Definition on_path b o p :=
In b (concat (lookup_path_oram o p)).

Lemma isEqvPath_lookup_path_oram : forall o n id lvl dlt p p',
is_p_b_tr o (S n) ->
length p = n ->
length p' = n ->
(lvl < n)%nat ->
In id (List.map block_blockid dlt) ->
isEqvPath p p' lvl = true ->
In id (List.map block_blockid
(concat (lookup_path_oram
(up_oram_tr o lvl dlt p) p'))).