(** 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')).

Lemma switch_ascent:
forall f n sp e m cenv xenv k ls k1,
let tbl := switch_table ls O in
let ls' := select_switch n ls in
transl_lblstmt_cont cenv xenv ls k k1 ->
exists k2,
star step tge (State f (Sexit (switch_target n (length tbl) tbl)) k1 sp e m)
E0 (State f (Sexit O) k2 sp e m)
/\ transl_lblstmt_cont cenv xenv ls' k k2.