Section CompileInftyThread.
Definition lift_state': forall {on on'},
ThreadPool on -> ThreadPool on'.

Lemma infinite_running:
forall (m : option mem) (cd : nth_index) (mu : meminj)
(c1 : ThreadPool (Some 0)%nat) (m1 : mem) (c2 : ThreadPool None)
(m2 : mem),
infty_match cd mu c1 m1 c2 m2 ->
forall i : nat,
machine_semantics.running_thread (HybConcSem (Some 0)%nat m) c1 i <->
machine_semantics.running_thread (HybConcSem None m) c2 i.