Nuprl Lemma : mu_ex_v5_State-token
es:EO'. m1,m2,p1,p2,init:Id. e:E. b1,b2:
.
(<b1, tt, b2> 
mu_ex_v5_State(init)(e)
(
e':E
(e' 
loc e
(
mu_ex_v5_Token()(e') 
((
first(e')) (init = loc(e)) (
mu_ex_v5_Token()(e'))))
(e'':E
(e' loc e''
e'' loc e
((((e'' = e')) ( mu_ex_v5_Token()(e'')))
(a1,a2,a3:. (<a1, a2, a3> mu_ex_v5_State(init)(e'') (a2)))))))))
Proof not projected
Definitions occuring in Statement :
mu_ex_v5_State: mu_ex_v5_State(initial_token),
mu_ex_v5_Token: mu_ex_v5_Token(),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: b,
btrue: tt,
bool: ,
it: ,
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],
equal: s = t
Definitions :
all: x:A. B[x],
implies: P Q,
squash: T,
or: P Q,
not: A,
member: t T,
uall: [x:A]. B[x],
nat: 
,
ge: i 
j ,
le: A B,
false: False,
prop: 
,
true: True,
top: Top,
so_lambda: 
x.t[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),
and: P Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype: S 
T,
band: p 
q,
btrue: tt,
exists: x:A. B[x],
guard: {T},
eq_atom: x =a y,
atom-deq: AtomDeq,
list-deq: list-deq(eq),
name-deq: NameDeq,
name_eq: name_eq(x;y),
name: Name,
uiff: uiff(P;Q),
assert: b,
pi2: snd(t),
pi1: fst(t),
es-le: e loc e' ,
Id: Id,
strongwellfounded: SWellFounded(R[x; y]),
uimplies: b supposing a,
so_apply: x[s],
outr: outr(x),
spreadn: spread3,
isl: isl(x),
mu_ex_v5_onLeaveCS: mu_ex_v5_onLeaveCS(),
mu_ex_v5_onUseSR: mu_ex_v5_onUseSR(),
mu_ex_v5_onToken: mu_ex_v5_onToken(),
mu_ex_v5_onRequest: mu_ex_v5_onRequest(),
disjoint-union-tr: tr1 + tr2,
sq_type: SQType(T),
decidable: Dec(P),
es-locl: (e <loc e'),
es-p-local-pred: es-p-local-pred(es;P),
iff: P 
Q,
rev_implies: P Q,
mu_ex_v5_Request: mu_ex_v5_Request(),
mu_ex_v5_Token: mu_ex_v5_Token(),
unit: Unit,
single-valued-classrel: single-valued-classrel(es;X;T),
deq: EqDecider(T),
mu_ex_v5_initState: mu_ex_v5_initState(initial_token),
mu_ex_v5_UseSR: mu_ex_v5_UseSR(),
atom2-deq: Atom2Deq,
id-deq: IdDeq,
mu_ex_v5_LeaveCS: mu_ex_v5_LeaveCS(),
it:
Lemmas :
es-causl-swellfnd,
event-ordering+_inc,
Message_wf,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
rec-combined-loc-class-opt-1-classrel,
simple-loc-comb-2-classrel,
unit_wf2,
bool_wf,
disjoint-union-tr_wf,
mu_ex_v5_onRequest_wf,
Id_wf,
mu_ex_v5_onToken_wf,
uall_wf,
all_wf,
equal_wf,
mu_ex_v5_onUseSR_wf,
mu_ex_v5_onLeaveCS_wf,
disjoint-union-class_wf,
mu_ex_v5_Request_wf,
mu_ex_v5_Token_wf,
mu_ex_v5_UseSR_wf,
mu_ex_v5_LeaveCS_wf,
primed-class-opt_wf,
mu_ex_v5_initState_wf,
rec-combined-loc-class-opt-1_wf,
lifting-loc-2_wf,
btrue_wf,
classrel_wf,
mu_ex_v5_State_wf,
es-E_wf,
event-ordering+_wf,
band_wf,
and_wf,
not_assert_elim,
assert_elim,
primed-class-opt-classrel,
bool_subtype_base,
subtype_base_sq,
btrue_neq_bfalse,
decidable__assert,
pi1_wf_top,
Error :pi2_wf,
implies-wf,
es-loc_wf,
es-first_wf,
assert_wf,
or_wf,
es-le_wf,
not_wf,
it_wf,
es-le_weakening,
es-locl_transitivity1,
es-le-loc,
es-le-not-locl,
decidable__es-locl,
es-locl_wf,
decidable__es-le,
mu_ex_v5_State-exists,
assert-name_eq,
atom_subtype_base,
list_subtype_base,
name_wf,
base-noloc-classrel,
disjoint-union-classrel,
mu_ex_v5_State-single-val,
es-init_wf,
deq_wf,
id-deq_wf,
bfalse_wf,
bag-member-single,
es-causle_weakening_locl,
es-causle_antisymmetry,
assert_of_eq_atom2,
es-init-le,
es-first-init,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
bool_cases,
bnot_wf
\mforall{}es:EO'. \mforall{}m1,m2,p1,p2,init:Id. \mforall{}e:E. \mforall{}b1,b2:\mBbbB{}.
(<b1, tt, b2> \mmember{} mu\_ex\_v5\_State(init)(e)
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
(e' \mleq{}loc e
\mwedge{} (\mcdot{} \mmember{} mu\_ex\_v5\_Token()(e')
\mvee{} ((\muparrow{}first(e')) \mwedge{} (init = loc(e)) \mwedge{} (\mneg{}\mcdot{} \mmember{} mu\_ex\_v5\_Token()(e'))))
\mwedge{} (\mforall{}e'':E
(e' \mleq{}loc e''
{}\mRightarrow{} e'' \mleq{}loc e
{}\mRightarrow{} (((\mneg{}(e'' = e')) {}\mRightarrow{} (\mneg{}\mcdot{} \mmember{} mu\_ex\_v5\_Token()(e'')))
\mwedge{} (\mforall{}a1,a2,a3:\mBbbB{}. (<a1, a2, a3> \mmember{} mu\_ex\_v5\_State(init)(e'') {}\mRightarrow{} (\muparrow{}a2)))))))))
Date html generated:
2012_02_20-PM-07_00_45
Last ObjectModification:
2012_02_02-PM-03_01_52
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