Admitted.
Inductive match_state:
forall n,
nth_index ->
Values.Val.meminj ->
ThreadPool (Some 0) -> Memory.Mem.mem -> ThreadPool (Some n) -> Memory.Mem.mem -> Prop:=
| refl_match: forall j tp m,
match_state 0 nil j tp m tp m
| step_match_state:
forall n ocd ils jn jSn tp0 m0 tpn mn tpSn mSn,
match_state n ils jn tp0 m0 tpn mn ->
concur_match n ocd jSn tpn mn tpSn mSn ->
match_state (S n) (cons ocd ils) (compose_meminj jn jSn) tp0 m0 tpSn mSn.

Lemma simulation_inductive_case:
forall n : nat,
(forall m : option mem,
HybridMachine_simulation_properties (HybConcSem (Some 0) m)
(HybConcSem (Some n) m) (match_state n)) ->
(forall m : option mem,
HybridMachine_simulation_properties (HybConcSem (Some n) m)
(HybConcSem (Some (S n)) m) (concur_match n)) ->
forall m : option mem,
HybridMachine_simulation_properties (HybConcSem (Some 0) m)
(HybConcSem (Some (S n)) m) (match_state (S n)).