Parameter lift_state: forall on, ThreadPool on -> forall on', ThreadPool on' -> Prop.Inductive infty_match:
             nth_index -> meminj ->
             ThreadPool (Some 0) -> mem ->
             ThreadPool None -> mem -> Prop:=
   | Build_infty_match:
       forall n cd j st0 m0 stn mn st,
         match_state n cd j st0 m0 stn mn ->
         lift_state (Some n) stn None st ->
         infty_match cd j st0 m0 st mn.Inductive infty_match:
             nth_index -> meminj ->
             ThreadPool (Some 0) -> mem ->
             ThreadPool None -> mem -> Prop:=
   | Build_infty_match:
       forall n cd j st0 m0 stn mn st,
         match_state n cd j st0 m0 stn mn ->
         lift_state (Some n) stn None st ->
         infty_match cd j st0 m0 st mn.

Lemma infinite_step_diagram: forall (m : option mem) (sge tge : HybridMachineSig.G) (U : list nat) tr1 (st1 : ThreadPool (Some 0)) (m1 : mem) (st1' : ThreadPool (Some 0)) (m1' : mem), machine_semantics.thread_step (HybConcSem (Some 0) m) sge U st1 m1 st1' m1' -> forall (cd : nth_index) tr2 (st2 : ThreadPool None) (mu : meminj) (m2 : mem), infty_match cd mu st1 m1 st2 m2 -> List.Forall2 (inject_mevent mu) tr1 tr2 -> exists (st2' : ThreadPool None) (m2' : mem) (cd' : nth_index) (mu' : meminj), infty_match cd' mu' st1' m1' st2' m2' /\ List.Forall2 (inject_mevent mu') tr1 tr2 /\ (machine_semantics_lemmas.thread_step_plus (HybConcSem None m) tge U st2 m2 st2' m2' \/ machine_semantics_lemmas.thread_step_star (HybConcSem None m) tge U st2 m2 st2' m2' /\ list_lt cd' cd).