Section HybridThreadDiagram.
Notation the_simulation := compiler_simulation.
Parameter option_compiler_order: option (Injindex the_simulation) -> option (Injindex the_simulation) -> Prop.
(* automatic rewrite gsoThreadCode *)
Ltac auto_gsoThreadCode:=
match goal with
| [ |- context[getThreadC ?cntJ'] ] =>
match type of cntJ' with
| containsThread (updThread ?cntI _ _) ?J =>
match type of cntI with
| containsThread ?hb ?I =>
match goal with
| [ cntJ: containsThread hb J |- _ ] =>
rewrite gsoThreadCode with
(cnti:= cntI)
(cntj:= cntJ)
(cntj':= cntJ') by eassumption
end
end
end
end.
Ltac simpl_getThreadC':=
first[ rewrite gssThreadCode |
auto_gsoThreadCode
].
(*Produces all the "containThreads" that might be missing "*)
Ltac containsThread_helper:=
match goal with
| [ cntj': containsThread (updThread ?cntj _ _) ?i  |- _ ] =>
match type of cntj with
| containsThread ?hb ?j =>
progress (
first [match goal with
| [ cnti: containsThread hb i |- _ ] => idtac
end |
let CNTI:= fresh "cnti" in
assert (CNTI: containsThread hb i)
by
(eapply cntUpdate'; eapply cntj') ])
| _ => fail
end
end.
Ltac simpl_getThreadC:=
match goal with
| [  |- context [@getThreadC _ _ ?j (@updThread _ _ _ ?hb _ _ _) _ ] ] =>
let cntJ:= fresh "cntj" in
evar (cntj : containsThread hb j);
let cntJ':= eval unfold cntJ in cntJ in
rewrite gsoThreadCode with
(tp := hb)
(cntj:= cntJ')
by eassumption;
instantiate (cntJ:= ltac:(eauto));
clear cntJ
end.
Ltac containsThread_cleanup:=
repeat match goal with
| [H1: containsThread ?TP ?M,
H2: containsThread (@updThread _ _ _ ?TP _ _ _) ?M |- _] =>
replace H2 with H1 in * by apply proof_irr; clear H2
| [H1: containsThread ?TP ?M,
H2: containsThread ?TP ?M |- _] =>
replace H2 with H1 in * by apply proof_irr; clear H2
end.
Admitted.

Lemma hybrid_thread_diagram:
forall (U0 : list nat) (st1 : C1) (m1 : mem) (st1' : C1) (m1' : mem),
machine_semantics.thread_step (HCSem Sems Semt hb1 U) genv U0 st1 m1 st1' m1' ->
forall cd (st2 : C2) (mu : meminj) (m2 : mem),
concur_match cd mu st1 m1 st2 m2 ->
exists (st2' : C2) (m2' : mem) cd' (mu' : meminj),
concur_match cd' mu' st1' m1' st2' m2' /\
(machine_semantics_lemmas.thread_step_plus
(HCSem Sems Semt hb2 U) genv U0 st2 m2 st2' m2' \/
machine_semantics_lemmas.thread_step_star
(HCSem Sems Semt hb2 U) genv U0 st2 m2 st2' m2'
/\ option_compiler_order cd' cd).