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 add_item_trace_map : forall h k v i s h' (Hlenh : Zlength h = size)
(Htrace : add_item_trace h k v i s h') (Hk : k <> 0) (Hrepk : repable_signed k) (Hrepv : repable_signed v),
let m' := make_map (upd_Znth i h' (Znth i h ([], []))) in
map_incl (make_map h) m' /\ lookup m' k = Some i /\
if s then get (make_map h) k = None /\ make_map h' = upd_Znth i m' (k, v)
else make_map h' = upd_Znth i m' (k, make_int (value_of_hist (snd (Znth i h' ([], []))))).