Inductive transl_lblstmt_cont(cenv: compilenv) (xenv: exit_env): lbl_stmt -> cont -> cont -> Prop :=
  | tlsc_default: forall k,
      transl_lblstmt_cont cenv xenv LSnil k (Kblock (Kseq Sskip k))
  | tlsc_case: forall i s ls k ts k',
      transl_stmt cenv (switch_env (LScons i s ls) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv ls k k' ->
      transl_lblstmt_cont cenv xenv (LScons 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 k,
      transl_lblstmt_cont cenv xenv LSnil k (Kblock (Kseq Sskip k))
  | tlsc_case: forall i s ls k ts k',
      transl_stmt cenv (switch_env (LScons i s ls) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv ls k k' ->
      transl_lblstmt_cont cenv xenv (LScons 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 k,
      transl_lblstmt_cont cenv xenv LSnil k (Kblock (Kseq Sskip k))
  | tlsc_case: forall i s ls k ts k',
      transl_stmt cenv (switch_env (LScons i s ls) xenv) s = OK ts ->
      transl_lblstmt_cont cenv xenv ls k k' ->
      transl_lblstmt_cont cenv xenv (LScons i s ls) k (Kblock (Kseq ts k')).

Lemma transl_find_label: forall s k xenv ts tk, transl_stmt cenv xenv s = OK ts -> match_cont k tk cenv xenv cs -> match Csharpminor.find_label lbl s k with | None => find_label lbl ts tk = None | Some(s', k') => exists ts', exists tk', exists xenv', find_label lbl ts tk = Some(ts', tk') /\ transl_stmt cenv xenv' s' = OK ts' /\ match_cont k' tk' cenv xenv' cs end with transl_lblstmt_find_label: forall ls xenv body k ts tk tk1, transl_lblstmt cenv (switch_env ls xenv) ls body = OK ts -> match_cont k tk cenv xenv cs -> transl_lblstmt_cont cenv xenv ls tk tk1 -> find_label lbl body tk1 = None -> match Csharpminor.find_label_ls lbl ls k with | None => find_label lbl ts tk = None | Some(s', k') => exists ts', exists tk', exists xenv', find_label lbl ts tk = Some(ts', tk') /\ transl_stmt cenv xenv' s' = OK ts' /\ match_cont k' tk' cenv xenv' cs end.