Nuprl Lemma : constant-data-stream
∀[L:Top List]. ∀[b:Top]. (data-stream(constant-dataflow(b);L) ~ map(λi.b;upto(||L||)))
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
constant-dataflow: constant-dataflow(b),
upto: upto(n),
map: map(f;as),
length: ||as||,
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
sqequal: s ~ t
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
top_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
list_wf,
list-cases,
data_stream_nil_lemma,
length_of_nil_lemma,
map_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
length_of_cons_lemma,
data-stream-cons,
const_df_ap_lemma,
upto_decomp2,
length_wf,
non_neg_length,
length_wf_nat,
map_cons_lemma,
map-map,
int_seg_wf,
list_subtype_base,
lelt_wf,
upto_wf,
squash_wf,
true_wf
Latex:
\mforall{}[L:Top List]. \mforall{}[b:Top]. (data-stream(constant-dataflow(b);L) \msim{} map(\mlambda{}i.b;upto(||L||)))
Date html generated:
2015_07_23-AM-11_06_24
Last ObjectModification:
2015_01_29-AM-00_11_26
Home
Index