Nuprl Lemma : nth_tl-es-before
[es:EO]. [e:E]. [n:
||before(e)||]. (nth_tl(n;before(e)) = filter(
a.before(e)[n] 
loc a;before(e)))
Proof not projected
Definitions occuring in Statement :
es-before: before(e),
es-ble: e loc e',
es-E: E,
event_ordering: EO,
select: l[i],
nth_tl: nth_tl(n;as),
length: ||as||,
int_seg: {i..j
},
uall: [x:A]. B[x],
lambda: x.A[x],
list: type List,
natural_number: $n,
equal: s = t,
filter: filter(P;l)
Definitions :
uall: [x:A]. B[x],
member: t 
T,
all: x:A. B[x],
nat: ,
implies: P 
Q,
ge: i 
j ,
le: A B,
not: 
A,
false: False,
squash: 
T,
true: True,
es-before: before(e),
filter: filter(P;l),
ycomb: Y,
ifthenelse: if b then t else f fi ,
btrue: tt,
reduce: reduce(f;k;as),
bfalse: ff,
prop: 
,
top: Top,
subtype: S 
T,
iff: P 
Q,
rev_implies: P Q,
int_seg: {i..j},
length: ||as||,
lelt: i j < k,
and: P 
Q,
label: ...$L... t,
strongwellfounded: SWellFounded(R[x; y]),
exists: 
x:A. B[x],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
guard: {T},
it: 
Lemmas :
es-causl-swellfnd,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
equal_wf,
int_seg_wf,
length_wf,
es-E_wf,
es-before_wf,
event_ordering_wf,
es-first_wf,
bool_wf,
eqtt_to_assert,
nth_tl_nil,
uiff_transitivity,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
es-pred-causl,
filter_append_sq,
es-before_wf3,
top_wf,
es-locl_wf,
nth_tl-append,
lt_int_wf,
assert_of_lt_int,
le_int_wf,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
ifthenelse_wf,
select_append_front,
filter_functionality,
true_wf,
squash_wf,
append_wf,
nth_tl_wf,
es-ble_wf,
select_wf,
length_nil,
length_wf_nil,
length_cons,
non_neg_length,
length_wf_nat,
length_append,
lelt_wf,
filter_wf,
iff_transitivity,
es-le_wf,
iff_weakening_uiff,
assert-es-ble,
not_functionality_wrt_iff,
member-es-before,
select_member,
es-pred-locl,
es-le_weakening
\mforall{}[es:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}||before(e)||].
(nth\_tl(n;before(e)) = filter(\mlambda{}a.before(e)[n] \mleq{}loc a;before(e)))
Date html generated:
2012_01_23-PM-12_11_22
Last ObjectModification:
2011_12_13-AM-10_31_16
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