Nuprl Lemma : ballot-less-order
Linorder(ballot-id();b1,b2.(
ballot-less(b1;b2)) 
(b1 = b2))
Proof not projected
Definitions occuring in Statement :
ballot-less: ballot-less(b1;b2),
ballot-id: ballot-id(),
linorder: Linorder(T;x,y.R[x; y]),
assert: b,
or: P Q,
equal: s = t
Definitions :
eclass: EClass(A[eo; e]),
pair: <a, b>,
fpf: a:A fp-> B[a],
universe: Type,
limited-type: LimitedType,
subtype: S 
T,
prop: 
,
ballot-less: ballot-less(b1;b2),
implies: P 
Q,
member: t 
T,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A r B,
isect: 
x:A. B[x],
uall: 
[x:A]. B[x],
function: x:A 
B[x],
all: x:A. B[x],
refl: Refl(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
ballot-id: ballot-id(),
linorder: Linorder(T;x,y.R[x; y]),
and: P 
Q,
connex: Connex(T;x,y.R[x; y]),
order: Order(T;x,y.R[x; y]),
so_lambda: 
x y.t[x; y],
or: P Q,
assert: b,
equal: s = t,
product: x:A 
B[x],
nat: 
,
unit: Unit,
union: left + right,
guard: {T},
fpf-dom: x dom(f),
pi2: snd(t),
lambda: x.A[x],
so_lambda: x.t[x],
isl: isl(x),
outl: outl(x),
btrue: tt,
sq_type: SQType(T),
axiom: Ax,
inr: inr x ,
natural_number: $n,
bool: 
,
true: True,
pi1: fst(t),
void: Void,
inl: inl x ,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c B,
l_member: (x l),
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
exists: x:A. B[x],
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
lg-edge: lg-edge(g;a;b),
ses-action: Action(e),
ses-legal-sequence: Legal(pas) given prvt,
decidable: Dec(P),
rev_uimplies: rev_uimplies(P;Q),
le_int: i z j,
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
apply: f a,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bnot: b,
bimplies: p q,
es-locl: (e <loc e'),
es-causl: (e < e'),
eq_int: (i =
j),
band: p q,
lt_int: i <z j,
bor: p q,
false: False,
set: {x:A| B[x]} ,
int: 
,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
real: 
,
grp_car: |g|,
top: Top,
sqequal: s ~ t,
list: type List,
iff: P 
Q,
decision: Decision,
nat_plus: 
,
rationals: 
,
atom: Atom$n,
dstype: dstype(TypeNames; d; a),
fset: FSet{T},
Id: Id,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
consensus-state3: consensus-state3(T),
consensus-rcv: consensus-rcv(V;A),
es-E: E,
es-E-interface: E(X),
runEvents: runEvents(r),
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
Decide: Error :Decide,
tactic: Error :tactic,
proper-iseg: L1 < L2,
iseg: l1 l2,
gt: i > j,
length: ||as||
Lemmas :
decidable__lt,
not_functionality_wrt_uiff,
decidable__equal_unit,
decidable__equal_nat,
decidable__equal_product,
decidable__equal_union,
decidable__or,
ifthenelse_wf,
decidable_wf,
pi1_wf_top,
top_wf,
pi2_wf,
nat_properties,
lt_int_wf,
eq_int_wf,
band_wf,
bor_wf,
decidable__assert,
assert_of_lt_int,
assert_of_eq_int,
and_functionality_wrt_uiff,
assert_of_band,
uiff_transitivity,
or_functionality_wrt_uiff,
assert_of_bor,
true_wf,
bool_wf,
subtype_base_sq,
bool_subtype_base,
outl_wf,
le_wf,
pi1_wf,
union_subtype_base,
product_subtype_base,
set_subtype_base,
int_subtype_base,
unit_subtype_base,
assert_elim,
false_wf,
nat_wf,
unit_wf,
assert_wf,
trans_wf,
anti_sym_wf,
refl_wf,
order_wf,
connex_wf,
linorder_wf,
member_wf,
ballot-less_wf,
ballot-id_wf
Linorder(ballot-id();b1,b2.(\muparrow{}ballot-less(b1;b2)) \mvee{} (b1 = b2))
Date html generated:
2011_10_20-PM-04_16_08
Last ObjectModification:
2011_01_29-AM-00_52_27
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