Nuprl Lemma : mu_ex_v5_closest-send-token
[es:EO']. [m1,m2,init,p1,p2,p:Id]. [e,e0:E].
((e0 < e)
<loc(e), make-Msg([token];Unit;
)> 
mu_ex_v5_main(init;m1;m2;p1;p2)(e0)
(
e':E
((e' < e)
<loc(e), make-Msg([token];Unit;)> mu_ex_v5_main(init;m1;m2;p1;p2)(e')
(e1:E. ((e1 < e) <loc(e), make-Msg([token];Unit;)> mu_ex_v5_main(init;m1;m2;p1;p2)(e1) e1 c
e')))))
Proof not projected
Definitions occuring in Statement :
mu_ex_v5_main: mu_ex_v5_main(initial_token;m1;m2;proc1;proc2),
make-Msg: make-Msg(hdr;typ;val),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-causle: e c e',
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
Id: Id,
it: ,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
implies: P Q,
and: P Q,
unit: Unit,
pair: <a, b>,
product: x:A 
B[x],
cons: [car / cdr],
nil: [],
token: "$token"
Definitions :
prop: 
,
true: True,
member: t T,
squash: T,
unit: Unit,
rev_implies: P 
Q,
and: P Q,
so_lambda: 
x.t[x],
implies: P Q,
isl: isl(x),
iff: P Q,
all: x:A. B[x],
exists: x:A. B[x],
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
assert: 
b,
cand: A c B,
so_lambda: x y.t[x; y],
guard: {T},
so_apply: x[s1;s2],
so_apply: x[s],
ycomb: Y,
top: Top,
subtype: S 
T,
list_accum: list_accum(x,a.f[x; a];y;l),
uall: [x:A]. B[x],
sq_or: a 
b,
decidable: Dec(P),
or: P Q,
false: False,
not: 
A,
uiff: uiff(P;Q),
uimplies: b supposing a,
bool: 
,
it: ,
!hyp_hide: x
Lemmas :
event-ordering+_wf,
es-E_wf,
es-causl_wf,
it_wf,
valueall-type_wf,
equal-valueall-type,
unit_wf2,
make-Msg_wf,
event-ordering+_inc,
es-loc_wf,
mu_ex_v5_main_wf,
Id_wf,
Message_wf,
classrel_wf,
mu_ex_v5_Token-ilf,
assert_wf,
iff_wf,
all_wf,
equal_wf,
bfalse_wf,
btrue_wf,
decidable_wf,
mu_ex_v5_send-token-dec,
false_wf,
true_wf,
es-causle_wf,
es-bcausl_wf,
band_wf,
ifthenelse_wf,
es-pred-list_wf,
list_accum_wf,
assert_of_bnot,
or_functionality_wrt_uiff,
assert_of_bor,
bnot_thru_band,
assert_functionality_wrt_uiff,
eqff_to_assert,
iff_weakening_uiff,
iff_transitivity,
assert_of_band,
eqtt_to_assert,
uiff_transitivity,
list_accum_invariant2,
not_wf,
or_wf,
bnot_wf,
bor_wf,
member-es-pred-list,
bool_wf,
l_member_wf,
member_wf,
append_wf,
top_wf,
list_accum_append,
nat_wf,
length_wf_nat,
l_member_decomp,
es-causle_weakening_eq,
assert-es-bcausl,
not_functionality_wrt_iff,
and_wf,
es-causle_weakening,
es-causl_weakening,
es-locl-trichotomy,
mu_ex_v5_send-token-from-same-loc,
es-causl_transitivity1
\mforall{}[es:EO']. \mforall{}[m1,m2,init,p1,p2,p:Id]. \mforall{}[e,e0:E].
((e0 < e)
{}\mRightarrow{} <loc(e), make-Msg([token];Unit;\mcdot{})> \mmember{} mu\_ex\_v5\_main(init;m1;m2;p1;p2)(e0)
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
((e' < e)
\mwedge{} <loc(e), make-Msg([token];Unit;\mcdot{})> \mmember{} mu\_ex\_v5\_main(init;m1;m2;p1;p2)(e')
\mwedge{} (\mforall{}e1:E
((e1 < e)
{}\mRightarrow{} <loc(e), make-Msg([token];Unit;\mcdot{})> \mmember{} mu\_ex\_v5\_main(init;m1;m2;p1;p2)(e1)
{}\mRightarrow{} e1 c\mleq{} e')))))
Date html generated:
2012_02_20-PM-07_04_03
Last ObjectModification:
2012_02_02-PM-03_03_14
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