intros. subst; reflexivity.
Defined.
Definition pos_pred (n:pos): nat.

(* Specifications: *)
Lemma lockSet_WorNE: forall js b ofs,
(lockSet js) !! b ofs = Some Memtype.Writable \/
(lockSet js) !! b ofs = None.
Lemma lockSet_spec_2 :
forall (js : t) (b : block) (ofs ofs' : Z),
Intv.In ofs' (ofs, (ofs + Z.of_nat lksize.LKSIZE_nat)%Z) ->
lockRes js (b, ofs) -> (lockSet js) !! b ofs' = Some Memtype.Writable.
Lemma lockSet_spec_1: forall js b ofs,
lockRes js (b,ofs) ->
(lockSet js) !! b ofs = Some Memtype.Writable.