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),
firstn: firstn(n;as),
select: L[n],
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
data-stream: data-stream(P;L),
top: Top,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla)
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:
2016_05_17-AM-10_21_30
Last ObjectModification:
2016_01_18-AM-00_19_25
Theory : process-model
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