Nuprl Lemma : last-data-stream
∀[L:Top List]. ∀[P:Top]. (last(data-stream(P;L)) ~ if null(L) then ⊥ else snd(P*(firstn(||L|| - 1;L))(last(L))) fi )
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
firstn: firstn(n;as),
last: last(L),
length: ||as||,
null: null(as),
list: T List,
bottom: ⊥,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
pi2: snd(t),
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
top: Top,
cons: [a / b],
last: last(L),
select: L[n],
nil: [],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
true: True,
satisfiable_int_formula: satisfiable_int_formula(fmla),
subtract: n - m,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
le: A ≤ B
Latex:
\mforall{}[L:Top List]. \mforall{}[P:Top].
(last(data-stream(P;L)) \msim{} if null(L) then \mbot{} else snd(P*(firstn(||L|| - 1;L))(last(L))) fi )
Date html generated:
2016_05_17-AM-10_21_36
Last ObjectModification:
2016_01_18-AM-00_20_25
Theory : process-model
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