Nuprl Lemma : nth_tl-es-before
∀[es:EO]. ∀[e:E]. ∀[n:ℕ||before(e)||]. (nth_tl(n;before(e)) = filter(λa.before(e)[n] ≤loc a;before(e)) ∈ (E List))
Proof
Definitions occuring in Statement :
es-before: before(e),
es-ble: e ≤loc e',
es-E: E,
event_ordering: EO,
filter: filter(P;l),
select: L[n],
nth_tl: nth_tl(n;as),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
natural_number: $n,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
length_wf,
es-before_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-E_wf,
event_ordering_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
nth_tl_nil,
filter_nil_lemma,
nil_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
filter_append_sq,
nth_tl-append,
subtype_rel_list,
top_wf,
lt_int_wf,
assert_of_lt_int,
filter_cons_lemma,
le_int_wf,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
list_wf,
append_wf,
nth_tl_wf,
cons_wf,
es-ble_wf,
select_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_cons,
length_wf_nat,
length_append,
filter_wf5,
l_member_wf,
squash_wf,
true_wf,
filter_functionality,
select_append_front,
ifthenelse_wf,
iff_weakening_equal,
assert-es-ble,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-le_wf,
member-es-before,
select_member,
bool_cases,
int_subtype_base,
select_append_back,
es-le_weakening_eq,
filter_is_nil,
nil-append,
l_all_iff,
es-locl_transitivity2,
es-locl_irreflexivity
\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:
2015_07_17-AM-08_43_31
Last ObjectModification:
2015_02_04-AM-07_09_25
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