Definition syncStep (isCoarse:bool) :
forall {tid0 ms m}, containsThread ms tid0 -> mem_compatible ms m ->
thread_pool -> mem -> sync_event ->  Prop:=
@syncStep' isCoarse.

Lemma syncstep_equal_run:
forall b i tp m cnt cmpt tp' m' tr,
@syncStep b i tp m cnt cmpt tp' m' tr ->
forall j,
(exists cntj q, @getThreadC _ _ _ j tp cntj = Krun q) <->
(exists cntj' q', @getThreadC _ _ _ j tp' cntj' = Krun q').