Nuprl Lemma : firstn-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. ∀[n:ℕ||(e1, e2)||]. (firstn(n;(e1, e2)) = (e1, (e1, e2)[n]) ∈ (E List))
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-E: E,
event_ordering: EO,
select: L[n],
firstn: firstn(n;as),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
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,
nat_wf,
int_seg_subtype-nat,
int_seg_wf,
length_wf,
es-E_wf,
es-open-interval_wf,
event_ordering_wf,
first0,
subtype_rel_list,
top_wf,
select0,
es-open-interval-nil,
hd_wf,
le-add-cancel2,
assert_wf,
es-first_wf2,
nil_wf,
member-es-open-interval,
le_wf,
select_wf,
sq_stable__le,
assert_elim,
es-locl-first,
btrue_neq_bfalse,
es-le_wf,
pred-hd-es-open-interval,
iff_weakening_equal,
es-le-self,
decidable__lt,
firstn_decomp,
le_weakening2,
length_wf_nat,
equal_wf,
list_wf,
append_wf,
cons_wf,
not-le-2,
filter_append_sq,
filter_cons_lemma,
filter_nil_lemma,
es-bless_wf,
bnot_wf,
not_wf,
es-locl_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-es-bless,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
filter_wf5,
squash_wf,
true_wf,
set_wf,
l_member_wf,
es-before_wf,
equal-wf-T-base,
uiff_transitivity,
select_member,
lelt_wf,
pred-member-es-open-interval
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[n:\mBbbN{}||(e1, e2)||]. (firstn(n;(e1, e2)) = (e1, (e1, e2)[n]))
Date html generated:
2015_07_17-AM-08_43_57
Last ObjectModification:
2015_02_04-AM-07_09_40
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