Definition timeless' (P : mpred) := forall (a a' : rmap),
  predicates_hered.app_pred P a' -> age a a' ->
  predicates_hered.app_pred P a.

Lemma union_pred_timeless : forall {CS : compspecs} sh m t off (IH : Forall (fun it : ident * type => forall (v : reptype (t it)) (p : val), timeless (data_at_rec sh (t it) v p)) m) v p, timeless (union_pred m (fun (it : ident * type) v => withspacer sh (sizeof (t it)) (off it) (data_at_rec sh (t it) v)) v p).