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.
Definition hists_mono (h1 h2 : list (hist * hist)) := Forall2 (fun a b =>
(exists l, fst b = fst a ++ l) /\ (exists l, snd b = snd a ++ l)) h1 h2.
Instance hists_mono_refl : RelationClasses.Reflexive hists_mono.
Hint Resolve hists_mono_refl.
Instance hists_mono_trans : RelationClasses.Transitive hists_mono.

Lemma one_add_succeeds : forall lr keys
(Hadd : Forall (fun '(la, h) => add_items_trace empty_hists la h) lr)
(Hfullk : Forall2 full_hist' (map fst (fold_right join_hists empty_hists (map snd lr))) (map (fun x => vint x) keys))
(Hkeys : Forall2 (fun h v => forall t e, In (t, e) h -> value_of e <> vint 0 -> vint v = value_of e)
(map fst (fold_right join_hists empty_hists (map snd lr))) keys)
(Hrepk : Forall repable_signed keys)
(Hnzk : Forall (fun x => Forall (fun x => let '(k, _, _, _) := x in k <> 0 /\ repable_signed k) (fst x)) lr)
k (Hin : In k (map fst (map fst (map fst (concat (map fst lr)))))),
exists v i th t, In (k, v, i, true) (fst (Znth th lr ([], []))) /\
In (t, CAS (vint 0) (vint 0) (vint k)) (fst (Znth i (snd (Znth th lr ([], []))) ([], []))).