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.
(*** NoDup general lemmas ***)

Lemma NoDup_up_oram_tree : forall o dlt lvl p,
NoDup (List.map block_blockid dlt) ->
NoDup (List.map block_blockid (get_all_blks_tree o)) ->
disjoint_list (List.map block_blockid (get_all_blks_tree o))
(List.map block_blockid dlt) ->
NoDup
(List.map block_blockid
(get_all_blks_tree (up_oram_tr o lvl dlt p))).