-Qed.
-
-Lemma collect_declare_freshreg_trans :
-  forall io n l s s' i,
-  HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  intros. eapply collect_freshreg_trans; try eassumption.
-  inversion 1. auto.
-Qed.
-
-Ltac unfold_match H :=
-  match type of H with
-  | context[match ?g with _ => _ end] => destruct g eqn:?; try discriminate
-  end.
-
-Lemma translate_eff_addressing_freshreg_trans :
-  forall op args s r s' i,
-  translate_eff_addressing op args s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
-Qed.
-Hint Resolve translate_eff_addressing_freshreg_trans : htlspec.
-
-Lemma translate_comparison_freshreg_trans :
-  forall op args s r s' i,
-  translate_comparison op args s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
-Qed.
-Hint Resolve translate_comparison_freshreg_trans : htlspec.
-
-Lemma translate_comparison_imm_freshreg_trans :
-  forall op args s r s' i n,
-  translate_comparison_imm op args n s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
-Qed.
-Hint Resolve translate_comparison_imm_freshreg_trans : htlspec.
-
-Lemma translate_condition_freshreg_trans :
-  forall op args s r s' i,
-  translate_condition op args s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; eauto with htlspec.
-Qed.
-Hint Resolve translate_condition_freshreg_trans : htlspec.
-
-Lemma translate_instr_freshreg_trans :
-  forall op args s r s' i,
-  translate_instr op args s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; eauto with htlspec.
-  monadInv H1. eauto with htlspec.
-Qed.
-Hint Resolve translate_instr_freshreg_trans : htlspec.
-
-Lemma translate_arr_access_freshreg_trans :
-  forall mem addr args st s r s' i,
-  translate_arr_access mem addr args st s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  intros. unfold translate_arr_access in H. repeat (unfold_match H); inv H; eauto with htlspec.
-Qed.
-Hint Resolve translate_arr_access_freshreg_trans : htlspec.
-
-Lemma add_instr_freshreg_trans :
-  forall n n' st s r s' i,
-  add_instr n n' st s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof. intros. unfold add_instr in H. repeat (unfold_match H). inv H. auto. Qed.
-Hint Resolve add_instr_freshreg_trans : htlspec.
-
-Lemma add_branch_instr_freshreg_trans :
-  forall n n0 n1 e s r s' i,
-  add_branch_instr e n n0 n1 s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof. intros. unfold add_branch_instr in H. repeat (unfold_match H). inv H. auto. Qed.
-Hint Resolve add_branch_instr_freshreg_trans : htlspec.
-
-Lemma add_node_skip_freshreg_trans :
-  forall n1 n2 s r s' i,
-  add_node_skip n1 n2 s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof. intros. unfold add_node_skip in H. repeat (unfold_match H). inv H. auto. Qed.
-Hint Resolve add_node_skip_freshreg_trans : htlspec.
-
-Lemma add_instr_skip_freshreg_trans :
-  forall n1 n2 s r s' i,
-  add_instr_skip n1 n2 s = OK r s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof. intros. unfold add_instr_skip in H. repeat (unfold_match H). inv H. auto. Qed.
-Hint Resolve add_instr_skip_freshreg_trans : htlspec.
-
-Lemma transf_instr_freshreg_trans :
-  forall fin ret st instr s v s' i,
-    transf_instr fin ret st instr s = OK v s' i ->
-    s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  intros. destruct instr eqn:?. subst. unfold transf_instr in H.
-  destruct i0; try (monadInv H); try (unfold_match H); eauto with htlspec.
-  - apply add_instr_freshreg_trans in EQ2. apply translate_instr_freshreg_trans in EQ.
-    apply declare_reg_freshreg_trans in EQ1. congruence.
-  - apply add_instr_freshreg_trans in EQ2. apply translate_arr_access_freshreg_trans in EQ.
-    apply declare_reg_freshreg_trans in EQ1. congruence.
-  - apply add_instr_freshreg_trans in EQ0. apply translate_arr_access_freshreg_trans in EQ. congruence.
-  - apply translate_condition_freshreg_trans in EQ. apply add_branch_instr_freshreg_trans in EQ0.
-    congruence.
-  - inv EQ. apply add_node_skip_freshreg_trans in EQ0. congruence.
-Qed.
-Hint Resolve transf_instr_freshreg_trans : htlspec.
-
-Lemma collect_trans_instr_freshreg_trans :
-  forall fin ret st l s s' i,
-  HTLMonadExtra.collectlist (transf_instr fin ret st) l s = OK tt s' i ->
-  s.(st_freshreg) = s'.(st_freshreg).
-Proof.
-  intros. eapply collect_freshreg_trans; try eassumption.
-  eauto with htlspec.
-Qed.
-
-Ltac rewrite_states :=
-  match goal with
-  | [ H: ?x ?s = ?x ?s' |- _ ] =>
-    let c1 := fresh "c" in
-    let c2 := fresh "c" in
-    remember (?x ?s) as c1; remember (?x ?s') as c2; try subst
-  end.
-
-Ltac inv_add_instr' H :=
-  match type of H with
-  | ?f _ _ _ = OK _ _ _ => unfold f in H
-  | ?f _ _ _ _ = OK _ _ _ => unfold f in H
-  | ?f _ _ _ _ _ = OK _ _ _ => unfold f in H
-  end; repeat unfold_match H; inversion H.
-
-Ltac inv_add_instr :=
-  lazymatch goal with
-  | H: context[add_instr_skip _ _ _] |- _ =>
-    inv_add_instr' H
-  | H: context[add_instr_skip _ _] |- _ =>
-    monadInv H; inv_incr; inv_add_instr
-  | H: context[add_instr _ _ _ _] |- _ =>
-    inv_add_instr' H
-  | H: context[add_instr _ _ _] |- _ =>
-    monadInv H; inv_incr; inv_add_instr
-  | H: context[add_branch_instr _ _ _ _ _] |- _ =>
-    inv_add_instr' H
-  | H: context[add_branch_instr _ _ _ _] |- _ =>
-    monadInv H; inv_incr; inv_add_instr
-  | H: context[add_node_skip _ _ _] |- _ =>
-    inv_add_instr' H
-  | H: context[add_node_skip _ _] |- _ =>
-    monadInv H; inv_incr; inv_add_instr
-  end.
-
-Ltac destruct_optional :=
-  match goal with H: option ?r |- _ => destruct H end.
-
-Lemma iter_expand_instr_spec :
-  forall l fin rtrn stack s s' i x c,
-    HTLMonadExtra.collectlist (transf_instr fin rtrn stack) l s = OK x s' i ->
-    list_norepet (List.map fst l) ->
-    (forall pc instr, In (pc, instr) l -> c!pc = Some instr) ->
-    (forall pc instr, In (pc, instr) l ->
-                      c!pc = Some instr ->
-                      tr_code c pc instr s'.(st_datapath) s'.(st_controllogic) fin rtrn s'.(st_st) stack).
-Proof.
-  induction l; simpl; intros; try contradiction.
-  destruct a as [pc1 instr1]; simpl in *. inv H0. monadInv H. inv_incr.
-  destruct (peq pc pc1).
-  - subst.
-    destruct instr1 eqn:?; try discriminate;
-      try destruct_optional; inv_add_instr; econstructor; try assumption.
-    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + inversion H2. inversion H9. rewrite H. apply tr_instr_Inop.
-      eapply in_map with (f := fst) in H9. contradiction.
-
-    + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
-    + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
-    + inversion H2. inversion H14. unfold nonblock. replace (st_st s4) with (st_st s2) by congruence.
-      econstructor. apply EQ1. eapply in_map with (f := fst) in H14. contradiction.
-
-    + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
-    + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
-    + inversion H2. inversion H14. rewrite <- e2. replace (st_st s2) with (st_st s0) by congruence.
-      econstructor. apply EQ1. eapply in_map with (f := fst) in H14. contradiction.
-
-    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct H2.
-      * inversion H2.
-        replace (st_st s2) with (st_st s0) by congruence.
-        eauto with htlspec.
-      * apply in_map with (f := fst) in H2. contradiction.
-
-    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct H2.
-      * inversion H2.
-        replace (st_st s2) with (st_st s0) by congruence.
-        eauto with htlspec.
-      * apply in_map with (f := fst) in H2. contradiction.
-
-    + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
-    + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
-    + inversion H2.
-      * inversion H14. constructor. congruence.
-      * apply in_map with (f := fst) in H14. contradiction.
-
-    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + inversion H2.
-      * inversion H9.
-        replace (st_st s2) with (st_st s0) by congruence.
-        eauto with htlspec.
-      * apply in_map with (f := fst) in H9. contradiction.
-
-    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
-    + inversion H2.
-      * inversion H9.
-        replace (st_st s2) with (st_st s0) by congruence.
-        eauto with htlspec.
-      * apply in_map with (f := fst) in H9. contradiction.
-
-  - eapply IHl. apply EQ0. assumption.
-    destruct H2. inversion H2. subst. contradiction.
-    intros. specialize H1 with pc0 instr0. destruct H1. tauto. trivial.
-    destruct H2. inv H2. contradiction. assumption. assumption.
-Qed.
-Hint Resolve iter_expand_instr_spec : htlspec.
-
-Lemma create_arr_inv : forall w x y z a b c d,
-    create_arr w x y z = OK (a, b) c d ->
-    y = b /\ a = z.(st_freshreg) /\ c.(st_freshreg) = Pos.succ (z.(st_freshreg)).
-Proof.
-  inversion 1; split; auto.
-Qed.
-
-Lemma create_reg_inv : forall a b s r s' i,
-    create_reg a b s = OK r s' i ->
-    r = s.(st_freshreg) /\ s'.(st_freshreg) = Pos.succ (s.(st_freshreg)).
-Proof.
-  inversion 1; auto.
-Qed.
-
-Theorem transl_module_correct :
-  forall f m,
-    transl_module f = Errors.OK m -> tr_module f m.
-Proof.
-  intros until m.
-  unfold transl_module.
-  unfold run_mon.
-  destruct (transf_module f (max_state f)) eqn:?; try discriminate.
-  intros. inv H.
-  inversion s; subst.
-
-  unfold transf_module in *.
-  unfold stack_correct in *.
-  destruct (0 <=? RTL.fn_stacksize f) eqn:STACK_BOUND_LOW;
-    destruct (RTL.fn_stacksize f <? Integers.Ptrofs.modulus) eqn:STACK_BOUND_HIGH;
-    destruct (RTL.fn_stacksize f mod 4 =? 0) eqn:STACK_ALIGN;
-    crush;
-    monadInv Heqr.
-
-  repeat unfold_match EQ9. monadInv EQ9.
-
-  (* TODO: We should be able to fold this into the automation. *)
-  pose proof (create_arr_inv _ _ _ _ _ _ _ _ EQ0) as STK_LEN. inv STK_LEN. inv H5.
-  pose proof (create_reg_inv _ _ _ _ _ _ EQ) as FIN_VAL. inv FIN_VAL.
-  pose proof (create_reg_inv _ _ _ _ _ _ EQ1) as RET_VAL. inv RET_VAL.
-  destruct x3. destruct x4.
-  pose proof (collect_trans_instr_freshreg_trans _ _ _ _ _ _ _ EQ2) as TR_INSTR.
-  pose proof (collect_declare_freshreg_trans _ _ _ _ _ _ EQ3) as TR_DEC.
-  pose proof (create_reg_inv _ _ _ _ _ _ EQ4) as START_VAL. inv START_VAL.
-  pose proof (create_reg_inv _ _ _ _ _ _ EQ5) as RESET_VAL. inv RESET_VAL.
-  pose proof (create_reg_inv _ _ _ _ _ _ EQ6) as CLK_VAL. inv CLK_VAL.
-  rewrite H9 in *. rewrite H8 in *. replace (st_freshreg s4) with (st_freshreg s2) in * by congruence.
-  rewrite H6 in *. rewrite H7 in *. rewrite H5 in *. simpl in *.
-  inv_incr.
-  econstructor; simpl; auto; try lia.
-  intros.
-  assert (EQ3D := EQ3).
-  apply collect_declare_datapath_trans in EQ3.
-  apply collect_declare_controllogic_trans in EQ3D.
-  replace (st_controllogic s10) with (st_controllogic s3) by congruence.
-  replace (st_datapath s10) with (st_datapath s3) by congruence.
-  replace (st_st s10) with (st_st s3) by congruence.
-  eapply iter_expand_instr_spec; eauto with htlspec.
-  apply PTree.elements_complete.
-Qed.
+(* Inductive tr_code (c : RTL.code) (pc : RTL.node) (i : RTL.instruction) (stmnts trans : PTree.t stmnt) *)
+(*           (fin rtrn st stk : reg) : Prop := *)
+(*   tr_code_intro : *)
+(*     forall s t, *)
+(*       c!pc = Some i -> *)
+(*       stmnts!pc = Some s -> *)
+(*       trans!pc = Some t -> *)
+(*       tr_instr fin rtrn st stk i s t -> *)
+(*       tr_code c pc i stmnts trans fin rtrn st stk. *)
+(* Hint Constructors tr_code : htlspec. *)
+
+(* Inductive tr_module (f : RTL.function) : module -> Prop := *)
+(*   tr_module_intro : *)
+(*     forall data control fin rtrn st stk stk_len m start rst clk scldecls arrdecls wf, *)
+(*       m = (mkmodule f.(RTL.fn_params) *)
+(*                         data *)
+(*                         control *)
+(*                         f.(RTL.fn_entrypoint) *)
+(*                         st stk stk_len fin rtrn start rst clk scldecls arrdecls wf) -> *)
+(*       (forall pc i, Maps.PTree.get pc f.(RTL.fn_code) = Some i -> *)
+(*                tr_code f.(RTL.fn_code) pc i data control fin rtrn st stk) -> *)
+(*       stk_len = Z.to_nat (f.(RTL.fn_stacksize) / 4) -> *)
+(*       Z.modulo (f.(RTL.fn_stacksize)) 4 = 0 -> *)
+(*       0 <= f.(RTL.fn_stacksize) < Integers.Ptrofs.modulus -> *)
+(*       st = ((RTL.max_reg_function f) + 1)%positive -> *)
+(*       fin = ((RTL.max_reg_function f) + 2)%positive -> *)
+(*       rtrn = ((RTL.max_reg_function f) + 3)%positive -> *)
+(*       stk = ((RTL.max_reg_function f) + 4)%positive -> *)
+(*       start = ((RTL.max_reg_function f) + 5)%positive -> *)
+(*       rst = ((RTL.max_reg_function f) + 6)%positive -> *)
+(*       clk = ((RTL.max_reg_function f) + 7)%positive -> *)
+(*       tr_module f m. *)
+(* Hint Constructors tr_module : htlspec. *)
+
+(* Lemma create_reg_datapath_trans : *)
+(*   forall sz s s' x i iop, *)
+(*     create_reg iop sz s = OK x s' i -> *)
+(*     s.(st_datapath) = s'.(st_datapath). *)
+(* Proof. intros. monadInv H. trivial. Qed. *)
+(* Hint Resolve create_reg_datapath_trans : htlspec. *)
+
+(* Lemma create_reg_controllogic_trans : *)
+(*   forall sz s s' x i iop, *)
+(*     create_reg iop sz s = OK x s' i -> *)
+(*     s.(st_controllogic) = s'.(st_controllogic). *)
+(* Proof. intros. monadInv H. trivial. Qed. *)
+(* Hint Resolve create_reg_controllogic_trans : htlspec. *)
+
+(* Lemma declare_reg_datapath_trans : *)
+(*   forall sz s s' x i iop r, *)
+(*     declare_reg iop r sz s = OK x s' i -> *)
+(*     s.(st_datapath) = s'.(st_datapath). *)
+(* Proof. intros. monadInv H. trivial. Qed. *)
+(* Hint Resolve create_reg_datapath_trans : htlspec. *)
+
+(* Lemma declare_reg_controllogic_trans : *)
+(*   forall sz s s' x i iop r, *)
+(*     declare_reg iop r sz s = OK x s' i -> *)
+(*     s.(st_controllogic) = s'.(st_controllogic). *)
+(* Proof. intros. monadInv H. trivial. Qed. *)
+(* Hint Resolve create_reg_controllogic_trans : htlspec. *)
+
+(* Lemma declare_reg_freshreg_trans : *)
+(*   forall sz s s' x i iop r, *)
+(*     declare_reg iop r sz s = OK x s' i -> *)
+(*     s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. inversion 1; auto. Qed. *)
+(* Hint Resolve declare_reg_freshreg_trans : htlspec. *)
+
+(* Lemma create_arr_datapath_trans : *)
+(*   forall sz ln s s' x i iop, *)
+(*     create_arr iop sz ln s = OK x s' i -> *)
+(*     s.(st_datapath) = s'.(st_datapath). *)
+(* Proof. intros. monadInv H. trivial. Qed. *)
+(* Hint Resolve create_arr_datapath_trans : htlspec. *)
+
+(* Lemma create_arr_controllogic_trans : *)
+(*   forall sz ln s s' x i iop, *)
+(*     create_arr iop sz ln s = OK x s' i -> *)
+(*     s.(st_controllogic) = s'.(st_controllogic). *)
+(* Proof. intros. monadInv H. trivial. Qed. *)
+(* Hint Resolve create_arr_controllogic_trans : htlspec. *)
+
+(* Lemma get_refl_x : *)
+(*   forall s s' x i, *)
+(*     get s = OK x s' i -> *)
+(*     s = x. *)
+(* Proof. inversion 1. trivial. Qed. *)
+(* Hint Resolve get_refl_x : htlspec. *)
+
+(* Lemma get_refl_s : *)
+(*   forall s s' x i, *)
+(*     get s = OK x s' i -> *)
+(*     s = s'. *)
+(* Proof. inversion 1. trivial. Qed. *)
+(* Hint Resolve get_refl_s : htlspec. *)
+
+(* Ltac inv_incr := *)
+(*   repeat match goal with *)
+(*   | [ H: create_reg _ _ ?s = OK _ ?s' _ |- _ ] => *)
+(*     let H1 := fresh "H" in *)
+(*     assert (H1 := H); eapply create_reg_datapath_trans in H; *)
+(*     eapply create_reg_controllogic_trans in H1 *)
+(*   | [ H: create_arr _ _ _ ?s = OK _ ?s' _ |- _ ] => *)
+(*     let H1 := fresh "H" in *)
+(*     assert (H1 := H); eapply create_arr_datapath_trans in H; *)
+(*     eapply create_arr_controllogic_trans in H1 *)
+(*   | [ H: get ?s = OK _ _ _ |- _ ] => *)
+(*     let H1 := fresh "H" in *)
+(*     assert (H1 := H); apply get_refl_x in H; apply get_refl_s in H1; *)
+(*     subst *)
+(*   | [ H: st_prop _ _ |- _ ] => unfold st_prop in H; destruct H *)
+(*   | [ H: st_incr _ _ |- _ ] => destruct st_incr *)
+(*   end. *)
+
+(* Lemma collect_controllogic_trans : *)
+(*   forall A f l cs cs' ci, *)
+(*   (forall s s' x i y, f y s = OK x s' i -> s.(st_controllogic) = s'.(st_controllogic)) -> *)
+(*   @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_controllogic) = cs'.(st_controllogic). *)
+(* Proof. *)
+(*   induction l; intros; monadInv H0. *)
+(*   - trivial. *)
+(*   - apply H in EQ. rewrite EQ. eauto. *)
+(* Qed. *)
+
+(* Lemma collect_datapath_trans : *)
+(*   forall A f l cs cs' ci, *)
+(*   (forall s s' x i y, f y s = OK x s' i -> s.(st_datapath) = s'.(st_datapath)) -> *)
+(*   @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_datapath) = cs'.(st_datapath). *)
+(* Proof. *)
+(*   induction l; intros; monadInv H0. *)
+(*   - trivial. *)
+(*   - apply H in EQ. rewrite EQ. eauto. *)
+(* Qed. *)
+
+(* Lemma collect_freshreg_trans : *)
+(*   forall A f l cs cs' ci, *)
+(*   (forall s s' x i y, f y s = OK x s' i -> s.(st_freshreg) = s'.(st_freshreg)) -> *)
+(*   @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_freshreg) = cs'.(st_freshreg). *)
+(* Proof. *)
+(*   induction l; intros; monadInv H0. *)
+(*   - trivial. *)
+(*   - apply H in EQ. rewrite EQ. eauto. *)
+(* Qed. *)
+
+(* Lemma collect_declare_controllogic_trans : *)
+(*   forall io n l s s' i, *)
+(*   HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i -> *)
+(*   s.(st_controllogic) = s'.(st_controllogic). *)
+(* Proof. *)
+(*   intros. eapply collect_controllogic_trans; try eassumption. *)
+(*   intros. eapply declare_reg_controllogic_trans. simpl in H0. eassumption. *)
+(* Qed. *)
+
+(* Lemma collect_declare_datapath_trans : *)
+(*   forall io n l s s' i, *)
+(*   HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i -> *)
+(*   s.(st_datapath) = s'.(st_datapath). *)
+(* Proof. *)
+(*   intros. eapply collect_datapath_trans; try eassumption. *)
+(*   intros. eapply declare_reg_datapath_trans. simpl in H0. eassumption. *)
+(* Qed. *)
+
+(* Lemma collect_declare_freshreg_trans : *)
+(*   forall io n l s s' i, *)
+(*   HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   intros. eapply collect_freshreg_trans; try eassumption. *)
+(*   inversion 1. auto. *)
+(* Qed. *)
+
+(* Ltac unfold_match H := *)
+(*   match type of H with *)
+(*   | context[match ?g with _ => _ end] => destruct g eqn:?; try discriminate *)
+(*   end. *)
+
+(* Lemma translate_eff_addressing_freshreg_trans : *)
+(*   forall op args s r s' i, *)
+(*   translate_eff_addressing op args s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto. *)
+(* Qed. *)
+(* Hint Resolve translate_eff_addressing_freshreg_trans : htlspec. *)
+
+(* Lemma translate_comparison_freshreg_trans : *)
+(*   forall op args s r s' i, *)
+(*   translate_comparison op args s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto. *)
+(* Qed. *)
+(* Hint Resolve translate_comparison_freshreg_trans : htlspec. *)
+
+(* Lemma translate_comparison_imm_freshreg_trans : *)
+(*   forall op args s r s' i n, *)
+(*   translate_comparison_imm op args n s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto. *)
+(* Qed. *)
+(* Hint Resolve translate_comparison_imm_freshreg_trans : htlspec. *)
+
+(* Lemma translate_condition_freshreg_trans : *)
+(*   forall op args s r s' i, *)
+(*   translate_condition op args s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   destruct op; intros; simpl in *; repeat (unfold_match H); inv H; eauto with htlspec. *)
+(* Qed. *)
+(* Hint Resolve translate_condition_freshreg_trans : htlspec. *)
+
+(* Lemma translate_instr_freshreg_trans : *)
+(*   forall op args s r s' i, *)
+(*   translate_instr op args s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   destruct op; intros; simpl in *; repeat (unfold_match H); inv H; eauto with htlspec. *)
+(*   monadInv H1. eauto with htlspec. *)
+(* Qed. *)
+(* Hint Resolve translate_instr_freshreg_trans : htlspec. *)
+
+(* Lemma translate_arr_access_freshreg_trans : *)
+(*   forall mem addr args st s r s' i, *)
+(*   translate_arr_access mem addr args st s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   intros. unfold translate_arr_access in H. repeat (unfold_match H); inv H; eauto with htlspec. *)
+(* Qed. *)
+(* Hint Resolve translate_arr_access_freshreg_trans : htlspec. *)
+
+(* Lemma add_instr_freshreg_trans : *)
+(*   forall n n' st s r s' i, *)
+(*   add_instr n n' st s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. intros. unfold add_instr in H. repeat (unfold_match H). inv H. auto. Qed. *)
+(* Hint Resolve add_instr_freshreg_trans : htlspec. *)
+
+(* Lemma add_branch_instr_freshreg_trans : *)
+(*   forall n n0 n1 e s r s' i, *)
+(*   add_branch_instr e n n0 n1 s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. intros. unfold add_branch_instr in H. repeat (unfold_match H). inv H. auto. Qed. *)
+(* Hint Resolve add_branch_instr_freshreg_trans : htlspec. *)
+
+(* Lemma add_node_skip_freshreg_trans : *)
+(*   forall n1 n2 s r s' i, *)
+(*   add_node_skip n1 n2 s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. intros. unfold add_node_skip in H. repeat (unfold_match H). inv H. auto. Qed. *)
+(* Hint Resolve add_node_skip_freshreg_trans : htlspec. *)
+
+(* Lemma add_instr_skip_freshreg_trans : *)
+(*   forall n1 n2 s r s' i, *)
+(*   add_instr_skip n1 n2 s = OK r s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. intros. unfold add_instr_skip in H. repeat (unfold_match H). inv H. auto. Qed. *)
+(* Hint Resolve add_instr_skip_freshreg_trans : htlspec. *)
+
+(* Lemma transf_instr_freshreg_trans : *)
+(*   forall fin ret st instr s v s' i, *)
+(*     transf_instr fin ret st instr s = OK v s' i -> *)
+(*     s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   intros. destruct instr eqn:?. subst. unfold transf_instr in H. *)
+(*   destruct i0; try (monadInv H); try (unfold_match H); eauto with htlspec. *)
+(*   - apply add_instr_freshreg_trans in EQ2. apply translate_instr_freshreg_trans in EQ. *)
+(*     apply declare_reg_freshreg_trans in EQ1. congruence. *)
+(*   - apply add_instr_freshreg_trans in EQ2. apply translate_arr_access_freshreg_trans in EQ. *)
+(*     apply declare_reg_freshreg_trans in EQ1. congruence. *)
+(*   - apply add_instr_freshreg_trans in EQ0. apply translate_arr_access_freshreg_trans in EQ. congruence. *)
+(*   - apply translate_condition_freshreg_trans in EQ. apply add_branch_instr_freshreg_trans in EQ0. *)
+(*     congruence. *)
+(*   - inv EQ. apply add_node_skip_freshreg_trans in EQ0. congruence. *)
+(* Qed. *)
+(* Hint Resolve transf_instr_freshreg_trans : htlspec. *)
+
+(* Lemma collect_trans_instr_freshreg_trans : *)
+(*   forall fin ret st l s s' i, *)
+(*   HTLMonadExtra.collectlist (transf_instr fin ret st) l s = OK tt s' i -> *)
+(*   s.(st_freshreg) = s'.(st_freshreg). *)
+(* Proof. *)
+(*   intros. eapply collect_freshreg_trans; try eassumption. *)
+(*   eauto with htlspec. *)
+(* Qed. *)
+
+(* Ltac rewrite_states := *)
+(*   match goal with *)
+(*   | [ H: ?x ?s = ?x ?s' |- _ ] => *)
+(*     let c1 := fresh "c" in *)
+(*     let c2 := fresh "c" in *)
+(*     remember (?x ?s) as c1; remember (?x ?s') as c2; try subst *)
+(*   end. *)
+
+(* Ltac inv_add_instr' H := *)
+(*   match type of H with *)
+(*   | ?f _ _ _ = OK _ _ _ => unfold f in H *)
+(*   | ?f _ _ _ _ = OK _ _ _ => unfold f in H *)
+(*   | ?f _ _ _ _ _ = OK _ _ _ => unfold f in H *)
+(*   end; repeat unfold_match H; inversion H. *)
+
+(* Ltac inv_add_instr := *)
+(*   lazymatch goal with *)
+(*   | H: context[add_instr_skip _ _ _] |- _ => *)
+(*     inv_add_instr' H *)
+(*   | H: context[add_instr_skip _ _] |- _ => *)
+(*     monadInv H; inv_incr; inv_add_instr *)
+(*   | H: context[add_instr _ _ _ _] |- _ => *)
+(*     inv_add_instr' H *)
+(*   | H: context[add_instr _ _ _] |- _ => *)
+(*     monadInv H; inv_incr; inv_add_instr *)
+(*   | H: context[add_branch_instr _ _ _ _ _] |- _ => *)
+(*     inv_add_instr' H *)
+(*   | H: context[add_branch_instr _ _ _ _] |- _ => *)
+(*     monadInv H; inv_incr; inv_add_instr *)
+(*   | H: context[add_node_skip _ _ _] |- _ => *)
+(*     inv_add_instr' H *)
+(*   | H: context[add_node_skip _ _] |- _ => *)
+(*     monadInv H; inv_incr; inv_add_instr *)
+(*   end. *)
+
+(* Ltac destruct_optional := *)
+(*   match goal with H: option ?r |- _ => destruct H end. *)
+
+(* Lemma iter_expand_instr_spec : *)
+(*   forall l fin rtrn stack s s' i x c, *)
+(*     HTLMonadExtra.collectlist (transf_instr fin rtrn stack) l s = OK x s' i -> *)
+(*     list_norepet (List.map fst l) -> *)
+(*     (forall pc instr, In (pc, instr) l -> c!pc = Some instr) -> *)
+(*     (forall pc instr, In (pc, instr) l -> *)
+(*                       c!pc = Some instr -> *)
+(*                       tr_code c pc instr s'.(st_datapath) s'.(st_controllogic) fin rtrn s'.(st_st) stack). *)
+(* Proof. *)
+(*   induction l; simpl; intros; try contradiction. *)
+(*   destruct a as [pc1 instr1]; simpl in *. inv H0. monadInv H. inv_incr. *)
+(*   destruct (peq pc pc1). *)
+(*   - subst. *)
+(*     destruct instr1 eqn:?; try discriminate; *)
+(*       try destruct_optional; inv_add_instr; econstructor; try assumption. *)
+(*     + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + inversion H2. inversion H9. rewrite H. apply tr_instr_Inop. *)
+(*       eapply in_map with (f := fst) in H9. contradiction. *)
+
+(*     + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. *)
+(*     + inversion H2. inversion H14. unfold nonblock. replace (st_st s4) with (st_st s2) by congruence. *)
+(*       econstructor. apply EQ1. eapply in_map with (f := fst) in H14. contradiction. *)
+
+(*     + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. *)
+(*     + inversion H2. inversion H14. rewrite <- e2. replace (st_st s2) with (st_st s0) by congruence. *)
+(*       econstructor. apply EQ1. eapply in_map with (f := fst) in H14. contradiction. *)
+
+(*     + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct H2. *)
+(*       * inversion H2. *)
+(*         replace (st_st s2) with (st_st s0) by congruence. *)
+(*         eauto with htlspec. *)
+(*       * apply in_map with (f := fst) in H2. contradiction. *)
+
+(*     + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct H2. *)
+(*       * inversion H2. *)
+(*         replace (st_st s2) with (st_st s0) by congruence. *)
+(*         eauto with htlspec. *)
+(*       * apply in_map with (f := fst) in H2. contradiction. *)
+
+(*     + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. *)
+(*     + inversion H2. *)
+(*       * inversion H14. constructor. congruence. *)
+(*       * apply in_map with (f := fst) in H14. contradiction. *)
+
+(*     + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + inversion H2. *)
+(*       * inversion H9. *)
+(*         replace (st_st s2) with (st_st s0) by congruence. *)
+(*         eauto with htlspec. *)
+(*       * apply in_map with (f := fst) in H9. contradiction. *)
+
+(*     + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. *)
+(*     + inversion H2. *)
+(*       * inversion H9. *)
+(*         replace (st_st s2) with (st_st s0) by congruence. *)
+(*         eauto with htlspec. *)
+(*       * apply in_map with (f := fst) in H9. contradiction. *)
+
+(*   - eapply IHl. apply EQ0. assumption. *)
+(*     destruct H2. inversion H2. subst. contradiction. *)
+(*     intros. specialize H1 with pc0 instr0. destruct H1. tauto. trivial. *)
+(*     destruct H2. inv H2. contradiction. assumption. assumption. *)
+(* Qed. *)
+(* Hint Resolve iter_expand_instr_spec : htlspec. *)
+
+(* Lemma create_arr_inv : forall w x y z a b c d, *)
+(*     create_arr w x y z = OK (a, b) c d -> *)
+(*     y = b /\ a = z.(st_freshreg) /\ c.(st_freshreg) = Pos.succ (z.(st_freshreg)). *)
+(* Proof. *)
+(*   inversion 1; split; auto. *)
+(* Qed. *)
+
+(* Lemma create_reg_inv : forall a b s r s' i, *)
+(*     create_reg a b s = OK r s' i -> *)
+(*     r = s.(st_freshreg) /\ s'.(st_freshreg) = Pos.succ (s.(st_freshreg)). *)
+(* Proof. *)
+(*   inversion 1; auto. *)
+(* Qed. *)
+
+(* Theorem transl_module_correct : *)
+(*   forall f m, *)
+(*     transl_module f = Errors.OK m -> tr_module f m. *)
+(* Proof. *)
+(*   intros until m. *)
+(*   unfold transl_module. *)
+(*   unfold run_mon. *)
+(*   destruct (transf_module f (max_state f)) eqn:?; try discriminate. *)
+(*   intros. inv H. *)
+(*   inversion s; subst. *)
+
+(*   unfold transf_module in *. *)
+(*   unfold stack_correct in *. *)
+(*   destruct (0 <=? RTL.fn_stacksize f) eqn:STACK_BOUND_LOW; *)
+(*     destruct (RTL.fn_stacksize f <? Integers.Ptrofs.modulus) eqn:STACK_BOUND_HIGH; *)
+(*     destruct (RTL.fn_stacksize f mod 4 =? 0) eqn:STACK_ALIGN; *)
+(*     crush; *)
+(*     monadInv Heqr. *)
+
+(*   repeat unfold_match EQ9. monadInv EQ9. *)
+
+(*   (* TODO: We should be able to fold this into the automation. *) *)
+(*   pose proof (create_arr_inv _ _ _ _ _ _ _ _ EQ0) as STK_LEN. inv STK_LEN. inv H5. *)
+(*   pose proof (create_reg_inv _ _ _ _ _ _ EQ) as FIN_VAL. inv FIN_VAL. *)
+(*   pose proof (create_reg_inv _ _ _ _ _ _ EQ1) as RET_VAL. inv RET_VAL. *)
+(*   destruct x3. destruct x4. *)
+(*   pose proof (collect_trans_instr_freshreg_trans _ _ _ _ _ _ _ EQ2) as TR_INSTR. *)
+(*   pose proof (collect_declare_freshreg_trans _ _ _ _ _ _ EQ3) as TR_DEC. *)
+(*   pose proof (create_reg_inv _ _ _ _ _ _ EQ4) as START_VAL. inv START_VAL. *)
+(*   pose proof (create_reg_inv _ _ _ _ _ _ EQ5) as RESET_VAL. inv RESET_VAL. *)
+(*   pose proof (create_reg_inv _ _ _ _ _ _ EQ6) as CLK_VAL. inv CLK_VAL. *)
+(*   rewrite H9 in *. rewrite H8 in *. replace (st_freshreg s4) with (st_freshreg s2) in * by congruence. *)
+(*   rewrite H6 in *. rewrite H7 in *. rewrite H5 in *. simpl in *. *)
+(*   inv_incr. *)
+(*   econstructor; simpl; auto; try lia. *)
+(*   intros. *)
+(*   assert (EQ3D := EQ3). *)
+(*   apply collect_declare_datapath_trans in EQ3. *)
+(*   apply collect_declare_controllogic_trans in EQ3D. *)
+(*   replace (st_controllogic s10) with (st_controllogic s3) by congruence. *)
+(*   replace (st_datapath s10) with (st_datapath s3) by congruence. *)
+(*   replace (st_st s10) with (st_st s3) by congruence. *)
+(*   eapply iter_expand_instr_spec; eauto with htlspec. *)
+(*   apply PTree.elements_complete. *)
+(* Qed. *)