Nuprl Lemma : firstn-data-stream
∀[n:ℕ]. ∀[L:Top List]. ∀[P:Top]. (firstn(n;data-stream(P;L)) ~ data-stream(P;firstn(n;L)))
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
firstn: firstn(n;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
top_wf,
list_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,
first0,
map_wf,
int_seg_wf,
length_wf,
upto_wf,
data_stream_nil_lemma,
list-cases,
list_ind_nil_lemma,
product_subtype_list,
data-stream-cons,
list_ind_cons_lemma,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
firstn_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[L:Top List]. \mforall{}[P:Top]. (firstn(n;data-stream(P;L)) \msim{} data-stream(P;firstn(n;L)))
Date html generated:
2015_07_23-AM-11_06_09
Last ObjectModification:
2015_01_29-AM-00_11_40
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