Nuprl Lemma : RSC_VotesInRound-inv
[Cmd:ValueAllType]. [es:EO']. [e:E]. [cmds:Cmd List]. [locs:Id List]. [n,i:
].
(<cmds, locs> 
RSC_VotesInRound{mark-simple-consensus-V2.esh:o}(Cmd) <n, i>(e)
{(||cmds|| = ||locs||)
no_repeats(Id;locs)
(k:{k:
| (k < ||cmds||) (k < ||locs||)}
(
e':{e':E| e' 
loc e } . <<<n, i>, cmds[k]>, locs[k]> RSC_Vote(Cmd)(e')))})
Proof not projected
Definitions occuring in Statement :
RSC_Vote: RSC_Vote(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-E: E,
Id: Id,
select: l[i],
length: ||as||,
nat: ,
uall: [x:A]. B[x],
guard: {T},
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
implies: P Q,
and: P Q,
less_than: a < b,
set: {x:A| B[x]} ,
apply: f a,
pair: <a, b>,
product: x:A 
B[x],
list: type List,
int: ,
equal: s = t,
no_repeats: no_repeats(T;l),
vatype: ValueAllType
Definitions :
vatype: ValueAllType,
implies: P Q,
RSC_VotesInRound: Error :RSC_VotesInRound,
guard: {T},
and: P Q,
all: x:A. B[x],
nat: ,
squash: T,
exists: x:A. B[x],
prop: 
,
member: t T,
true: True,
cand: A c B,
ge: i 
j ,
le: A B,
not: 
A,
false: False,
so_lambda: 
x.t[x],
top: Top,
uall: [x:A]. B[x],
subtype: S 
T,
or: P 
Q,
label: ...$L... t,
so_lambda: x y.t[x; y],
iff: P 
Q,
rev_implies: P Q,
gt: i > j,
ycomb: Y,
length: ||as||,
btrue: tt,
bfalse: ff,
lt_int: i <z j,
bnot: 
b,
le_int: i z j,
ifthenelse: if b then t else f fi ,
select: l[i],
es-le: e loc e' ,
assert: 
b,
lelt: i j < k,
int_seg: {i..j
},
append: as @ bs,
Id: Id,
sq_stable: SqStable(P),
uimplies: b supposing a,
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
Accum-class: Accum-class(f;init;X),
RSC_collect: Error :RSC_collect,
uiff: uiff(P;Q),
es-p-local-pred: es-p-local-pred(es;P),
pi2: snd(t),
pi1: fst(t),
es-locl: (e <loc e'),
sq_type: SQType(T),
rev_uimplies: rev_uimplies(P;Q),
so_apply: x[s1;s2]
Lemmas :
sq_stable__and,
sq_stable__valueall-type,
valueall-type_wf,
length_wf,
Id_wf,
no_repeats_wf,
nat_wf,
nat_properties,
squash_wf,
es-E_wf,
event-ordering+_inc,
Message_wf,
es-le_wf,
classrel_wf,
Error :RSC_Vote_wf,
select_wf,
sq_stable__equal,
sq_stable__no_repeats,
sq_stable__all,
sq_stable__squash,
es-causl-swellfnd,
ge_wf,
le_wf,
es-causl_wf,
rec-combined-class-opt-1-classrel,
Accum-class_wf,
Error :RSC_collect_wf,
single-bag_wf,
simple-comb-2_wf,
lifting-2_wf,
primed-class-opt_wf,
simple-comb-2-classrel,
Error :RSC_VotesInRound_wf,
primed-class-opt-classrel,
event-ordering+_wf,
no_repeats_witness,
Error :pi2_wf,
pi1_wf_top,
band_wf,
eq_int_wf,
bnot_wf,
deq-member_wf,
id-deq_wf,
bool_wf,
assert_wf,
product-wf,
not_wf,
l_member_wf,
bor_wf,
union-wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
iff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
assert_of_band,
and_functionality_wrt_iff,
uiff_transitivity,
and_functionality_wrt_uiff,
assert_of_eq_int,
assert_of_bnot,
not_functionality_wrt_iff,
assert-deq-member,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_thru_band,
true_wf,
assert_of_bor,
or_functionality_wrt_iff,
or_functionality_wrt_uiff,
not_functionality_wrt_uiff,
no_repeats_cons,
and_functionality_wrt_uiff2,
squash_functionality_wrt_uiff,
Error :eclass_wf,
Error :RSC_Vote_wf,
es-locl_wf,
int_subtype_base,
es-le_weakening,
es-locl_transitivity1,
assert_of_lt_int,
false_wf,
iff_functionality_wrt_iff,
bfalse_wf,
lt_int_wf,
iff_imp_equal_bool,
select_append,
atom2_subtype_base,
list_subtype_base,
bag-member-single,
length_wf_nat,
top_wf,
ifthenelse_wf,
member_wf,
length_cons,
length_nil,
non_neg_length,
no_repeats_singleton,
no_repeats_nil,
length_wf2
\mforall{}[Cmd:ValueAllType]. \mforall{}[es:EO']. \mforall{}[e:E]. \mforall{}[cmds:Cmd List]. \mforall{}[locs:Id List]. \mforall{}[n,i:\mBbbZ{}].
(<cmds, locs> \mmember{} RSC\_VotesInRound\{mark-simple-consensus-V2.esh:o\}(Cmd) <n, i>(e)
{}\mRightarrow{} \{(||cmds|| = ||locs||)
\mwedge{} no\_repeats(Id;locs)
\mwedge{} (\mforall{}k:\{k:\mBbbN{}| (k < ||cmds||) \mwedge{} (k < ||locs||)\}
(\mdownarrow{}\mexists{}e':\{e':E| e' \mleq{}loc e \} . <<<n, i>, cmds[k]>, locs[k]> \mmember{} RSC\_Vote(Cmd)(e')))\})
Date html generated:
2012_02_20-PM-04_03_16
Last ObjectModification:
2012_02_02-PM-01_59_45
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