(* Lemma typecheck_environ_join_switch2: forall sl Delta rho, typecheck_environ Delta rho -> typecheck_environ (join_tycon_labeled sl Delta) rho.  Lemma typecheck_environ_join_switch1: forall n sl rho Delta, typecheck_environ (update_tycon Delta (seq_of_labeled_statement (select_switch n sl))) rho -> typecheck_environ (join_tycon_labeled sl Delta) rho. *)

Lemma subp_trans':
forall A (NA: ageable A) (P Q R: pred A) w,
app_pred (P >=> Q) w ->
app_pred (Q >=> R) w ->
app_pred (P >=> R) w.