(** Properties of [switch] compilation *)

Remark switch_table_shift:
  forall n sl base dfl,
  switch_target n (S dfl) (switch_table sl (S base)) =
  S (switch_target n dfl (switch_table sl base)).Remark length_switch_table:
  forall sl base1 base2,
  length (switch_table sl base1) = length (switch_table sl base2).Inductive transl_lblstmt_cont(cenv: compilenv) (xenv: exit_env): lbl_stmt -> cont -> cont -> Prop :=
  | tlsc_default: forall s k ts,
      transl_stmt cenv (switch_env (LSdefault s) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv (LSdefault s) k (Kblock (Kseq ts k))
  | tlsc_case: forall i s ls k ts k',
      transl_stmt cenv (switch_env (LScase i s ls) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv ls k k' ->
      transl_lblstmt_cont cenv xenv (LScase i s ls) k (Kblock (Kseq ts k')).Inductive transl_lblstmt_cont(cenv: compilenv) (xenv: exit_env): lbl_stmt -> cont -> cont -> Prop :=
  | tlsc_default: forall s k ts,
      transl_stmt cenv (switch_env (LSdefault s) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv (LSdefault s) k (Kblock (Kseq ts k))
  | tlsc_case: forall i s ls k ts k',
      transl_stmt cenv (switch_env (LScase i s ls) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv ls k k' ->
      transl_lblstmt_cont cenv xenv (LScase i s ls) k (Kblock (Kseq ts k')).Inductive transl_lblstmt_cont(cenv: compilenv) (xenv: exit_env): lbl_stmt -> cont -> cont -> Prop :=
  | tlsc_default: forall s k ts,
      transl_stmt cenv (switch_env (LSdefault s) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv (LSdefault s) k (Kblock (Kseq ts k))
  | tlsc_case: forall i s ls k ts k',
      transl_stmt cenv (switch_env (LScase i s ls) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv ls k k' ->
      transl_lblstmt_cont cenv xenv (LScase i s ls) k (Kblock (Kseq ts k')).

Lemma transl_lblstmt_find_label_context: forall xenv ls body ts tk1 tk2 ts' tk', transl_lblstmt cenv (switch_env ls xenv) ls body = OK ts -> transl_lblstmt_cont cenv xenv ls tk1 tk2 -> find_label lbl body tk2 = Some (ts', tk') -> find_label lbl ts tk1 = Some (ts', tk').