Ltac exploit_match:=
      unfold match_thread_target,match_thread_source,match_thread_compiled in *;
      match goal with
      | [ H: getThreadC ?i = _ ?c,
             H0: context[match_state2match_thread] |- _ ] =>
        rewrite H in H0; inversion H0; subst; simpl in *; clear H0
      end;
      fold match_thread_target in *;
      fold match_thread_source in *;
      fold match_thread_compiled in *.(* Build the concur_match *)
    Ltac destroy_ev_step_sum:=
      match goal with
      | [ H: ev_step_sum _ _ _ _ _ _ _ |- _ ] => inversion H; clear H
      end.

Lemma external_step_diagram: forall (U : list nat) (tr1 tr2 : HybridMachineSig.event_trace) (st1 : ThreadPool.t) (m1 : mem) (st1' : ThreadPool.t) (m1' : mem) (tid : nat) (ev : Events.sync_event), forall (cd : option compiler_index) (st2 : ThreadPool.t) (mu : meminj) (m2 : mem), concur_match cd mu st1 m1 st2 m2 -> List.Forall2 (inject_mevent mu) tr1 tr2 -> forall (Htid : ThreadPool.containsThread st1 tid) (Hcmpt : mem_compatible st1 m1), HybridMachineSig.schedPeek U = Some tid -> syncStep true Htid Hcmpt st1' m1' ev -> exists ev' (st2' : t) (m2' : mem) (cd' : option compiler_index) (mu' : meminj), concur_match cd' mu' st1' m1' st2' m2' /\ List.Forall2 (inject_mevent mu') (seq.cat tr1 (Events.external tid ev :: nil)) (seq.cat tr2 (Events.external tid ev' :: nil)) /\ HybridMachineSig.external_step (scheduler:=HybridMachineSig.HybridCoarseMachine.scheduler) U tr2 st2 m2 (HybridMachineSig.schedSkip U) (seq.cat tr2 (Events.external tid ev' :: nil)) st2' m2'.