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

Lemma get_pre_wb_st_Write_state_state : forall (id id' : block_id) (v v': nat) (s : state) (p_new : path), id <> id' -> blk_in_state id v s -> blk_in_state id v ((get_pre_wb_st id' (Write v') s (calc_path id' s) p_new)).