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

Lemma disjoint_weaken2 : forall dlt l lst, disjoint_list (List.map block_blockid l) (List.map block_blockid lst) -> subset_rel dlt lst -> disjoint_list (List.map block_blockid l) (List.map block_blockid dlt).