Notation schedule := (seq nat).(** Internal steps are just thread coresteps or resume steps or start steps,
          they mimic fine-grained internal steps *)
      Definition internal_step {tid} {tp} m (cnt: containsThread tp tid)
                 (Hcomp: mem_compatible tp m) tp' m' :=
      (exists ev, threadStep cnt Hcomp tp' m' ev) \/
      (resume_thread m cnt tp' /\ m = m') \/
      (start_thread m cnt tp' m').

Lemma internal_execution_trans : forall i U tp tp' tp'' m m' m'' (pf': containsThread tp' i) (Hcomp: mem_compatible tp' m') (Hstep: internal_step pf' Hcomp tp'' m'') (Hexec: internal_execution U tp m tp' m'), internal_execution (U ++ (i :: nil))%list tp m tp'' m''.