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

Lemma get_write_back_blocks_pos_map : forall id p stsh lvl pos_map, In id (List.map block_blockid (get_write_back_blocks p stsh 4 lvl pos_map)) -> let p' := lookup_dict (makeBoolList false LOP) id pos_map in isEqvPath p p' lvl = true.