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-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Xavier Leroy, INRIA Paris-Rocquencourt *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-(** Type preservation for the CleanupLabels pass *)
-
-Require Import Coqlib.
-Require Import Maps.
-Require Import AST.
-Require Import Op.
-Require Import Locations.
-Require Import LTLin.
-Require Import CleanupLabels.
-Require Import LTLintyping.
-
-Lemma in_remove_unused_labels:
- forall bto i c, In i (remove_unused_labels bto c) -> In i c.
-Proof.
- unfold remove_unused_labels, remove_unused. induction c; simpl.
- auto.
- rewrite list_fold_right_eq. destruct a; simpl; intuition.
- destruct (Labelset.mem l bto); simpl in H; intuition.
-Qed.
-
-Lemma wt_transf_function:
- forall f,
- wt_function f ->
- wt_function (transf_function f).
-Proof.
- intros. inv H. constructor; simpl; auto.
- unfold cleanup_labels; red; intros.
- apply wt_instrs. eapply in_remove_unused_labels; eauto.
-Qed.
-
-Lemma wt_transf_fundef:
- forall f,
- wt_fundef f ->
- wt_fundef (transf_fundef f).
-Proof.
- induction 1. constructor. constructor. apply wt_transf_function; auto.
-Qed.
-
-Lemma program_typing_preserved:
- forall p,
- wt_program p ->
- wt_program (transf_program p).
-Proof.
- intros; red; intros.
- exploit transform_program_function; eauto. intros [f1 [A B]]. subst f.
- apply wt_transf_fundef. eapply H; eauto.
-Qed.