Nuprl Lemma : nth_tl-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. ∀[n:ℕ||(e1, e2)||].
nth_tl(n + 1;(e1, e2)) = ((e1, e2)[n], e2) ∈ (E List) supposing loc(e1) = loc(e2) ∈ Id
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
select: L[n],
nth_tl: nth_tl(n;as),
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Lemmas :
es-locl-trichotomy,
es-open-interval-nil,
decidable__assert,
es-first_wf2,
not_wf,
assert_wf,
es-le_wf,
es-pred_wf,
es-pred-locl,
es-locl_transitivity2,
es-le_weakening_eq,
es-le_weakening,
length_of_nil_lemma,
es-pred-exists-between,
es-open-interval_wf,
es-E_wf,
list_wf,
equal_wf,
es-open-interval-closed,
es-causl_irreflexivity,
es-causle_weakening_locl,
es-causle_weakening,
es-causl_transitivity2,
es-locl_irreflexivity,
es-causl_weakening,
iff_weakening_equal,
es-pred_property,
squash_wf,
es-le-self,
le-add-cancel,
add-zero,
add-associates,
add_functionality_wrt_le,
add-commutes,
zero-add,
minus-one-mul,
minus-add,
condition-implies-le,
decidable__lt,
length_of_cons_lemma,
product_subtype_list,
less_than_irreflexivity,
le_weakening,
length_wf,
less_than_transitivity1,
le_wf,
list-cases,
false_wf,
select_wf,
tl_wf,
reduce_tl_cons_lemma,
nat_wf,
length_wf_nat,
es-closed-open-interval-decomp,
es-loc_wf,
and_wf,
es-loc-pred,
btrue_neq_bfalse,
assert_elim,
es-locl-first,
subtract_wf,
less-iff-le,
add-swap,
le-add-cancel2,
trivial-int-eq1,
nth_tl_decomp,
le_weakening2,
member-es-open-interval,
decidable__le,
not-le-2,
minus-minus,
less_than_wf,
sq_stable__le,
nth_tl_wf,
cons_wf,
es-closed-open-interval_wf,
es-pred-one-one,
subtract-is-less,
es-open-interval-ordered-inst,
lelt_wf,
pred-member-es-open-interval,
select_member,
assert_functionality_wrt_uiff
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[n:\mBbbN{}||(e1, e2)||].
nth\_tl(n + 1;(e1, e2)) = ((e1, e2)[n], e2) supposing loc(e1) = loc(e2)
Date html generated:
2015_07_17-AM-08_44_11
Last ObjectModification:
2015_07_16-AM-09_51_50
Home
Index