Nuprl Lemma : hdf-parallel-halt-right
∀[A,B:Type]. ∀[X:hdataflow(A;B)]. X || hdf-halt() = X ∈ hdataflow(A;B) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
hdf-halt: hdf-halt(),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
hdf-parallel: X || Y,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-ap: X(a),
hdf-halt: hdf-halt(),
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
pi2: snd(t),
evalall: evalall(t),
bag-append: as + bs,
append: as @ bs,
list_ind: list_ind,
empty-bag: {},
nil: [],
not: ¬A,
true: True,
pi1: fst(t)
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:hdataflow(A;B)]. X || hdf-halt() = X supposing valueall-type(B)
Date html generated:
2016_05_16-AM-10_41_40
Last ObjectModification:
2015_12_28-PM-07_45_59
Theory : halting!dataflow
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