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)
).