(** Properties of [switch] compilation *)
Inductive lbl_stmt_tail: lbl_stmt -> nat -> lbl_stmt -> Prop :=
| lstail_O: forall sl,
lbl_stmt_tail sl O sl
| lstail_S: forall c s sl n sl',
lbl_stmt_tail sl n sl' ->
lbl_stmt_tail (LScons c s sl) (S n) sl'.

Lemma switch_table_default:
forall sl base,
exists n,
lbl_stmt_tail sl n (select_switch_default sl)
/\ snd (switch_table sl base) = (n + base)%nat.