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 start_step_diagram: forall (m : option mem) (tge : HybridMachineSig.G) (U : list nat) (st1 : ThreadPool (Some hb)) (m1 : mem) (tr1 tr2 : HybridMachineSig.event_trace) (st1' : ThreadPool (Some hb)) (m' : mem) (cd : option compiler_index) (st2 : ThreadPool (Some (S hb))) (mu : meminj) (m2 : mem) (tid : nat) (Htid : ThreadPool.containsThread st1 tid), concur_match cd mu st1 m1 st2 m2 -> List.Forall2 (inject_mevent mu) tr1 tr2 -> HybridMachineSig.schedPeek U = Some tid -> HybridMachineSig.start_thread m1 Htid st1' m' -> exists (st2' : ThreadPool (Some (S hb))) (m2' : mem) (cd' : option compiler_index) (mu' : meminj), concur_match cd' mu' st1' (HybridMachineSig.diluteMem m') st2' m2' /\ List.Forall2 (inject_mevent mu') tr1 tr2 /\ machine_semantics.machine_step(HybConcSem (Some (S hb)) m) tge U tr2 st2 m2 (HybridMachineSig.yield (Scheduler:=HybridMachineSig.HybridCoarseMachine.scheduler) U) tr2 st2' m2'.