Set Bullet Behavior "Strict Subproofs".
Instance CompSpecs : compspecs. make_compspecs prog. Defined.
Definition Vprog : varspecs. mk_varspecs prog. Defined.
Definition release2_spec := DECLARE _release2 release2_spec.
Definition freelock2_spec := DECLARE _freelock2 (freelock2_spec _).
Definition spawn_spec := DECLARE _spawn spawn_spec.
Definition integer_hash_spec :=
DECLARE _integer_hash
WITH i : Z
PRE [ _i OF tint ]
PROP () LOCAL (temp _i (vint i)) SEP ()
POST [ tint ]
PROP () LOCAL (temp ret_temp (vint (i * 654435761))) SEP ().
(* One might think it should just return an unknown number, but in fact it needs to follow a known hash function at the logic level to be useful. *)
Definition tentry := Tstruct _entry noattr.
Instance hf1 : hash_fun := { size := 16384; hash i := (i * 654435761) mod 16384 }.
Opaque upto.
Ltac cancel_for_forward_call ::= repeat (rewrite ?sepcon_andp_prop', ?sepcon_andp_prop);
repeat (apply andp_right; [auto; apply prop_right; auto|]); fast_cancel.
Ltac entailer_for_return ::= go_lower; entailer'.
Hint Resolve k_R_precise v_R_precise.
Opaque size.
Opaque Znth.
Hint Resolve wf_empty.
Hint Resolve f_pred_precise f_pred_positive.
Fixpoint join_hists (h1 h2 : list (hist * hist)) :=
match (h1, h2) with
| ((k1, v1) :: rest1, (k2, v2) :: rest2) => (k1 ++ k2, v1 ++ v2) :: join_hists rest1 rest2
| _ => []
end.

Lemma atomic_entries_join : forall sh1 sh2 sh entries ghosts hists1 hists2 hists
(Hjoin : sepalg.join sh1 sh2 sh) (Hhists : join_hists hists1 hists2 = hists)
(Hghosts : Zlength ghosts = Zlength entries)
(Hlen : Zlength entries = Zlength hists1) (Hlen1 : Zlength hists1 = Zlength hists2)
(Hsh1 : readable_share sh1) (Hsh2 : readable_share sh2),
atomic_entries sh1 entries ghosts hists1 * atomic_entries sh2 entries ghosts hists2 =
!!(forall i, disjoint (fst (Znth i hists1 ([], []))) (fst (Znth i hists2 ([], []))) /\
disjoint (snd (Znth i hists1 ([], []))) (snd (Znth i hists2 ([], [])))) &&
atomic_entries sh entries ghosts hists.