Nuprl Lemma : hdf-bind-gen-halted
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:B ⟶ hdataflow(A;C)]. ∀[hdfs:bag(hdataflow(A;C))].
hdf-halted(X (hdfs) >>= Y) = hdf-halted(X) ∧b bag-null(hdfs) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-bind-gen: X (hdfs) >>= Y,
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
band: p ∧b q,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
hdf-halted: hdf-halted(P),
hdf-bind-gen: X (hdfs) >>= Y,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
assert: ↑b,
false: False,
bnot: ¬bb,
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)]. \mforall{}[hdfs:bag(hdataflow(A;C))].
hdf-halted(X (hdfs) >>= Y) = hdf-halted(X) \mwedge{}\msubb{} bag-null(hdfs) supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_42_59
Last ObjectModification:
2015_12_28-PM-07_43_06
Theory : halting!dataflow
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