Nuprl Lemma : data-stream-cons
∀[L:Top List]. ∀[a,P:Top]. (data-stream(P;[a / L]) ~ [snd(P(a)) / data-stream(fst(P(a));L)])
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
dataflow-ap: df(a),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
data-stream: data-stream(P;L),
nat_plus: ℕ+,
all: ∀x:A. B[x],
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
select: L[n],
cons: [a / b],
compose: f o g,
nat: ℕ,
subtype_rel: A ⊆r B,
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
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),
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
lelt: i ≤ j < k,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
firstn: firstn(n;as),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[L:Top List]. \mforall{}[a,P:Top]. (data-stream(P;[a / L]) \msim{} [snd(P(a)) / data-stream(fst(P(a));L)])
Date html generated:
2016_05_17-AM-10_21_06
Last ObjectModification:
2016_01_18-AM-00_20_43
Theory : process-model
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