Nuprl Lemma : assert-eq_ballot
[b1,b2:ballot-id()]. (
eq_ballot(b1;b2) 
b1 = b2)
Proof not projected
Definitions occuring in Statement :
eq_ballot: eq_ballot(b1;b2),
ballot-id: ballot-id(),
assert: b,
uall: [x:A]. B[x],
iff: P Q,
equal: s = t
Definitions :
list: type List,
pi2: snd(t),
real: 
,
grp_car: |g|,
cand: A c
B,
squash: 
T,
outl: outl(x),
btrue: tt,
sq_type: SQType(T),
natural_number: $n,
inr: inr x ,
in-eclass: e 
X,
apply: f a,
so_apply: x[s],
or: P 
Q,
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
pi1: fst(t),
eq_int: (i =
j),
band: p q,
inl: inl x ,
set: {x:A| B[x]} ,
int: 
,
bool: 
,
limited-type: LimitedType,
universe: Type,
subtype: S 
T,
eq_ballot: eq_ballot(b1;b2),
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
prop: 
,
axiom: Ax,
lambda: 
x.A[x],
pair: <a, b>,
void: Void,
false: False,
member: t T,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
rev_implies: P Q,
function: x:A 
B[x],
implies: P Q,
and: P Q,
ballot-id: ballot-id(),
uall: [x:A]. B[x],
so_lambda: 
x.t[x],
iff: P Q,
equal: s = t,
assert: b,
isect: 
x:A. B[x],
union: left + right,
product: x:A 
B[x],
nat: 
,
unit: Unit,
top: Top,
sqequal: s ~ t,
bor: p q,
bimplies: p q,
bnot: b,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$n(x;y),
eq_type: eq_type(T;T'),
b-exists: (
i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
grp_blt: a < b,
set_blt: a < b,
infix_ap: x f y,
null: null(as),
eq_atom: x =a y
Lemmas :
subtype_rel_wf,
uiff_transitivity,
assert_of_band,
and_functionality_wrt_uiff,
assert_of_eq_int,
pi1_wf_top,
top_wf,
pi2_wf,
member_wf,
ballot-id_wf,
unit_wf,
nat_wf,
eq_ballot_wf,
assert_wf,
assert_witness,
uall_wf,
iff_wf,
false_wf,
ifthenelse_wf,
true_wf,
band_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,
eq_int_eq_true,
nat_properties,
eq_int_wf
\mforall{}[b1,b2:ballot-id()]. (\muparrow{}eq\_ballot(b1;b2) \mLeftarrow{}{}\mRightarrow{} b1 = b2)
Date html generated:
2011_10_20-PM-04_15_07
Last ObjectModification:
2011_01_29-AM-00_44_12
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