Nuprl Lemma : mu_ex_v5_send-token-received-or-born
[es:EO']. [m1,m2,init,p1,p2,p:Id]. [e:E].
(<p, make-Msg([token];Unit;
)> 
mu_ex_v5_main(init;m1;m2;p1;p2)(e)
(
e':E
((( mu_ex_v5_Token()(e') 
(e' <loc e))
((loc(e') = init) (
first(e')) (
mu_ex_v5_Token()(e')) e' 
loc e ))
(e'':E
(e' loc e'' (e'' <loc e) (b1,b2,b3:
. (<b1, b2, b3> mu_ex_v5_State(init)(e'') (b2)))))
(e'':E. ((e' <loc e'') (e'' <loc e) ( mu_ex_v5_Token()(e'')))))))
Proof not projected
Definitions occuring in Statement :
mu_ex_v5_main: mu_ex_v5_main(initial_token;m1;m2;proc1;proc2),
mu_ex_v5_State: mu_ex_v5_State(initial_token),
mu_ex_v5_Token: mu_ex_v5_Token(),
make-Msg: make-Msg(hdr;typ;val),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: b,
bool: ,
it: ,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
squash: T,
implies: P Q,
or: P Q,
and: P Q,
unit: Unit,
pair: <a, b>,
product: x:A 
B[x],
cons: [car / cdr],
nil: [],
token: "$token",
equal: s = t
Definitions :
prop: 
,
false: False,
le: A B,
ge: i 
j ,
nat: 
,
true: True,
member: t T,
implies: P Q,
all: x:A. B[x],
not: A,
or: P Q,
squash: T,
unit: Unit,
so_lambda: 
x.t[x],
top: Top,
uall: [x:A]. B[x],
Accum-loc-class: Accum-loc-class(f;init;X),
SM4-class-du: SM4-class-du(init;trX1;trX2;trX3;trX4),
mu_ex_v5_State: mu_ex_v5_State(initial_token),
eq_atom: x =a y,
atom-deq: AtomDeq,
list-deq: list-deq(eq),
name-deq: NameDeq,
name_eq: name_eq(x;y),
name: Name,
subtype: S 
T,
bfalse: ff,
band: p 
q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
assert: b,
and: P Q,
exists: x:A. B[x],
btrue: tt,
guard: {T},
cand: A c B,
pi2: snd(t),
pi1: fst(t),
Id: Id,
uimplies: b supposing a,
strongwellfounded: SWellFounded(R[x; y]),
es-locl: (e <loc e'),
so_apply: x[s],
es-p-local-pred: es-p-local-pred(es;P),
sq_type: SQType(T),
spreadn: spread3,
isl: isl(x),
mu_ex_v5_onRequest: mu_ex_v5_onRequest(),
disjoint-union-tr: tr1 + tr2,
mu_ex_v5_Request: mu_ex_v5_Request(),
mu_ex_v5_Token: mu_ex_v5_Token(),
single-valued-classrel: single-valued-classrel(es;X;T),
iff: P 
Q,
outr: outr(x),
mu_ex_v5_onToken: mu_ex_v5_onToken(),
es-le: e loc e' ,
mu_ex_v5_onLeaveCS: mu_ex_v5_onLeaveCS(),
mu_ex_v5_onUseSR: mu_ex_v5_onUseSR(),
deq: EqDecider(T),
mu_ex_v5_initState: mu_ex_v5_initState(initial_token),
rev_implies: P Q,
it: ,
eq_id: a = b
Lemmas :
event-ordering+_wf,
it_wf,
valueall-type_wf,
equal-valueall-type,
make-Msg_wf,
mu_ex_v5_main_wf,
Id_wf,
es-E_wf,
equal_wf,
btrue_wf,
mu_ex_v5_State_wf,
mu_ex_v5_initState_wf,
primed-class-opt_wf,
bool_wf,
mu_ex_v5_Token_wf,
unit_wf2,
classrel_wf,
not_wf,
primed-class-opt-classrel,
es-causl_wf,
le_wf,
nat_wf,
less_than_wf,
ge_wf,
nat_properties,
Message_wf,
event-ordering+_inc,
es-causl-swellfnd,
mu_ex_v5_send-token-not-token,
mu_ex_v5_send-token-had-token,
lifting-loc-2_wf,
rec-combined-loc-class-opt-1_wf,
mu_ex_v5_LeaveCS_wf,
mu_ex_v5_UseSR_wf,
mu_ex_v5_Request_wf,
disjoint-union-class_wf,
mu_ex_v5_onLeaveCS_wf,
mu_ex_v5_onUseSR_wf,
all_wf,
uall_wf,
mu_ex_v5_onToken_wf,
mu_ex_v5_onRequest_wf,
disjoint-union-tr_wf,
simple-loc-comb-2-classrel,
rec-combined-loc-class-opt-1-classrel,
band_wf,
assert_elim,
es-first_wf,
assert_wf,
es-loc_wf,
or_wf,
and_wf,
es-le_wf,
es-locl_wf,
assert-name_eq,
atom_subtype_base,
list_subtype_base,
name_wf,
base-noloc-classrel,
assert_of_band,
bool_subtype_base,
subtype_base_sq,
pi1_wf_top,
pi2_wf,
disjoint-union-classrel,
es-locl_transitivity1,
es-le_weakening,
es-locl_transitivity2,
mu_ex_v5_State-single-val,
es-locl-trichotomy,
mu_ex_v5_token-implies-state,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
bool_cases,
bnot_wf,
btrue_neq_bfalse,
assert-eq-id,
deq_wf,
id-deq_wf,
bfalse_wf,
bag-member-single,
es-init_wf,
atom2_subtype_base,
es-loc-init,
es-init-le,
es-first-init
\mforall{}[es:EO']. \mforall{}[m1,m2,init,p1,p2,p:Id]. \mforall{}[e:E].
(<p, make-Msg([token];Unit;\mcdot{})> \mmember{} mu\_ex\_v5\_main(init;m1;m2;p1;p2)(e)
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
(((\mcdot{} \mmember{} mu\_ex\_v5\_Token()(e') \mwedge{} (e' <loc e))
\mvee{} ((loc(e') = init) \mwedge{} (\muparrow{}first(e')) \mwedge{} (\mneg{}\mcdot{} \mmember{} mu\_ex\_v5\_Token()(e')) \mwedge{} e' \mleq{}loc e ))
\mwedge{} (\mforall{}e'':E
(e' \mleq{}loc e''
{}\mRightarrow{} (e'' <loc e)
{}\mRightarrow{} (\mforall{}b1,b2,b3:\mBbbB{}. (<b1, b2, b3> \mmember{} mu\_ex\_v5\_State(init)(e'') {}\mRightarrow{} (\muparrow{}b2)))))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\mcdot{} \mmember{} mu\_ex\_v5\_Token()(e'')))))))
Date html generated:
2012_02_20-PM-07_02_10
Last ObjectModification:
2012_02_02-PM-03_02_26
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