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

Lemma stash_block_selection : forall p s id v lvl, well_formed s -> length p = LOP -> Nat.le lvl LOP -> blk_in_stash id v s -> blk_in_stash id v (blocks_selection p lvl s) \/ (at_lvl_in_path (state_oram (blocks_selection p lvl s)) lvl p (Block id v) /\ at_lvl_in_path (state_oram (blocks_selection p lvl s)) lvl (calc_path id s) (Block id v) ).