Definition lockSet_Writable (lset : lockMap) m :=
      forall b ofs, AMap.find (b,ofs) lset ->
               forall ofs0, Intv.In ofs0 (ofs, ofs + LKSIZE)%Z ->
             Mem.perm_order'' ((Mem.mem_access m)!! b ofs0 Max) (Some Writable) .Record mem_compatible_with' (tp : thread_pool) m all_juice : Prop :=
      {   juice_join : join_all tp all_juice
        ; all_cohere : mem_cohere' m all_juice
        ; loc_writable : lockSet_Writable (lockGuts tp) m
        ; jloc_in_set : juicyLocks_in_lockSet (lockGuts tp) all_juice
        ; lset_in_juice: lockSet_in_juicyLocks  (lockGuts tp) all_juice
      }.Record mem_compatible_with' (tp : thread_pool) m all_juice : Prop :=
      {   juice_join : join_all tp all_juice
        ; all_cohere : mem_cohere' m all_juice
        ; loc_writable : lockSet_Writable (lockGuts tp) m
        ; jloc_in_set : juicyLocks_in_lockSet (lockGuts tp) all_juice
        ; lset_in_juice: lockSet_in_juicyLocks  (lockGuts tp) all_juice
      }.Record mem_compatible_with' (tp : thread_pool) m all_juice : Prop :=
      {   juice_join : join_all tp all_juice
        ; all_cohere : mem_cohere' m all_juice
        ; loc_writable : lockSet_Writable (lockGuts tp) m
        ; jloc_in_set : juicyLocks_in_lockSet (lockGuts tp) all_juice
        ; lset_in_juice: lockSet_in_juicyLocks  (lockGuts tp) all_juice
      }.Record mem_compatible_with' (tp : thread_pool) m all_juice : Prop :=
      {   juice_join : join_all tp all_juice
        ; all_cohere : mem_cohere' m all_juice
        ; loc_writable : lockSet_Writable (lockGuts tp) m
        ; jloc_in_set : juicyLocks_in_lockSet (lockGuts tp) all_juice
        ; lset_in_juice: lockSet_in_juicyLocks  (lockGuts tp) all_juice
      }.Record mem_compatible_with' (tp : thread_pool) m all_juice : Prop :=
      {   juice_join : join_all tp all_juice
        ; all_cohere : mem_cohere' m all_juice
        ; loc_writable : lockSet_Writable (lockGuts tp) m
        ; jloc_in_set : juicyLocks_in_lockSet (lockGuts tp) all_juice
        ; lset_in_juice: lockSet_in_juicyLocks  (lockGuts tp) all_juice
      }.Record mem_compatible_with' (tp : thread_pool) m all_juice : Prop :=
      {   juice_join : join_all tp all_juice
        ; all_cohere : mem_cohere' m all_juice
        ; loc_writable : lockSet_Writable (lockGuts tp) m
        ; jloc_in_set : juicyLocks_in_lockSet (lockGuts tp) all_juice
        ; lset_in_juice: lockSet_in_juicyLocks  (lockGuts tp) all_juice
      }.Definition mem_compatible_with := mem_compatible_with'.Definition mem_compatible tp m := ex (mem_compatible_with tp m).

Lemma jlocinset_lr_valid: forall ls juice, lockSet_in_juicyLocks ls juice -> lr_valid (AMap.find (elt:=lock_info)^~ (ls)).