Nuprl Lemma : prior-classrel-list-unique
[A:
']. [X:EClass'(A)]. [es:EO']. [e:E].
L1,L2:(A 
E) List.
(single-valued-classrel(es;X;A)
prior-classrel-list(es;A;X;L1;e)
prior-classrel-list(es;A;X;L2;e)
(L1 = L2))
Proof not projected
Definitions occuring in Statement :
prior-classrel-list: prior-classrel-list(es;A;X;L;e),
single-valued-classrel: single-valued-classrel(es;X;T),
Message: Message,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
product: x:A B[x],
list: type List,
universe: Type,
equal: s = t
Definitions :
member: t 
T,
label: ...$L... t,
or: P 
Q,
gt: i > j,
all: x:A. B[x],
and: P 
Q,
exists: 
x:A. B[x],
decidable: Dec(P),
implies: P Q,
not: 
A,
subtype: S 
T,
ifthenelse: if b then t else f fi ,
it: 
,
btrue: tt,
prop: 
,
bfalse: ff,
so_lambda: 
x.t[x],
top: Top,
squash: 
T,
true: True,
ge: i 
j ,
le: A 
B,
false: False,
int_seg: {i..j
},
lelt: i j < k,
so_lambda: x y.t[x; y],
iff: P 
Q,
rev_implies: P Q,
prior-classrel-list: prior-classrel-list(es;A;X;L;e),
uall: [x:A]. B[x],
l_all: (xL.P[x]),
bool: 
,
deq: EqDecider(T),
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
so_apply: x[s],
nat: 
,
es-locl: (e <loc e'),
l_member: (x l),
cand: A c B,
single-valued-classrel: single-valued-classrel(es;X;T),
sq_type: SQType(T),
guard: {T},
so_apply: x[s1;s2],
sorted-by: sorted-by(R;L)
Lemmas :
prior-classrel-list_wf,
single-valued-classrel_wf,
Message_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf2,
length_wf1,
longer-list-not-member,
es-eq_wf,
deq_wf,
bool_wf,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert-deq,
inl_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
inr_wf,
map_wf,
pi2_wf,
member_map,
l_member_wf,
classrel_wf,
length-map,
length_wf_nat,
top_wf,
nat_properties,
nat_wf,
gt_wf,
squash_wf,
true_wf,
es-locl_wf,
list_extensionality,
ge_wf,
select_wf,
select_member,
le_wf,
subtype_base_sq,
int_subtype_base,
pi1_wf_top,
pair-eta,
eclass_wf,
es-locl_irreflexivity,
es-locl_transitivity2,
es-le_weakening,
es-le_weakening_eq,
event_ordering_wf
\mforall{}[A:\mBbbU{}']. \mforall{}[X:EClass'(A)]. \mforall{}[es:EO']. \mforall{}[e:E].
\mforall{}L1,L2:(A \mtimes{} E) List.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} prior-classrel-list(es;A;X;L1;e)
{}\mRightarrow{} prior-classrel-list(es;A;X;L2;e)
{}\mRightarrow{} (L1 = L2))
Date html generated:
2011_10_20-PM-03_45_16
Last ObjectModification:
2011_09_01-PM-11_53_44
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