Definition inj_on_list {A B} (l : list A) (f : A -> B) :=
  forall x y, In x l -> In y l -> f x = f y -> x = y.Definition subset_rel {X} (sub lst : list X) : Prop :=
  forall x,
    In x sub ->
    In x lst.

Lemma up_oram_tr_tree_or_delta o : forall id lvl dlt p, In id (List.map block_blockid (get_all_blks_tree (up_oram_tr o lvl dlt p))) -> In id (List.map block_blockid (get_all_blks_tree o)) \/ In id (List.map block_blockid dlt).