Nuprl Lemma : firstn-data-stream
∀[n:ℕ]. ∀[L:Top List]. ∀[P:Top]. (firstn(n;data-stream(P;L)) ~ data-stream(P;firstn(n;L)))
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
firstn: firstn(n;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
data-stream: data-stream(P;L),
firstn: firstn(n;as),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
cons: [a / b],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[L:Top List]. \mforall{}[P:Top]. (firstn(n;data-stream(P;L)) \msim{} data-stream(P;firstn(n;L)))
Date html generated:
2016_05_17-AM-10_21_25
Last ObjectModification:
2016_01_18-AM-00_20_18
Theory : process-model
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