Nuprl Lemma : select-data-stream
∀[L:Top List]. ∀[P:Top]. ∀[i:ℕ]. (data-stream(P;L)[i] ~ if i <z ||L|| then snd(P*(firstn(i;L))(L[i])) else ⊥ fi )
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
select: L[n],
firstn: firstn(n;as),
length: ||as||,
list: T List,
nat: ℕ,
bottom: ⊥,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
top: Top,
pi2: snd(t),
sqequal: s ~ t
Lemmas :
select-map,
upto_wf,
length_wf,
top_wf,
subtype_rel_list,
int_seg_wf,
length_upto,
length_wf_nat,
lelt_wf,
select_upto,
subtype_base_sq,
int_subtype_base,
select-is-bottom,
map_wf,
length-data-stream
Latex:
\mforall{}[L:Top List]. \mforall{}[P:Top]. \mforall{}[i:\mBbbN{}].
(data-stream(P;L)[i] \msim{} if i <z ||L|| then snd(P*(firstn(i;L))(L[i])) else \mbot{} fi )
Date html generated:
2015_07_23-AM-11_06_15
Last ObjectModification:
2015_01_29-AM-00_11_15
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