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 switch_descent: forall cenv xenv k ls body s, transl_lblstmt cenv (switch_env ls xenv) ls body = OK s -> exists k', transl_lblstmt_cont cenv xenv ls k k' /\ (forall f sp e m, plus step tge (State f s k sp e m) E0 (State f body k' sp e m)).