Inductive threadHalted': forall {tid0 ms},
      containsThread(resources:=LockInvsAndResources) ms tid0 -> Prop:=
  | thread_halted':
      forall tp c tid0 i
        (cnt: containsThread tp tid0),
      forall
        (Hthread: getThreadC cnt = Krun c)
        (Hcant: halted the_sem c i),
        threadHalted' cnt.Inductive threadHalted': forall {tid0 ms},
      containsThread(resources:=LockInvsAndResources) ms tid0 -> Prop:=
  | thread_halted':
      forall tp c tid0 i
        (cnt: containsThread tp tid0),
      forall
        (Hthread: getThreadC cnt = Krun c)
        (Hcant: halted the_sem c i),
        threadHalted' cnt.Definition threadHalted: forall {tid0 ms},
      containsThread ms tid0 -> Prop:= @threadHalted'.

(* Specifications: *)
Lemma threadHalt_update: forall i j, i <> j -> forall tp cnt cnti c' cnt', (@threadHalted j tp cnt) <-> (@threadHalted j (@updThreadC _ _ _ i tp cnti c') cnt') .
Lemma syncstep_equal_halted: forall b i tp m cnti cmpt tp' m' tr, @syncStep b i tp m cnti cmpt tp' m' tr -> forall j cnt cnt', (@threadHalted j tp cnt) <-> (@threadHalted j tp' cnt').