Section InvMachineShell.
Context {Sem: Semantics}.
Notation C:= (semC).
Notation G:= (semG).
Notation tid:= nat.
Notation lockMap:= (AMap.t lock_info).
(** Memories*)
Definition richMem: Type:= juicy_mem.
Definition dryMem: richMem -> mem:= m_dry.
(** Environment and Threadwise semantics *)
(* This all comes from the SEM. *)
(*Parameter G : Type. Parameter Sem : CoreSemantics G code mem.*)
Notation the_sem := (csem (event_semantics.msem semSem)).
(*thread pool*)
Existing Instance OrdinalThreadPool.
Notation thread_pool := (@ThreadPool.t _ _ OrdinalThreadPool).
(** Machine Variables*)
Definition lp_id : tid:= (0)%nat. (*lock pool thread id*)
(** Invariants*)
(** The state respects the memory*)
Definition access_cohere' m phi:= forall loc,
Mem.perm_order'' (max_access_at m loc) (perm_of_res (phi @ loc)).
(* This is similar to the coherence of juicy memories, * * but for entire machines. It is slighly weaker in one way: * - acc_coh is looser and only talks about maxcoh. * - alse acc_coh  might me redundant with max_coh IDK... x*)
Record mem_cohere' m phi :=
{ cont_coh: contents_cohere m phi;
(*acc_coh: access_cohere m phi;*)
(*acc_coh: access_cohere' m phi;*)
max_coh: max_access_cohere m phi;
all_coh: alloc_cohere m phi
}.
Definition mem_thcohere (tp : thread_pool) m :=
forall {tid} (cnt: containsThread tp tid), mem_cohere' m (getThreadR cnt).
Definition mem_lock_cohere (ls:lockMap) m:=
forall loc R rm, AMap.find loc ls = Some (R, Some rm) -> mem_cohere' m rm.
(*Join juice from all threads *)
Definition getThreadsR (tp : thread_pool):=
map (perm_maps tp) (enums_equality.enum (num_threads tp)).
Fixpoint join_list (ls: seq.seq res) r:=
if ls is phi::ls' then exists r', join phi r' r /\ join_list ls' r' else
app_pred emp r.  (*Or is is just [amp r]?*)
Definition join_threads (tp : thread_pool) r:= join_list (getThreadsR tp) r.

Lemma minus_comm : forall a b c, ((a - b)%coq_nat - c = (a - c)%coq_nat - b)%coq_nat.