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

Lemma get_pre_wb_st_Write_stsh : forall (id : block_id) (v : nat) (s : state) (p_new : path), blk_in_stash id v ((get_pre_wb_st id (Write v) s (calc_path id s) p_new)).