Nuprl Lemma : last-data-stream
∀[L:Top List]. ∀[P:Top]. (last(data-stream(P;L)) ~ if null(L) then ⊥ else snd(P*(firstn(||L|| - 1;L))(last(L))) fi )
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
last: last(L),
firstn: firstn(n;as),
length: ||as||,
null: null(as),
list: T List,
bottom: ⊥,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
pi2: snd(t),
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions :
select: L[n],
nil: [],
it: ⋅
Lemmas :
top_wf,
list-cases,
data_stream_nil_lemma,
product_subtype_list,
stuck-spread,
base_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
list_wf,
not_wf,
less_than_wf,
select-data-stream,
length-data-stream,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
subtract_wf,
length_wf,
condition-implies-le,
add-associates,
minus-one-mul,
add-mul-special,
zero-mul,
add-zero,
add-swap,
le-add-cancel-alt,
length_of_nil_lemma,
length_of_cons_lemma,
nil_wf,
non_neg_length,
length_wf_nat
Latex:
\mforall{}[L:Top List]. \mforall{}[P:Top].
(last(data-stream(P;L)) \msim{} if null(L) then \mbot{} else snd(P*(firstn(||L|| - 1;L))(last(L))) fi )
Date html generated:
2015_07_23-AM-11_06_18
Last ObjectModification:
2015_01_29-AM-00_11_54
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