{ 
[V:Type]
A:Id List. s:ConsensusState. a:{a:Id| (a 
A)} . i:
.
((by state s, a passed inning i without archiving a value
(
in state s, a has not completed inning i)
(v:V. (by state s, a archived v in inning i)))
(in state s, a has not completed inning i
(by state s, a passed inning i without archiving a value)
(v:V. (by state s, a archived v in inning i)))
(
v:V
(by state s, a archived v in inning i
(by state s, a passed inning i without archiving a value)
(in state s, a has not completed inning i)
(v':V
by state s, a archived v' in inning i supposing (v' = v))))) }
{ Proof }
Definitions occuring in Statement :
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
consensus-state4: ConsensusState,
Id: Id,
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
or: P Q,
and: P Q,
set: {x:A| B[x]} ,
list: type List,
int: ,
universe: Type,
equal: s = t,
l_member: (x l)
Definitions :
bool: 
,
nat: 
,
cand: A c B,
squash: 
T,
bag: bag(T),
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
apply: f a,
fpf-dom: x dom(f),
tag-by: z
T,
rev_implies: P 
Q,
iff: P 
Q,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
true: True,
fpf-cap: f(x)?z,
assert: 
b,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
uiff: uiff(P;Q),
subtype_rel: A r B,
cs-inning: Inning(s;a),
top: Top,
cs-estimate: Estimate(s;a),
fpf-domain: fpf-domain(f),
lambda: 
x.A[x],
axiom: Ax,
pair: <a, b>,
void: Void,
false: False,
implies: P Q,
less_than: a < b,
guard: {T},
limited-type: LimitedType,
prop: 
,
member: t T,
universe: Type,
list: type List,
consensus-state4: ConsensusState,
Id: Id,
l_member: (x l),
set: {x:A| B[x]} ,
int: ,
equal: s = t,
uimplies: b supposing a,
isect: x:A. B[x],
uall: [x:A]. B[x],
so_lambda: 
x.t[x],
or: P Q,
union: left + right,
all: x:A. B[x],
function: x:A 
B[x],
cs-archived: by state s, a archived v in inning i,
not: A,
cs-passed: by state s, a passed inning i without archiving a value,
cs-not-completed: in state s, a has not completed inning i,
exists: x:A. B[x],
and: P Q,
product: x:A B[x],
int-deq: IntDeq,
fpf-ap: f(x),
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
ExRepD: Error :ExRepD,
D: Error :D,
MaAuto: Error :MaAuto,
Try: Error :Try,
RepeatFor: Error :RepeatFor
Lemmas :
fpf-ap_wf,
cs-passed_wf,
not_wf,
cs-not-completed_wf,
cs-archived_wf,
Id_wf,
consensus-state4_wf,
l_member_wf,
uall_wf,
consensus-state4-cases,
false_wf,
fpf-domain_wf,
top_wf,
cs-estimate_wf,
member_wf,
subtype_rel_wf,
cs-inning_wf,
fpf_wf,
subtype_rel_function,
subtype_rel_self,
subtype_rel_simple_product,
true_wf,
squash_wf,
subtype-fpf2,
subtype-top
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}s:ConsensusState. \mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}i:\mBbbZ{}.
((by state s, a passed inning i without archiving a value
\mwedge{} (\mneg{}in state s, a has not completed inning i)
\mwedge{} (\mforall{}v:V. (\mneg{}by state s, a archived v in inning i)))
\mvee{} (in state s, a has not completed inning i
\mwedge{} (\mneg{}by state s, a passed inning i without archiving a value)
\mwedge{} (\mforall{}v:V. (\mneg{}by state s, a archived v in inning i)))
\mvee{} (\mexists{}v:V
(by state s, a archived v in inning i
\mwedge{} (\mneg{}by state s, a passed inning i without archiving a value)
\mwedge{} (\mneg{}in state s, a has not completed inning i)
\mwedge{} (\mforall{}v':V. \mneg{}by state s, a archived v' in inning i supposing \mneg{}(v' = v)))))
Date html generated:
2011_08_16-AM-09_59_27
Last ObjectModification:
2011_06_18-AM-08_57_43
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