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')).

(* Specifications: *)
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)).
Lemma switch_ascent: forall f sp e m cenv xenv ls n ls', lbl_stmt_tail ls n ls' -> forall k k1, transl_lblstmt_cont cenv xenv ls k k1 -> exists k2, star step tge (State f (Sexit n) k1 sp e m) E0 (State f (Sexit O) k2 sp e m) /\ transl_lblstmt_cont cenv xenv ls' k k2.
Lemma switch_match_cont: forall cenv xenv k cs tk ls tk', match_cont k tk cenv xenv cs -> transl_lblstmt_cont cenv xenv ls tk tk' -> match_cont (Csharpminor.Kseq (seq_of_lbl_stmt ls) k) tk' cenv (false :: switch_env ls xenv) cs.
Lemma switch_match_states: forall fn k e le m tfn ts tk sp te tm cenv xenv f lo hi cs sz ls body tk' (TRF: transl_funbody cenv sz fn = OK tfn) (TR: transl_lblstmt cenv (switch_env ls xenv) ls body = OK ts) (MINJ: Mem.inject f m tm) (MCS: match_callstack f m tm (Frame cenv tfn e le te sp lo hi :: cs) (Mem.nextblock m) (Mem.nextblock tm)) (MK: match_cont k tk cenv xenv cs) (TK: transl_lblstmt_cont cenv xenv ls tk tk'), exists S, plus step tge (State tfn (Sexit O) tk' (Vptr sp Ptrofs.zero) te tm) E0 S /\ match_states (Csharpminor.State fn (seq_of_lbl_stmt ls) k e le m) S.
Lemma transl_lblstmt_suffix: forall cenv xenv ls n ls', lbl_stmt_tail ls n ls' -> forall body ts, transl_lblstmt cenv (switch_env ls xenv) ls body = OK ts -> exists body', exists ts', transl_lblstmt cenv (switch_env ls' xenv) ls' body' = OK ts'.
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').
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.
Lemma transl_find_label_body: forall cenv xenv size f tf k tk cs lbl s' k', transl_funbody cenv size f = OK tf -> match_cont k tk cenv xenv cs -> Csharpminor.find_label lbl f.(Csharpminor.fn_body) (Csharpminor.call_cont k) = Some (s', k') -> exists ts', exists tk', exists xenv', find_label lbl tf.(fn_body) (call_cont tk) = Some(ts', tk') /\ transl_stmt cenv xenv' s' = OK ts' /\ match_cont k' tk' cenv xenv' cs.