Nuprl Lemma : data-stream-cons
∀[L:Top List]. ∀[a,P:Top]. (data-stream(P;[a / L]) ~ [snd(P(a)) / data-stream(fst(P(a));L)])
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
dataflow-ap: df(a),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
sqequal: s ~ t
Lemmas :
top_wf,
list_wf,
upto_decomp2,
length_wf,
cons_wf,
non_neg_length,
length_wf_nat,
length_cons,
less_than_wf,
length_of_cons_lemma,
trivial-int-eq1,
map_cons_lemma,
first0,
iter_df_nil_lemma,
map-map,
upto_wf,
int_seg_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
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,
nat_wf,
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,
select-cons,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
list_ind_cons_lemma,
lt_int_wf,
assert_of_lt_int,
iter_df_cons_lemma
Latex:
\mforall{}[L:Top List]. \mforall{}[a,P:Top]. (data-stream(P;[a / L]) \msim{} [snd(P(a)) / data-stream(fst(P(a));L)])
Date html generated:
2015_07_23-AM-11_06_02
Last ObjectModification:
2015_01_29-AM-00_11_46
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