{ 
[V:Type]. [L:ts-reachable(consensus-ts3(V))].
uiff(([v:V]. (
(COMMITED[v] 
L)))
([v:V]. ((CONSIDERING[v] L)));cs-ref-map3(L) = AMBIVALENT) }
{ Proof }
Definitions occuring in Statement :
cs-ref-map3: cs-ref-map3(L),
consensus-ts3: consensus-ts3(T),
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
cs-ambivalent: AMBIVALENT,
consensus-state2: consensus-state2(T),
uiff: uiff(P;Q),
uall: [x:A]. B[x],
not: A,
and: P Q,
universe: Type,
equal: s = t,
l_member: (x l),
ts-reachable: ts-reachable(ts)
Definitions :
bool: 
,
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
ts-rel: ts-rel(ts),
rel_star: R^*,
tag-by: z
T,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
true: True,
fpf-cap: f(x)?z,
spread: spread def,
pi1: fst(t),
filter: filter(P;l),
natural_number: $n,
top: Top,
select: l[i],
length: ||as||,
real: 
,
grp_car: |g|,
subtype: S 
T,
int: 
,
nat: 
,
intensional-universe: IType,
cand: A c B,
so_apply: x[s],
union: left + right,
or: P 
Q,
guard: {T},
cons: [car / cdr],
nil: [],
limited-type: LimitedType,
assert: 
b,
list: type List,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
apply: f a,
infix_ap: x f y,
le: A 
B,
ge: i 
j ,
less_than: a < b,
cs-considering: CONSIDERING[v],
cs-commited: COMMITED[v],
rev_implies: P 
Q,
iff: P 
Q,
lambda: 
x.A[x],
axiom: Ax,
cs-ambivalent: AMBIVALENT,
cs-ref-map3: cs-ref-map3(L),
consensus-state2: consensus-state2(T),
prop: 
,
consensus-state3: consensus-state3(T),
l_member: (x l),
so_lambda: 
x.t[x],
pair: <a, b>,
void: Void,
false: False,
implies: P Q,
not: A,
uimplies: b supposing a,
product: x:A B[x],
and: P Q,
uiff: uiff(P;Q),
transition-system: transition-system{i:l},
ts-type: ts-type(ts),
subtype_rel: A r B,
set: {x:A| B[x]} ,
universe: Type,
ts-reachable: ts-reachable(ts),
all: x:A. B[x],
function: x:A 
B[x],
consensus-ts3: consensus-ts3(T),
uall: [x:A]. B[x],
isect: x:A. B[x],
member: t T,
equal: s = t,
Auto: Error :Auto,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
tactic: Error :tactic,
Try: Error :Try,
MaAuto: Error :MaAuto,
cs-decided: Decided[v],
cs-predecided: PREDECIDED[v],
exists: 
x:A. B[x],
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
set_blt: a <
b,
grp_blt: a < b,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
bimplies: p q,
band: p q,
bor: p q,
null: null(as),
bnot: b,
unit: Unit,
let: let,
hd: hd(l),
cs-is-committed: cs-is-committed(x),
cs-is-considering: cs-is-considering(x),
lelt: i j < k,
rationals: 
,
int_seg: {i..j
},
cs-considered-val: cs-considered-val(x),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
cs-committed-val: cs-committed-val(x),
inl: inl x ,
it: 
,
inr: inr x ,
eq_bool: p =b q,
eq_int: (i =
j),
eq_atom: x =a y,
isl: isl(x),
sq_type: SQType(T),
outr: outr(x)
Lemmas :
outr_wf,
ifthenelse_wf,
isl_wf,
assert-cs-is-committed,
cs-committed-val_wf,
cs-decided_wf,
select_member,
assert-cs-is-considering,
cs-predecided_wf,
cs-considered-val_wf,
hd_wf,
true_wf,
int_seg_wf,
length_wf1,
cs-is-considering_wf,
filter_is_empty,
eqtt_to_assert,
iff_weakening_uiff,
eqff_to_assert,
uiff_transitivity,
assert_of_bnot,
not_functionality_wrt_uiff,
assert_of_null,
null_wf3,
filter_wf_top,
cs-is-committed_wf,
bool_wf,
filter_wf,
bnot_wf,
assert_wf,
cs-ref-map3-predecided,
cs-ref-map3-decided,
consensus-ts3-invariant1,
l_member_wf,
consensus-state3_wf,
false_wf,
not_wf,
consensus-state2_wf,
uall_wf,
uiff_wf,
consensus-ts3_wf,
ts-type_wf,
subtype_rel_wf,
ts-reachable_wf,
cs-commited_wf,
cs-considering_wf,
member_wf,
cs-ref-map3_wf,
cs-ambivalent_wf,
rev_implies_wf,
iff_wf,
uiff_inversion,
intensional-universe_wf,
nat_wf,
length_wf_nat,
select_wf,
top_wf,
ts-rel_wf,
rel_star_wf
\mforall{}[V:Type]. \mforall{}[L:ts-reachable(consensus-ts3(V))].
uiff((\mforall{}[v:V]. (\mneg{}(COMMITED[v] \mmember{} L))) \mwedge{} (\mforall{}[v:V]. (\mneg{}(CONSIDERING[v] \mmember{} L)));cs-ref-map3(L)
= AMBIVALENT)
Date html generated:
2011_08_16-AM-09_57_15
Last ObjectModification:
2011_06_18-AM-08_56_27
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