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

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