Nuprl Lemma : constant-data-stream
∀[L:Top List]. ∀[b:Top]. (data-stream(constant-dataflow(b);L) ~ map(λi.b;upto(||L||)))
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
constant-dataflow: constant-dataflow(b),
upto: upto(n),
length: ||as||,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
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,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
upto: upto(n),
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bfalse: ff,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
pi2: snd(t),
pi1: fst(t),
nat_plus: ℕ+,
true: True,
uiff: uiff(P;Q),
compose: f o g,
int_seg: {i..j-},
subtract: n - m
Latex:
\mforall{}[L:Top List]. \mforall{}[b:Top]. (data-stream(constant-dataflow(b);L) \msim{} map(\mlambda{}i.b;upto(||L||)))
Date html generated:
2016_05_17-AM-10_21_48
Last ObjectModification:
2016_01_18-AM-00_19_20
Theory : process-model
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