Section CompileNThreads.
Definition nth_index:= (list (option compiler_index)).
Definition list_lt: nth_index -> nth_index -> Prop:=
list_ord (opt_rel' (InjorderX compiler_sim)).
Local Ltac subst_sig:=
match goal with
H': existT _ _ _ = existT _ _ _ |- _ =>
eapply Eqdep.EqdepTheory.inj_pair2 in H'; subst
end.
Local Ltac inv_match0:=
match goal with
H: match_state 0 _ _ _ _ _ _ |- _ =>
inversion H; subst_sig; try clear H
end.
Admitted.

Lemma inject_mem_sync_interpolation:
forall jn jSn ev1 ev3,
(inject_sync_event (compose_meminj jn jSn)) ev1 ev3 ->
exists ev2,
inject_sync_event jn ev1 ev2 /\
inject_sync_event jSn ev2 ev3 .