Nuprl Lemma : hdf-parallel-halted
∀[A,B:Type].
∀[inputs:A List]. ∀[X,Y:hdataflow(A;B)].
hdf-halted(X || Y*(inputs)) = hdf-halted(X*(inputs)) ∧b hdf-halted(Y*(inputs))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
list: T List,
band: p ∧b q,
valueall-type: valueall-type(T),
bool: 𝔹,
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,
so_lambda: λ2x.t[x],
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),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
true: True,
subtype_rel: A ⊆r B,
pi1: fst(t),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Latex:
\mforall{}[A,B:Type].
\mforall{}[inputs:A List]. \mforall{}[X,Y:hdataflow(A;B)].
hdf-halted(X || Y*(inputs)) = hdf-halted(X*(inputs)) \mwedge{}\msubb{} hdf-halted(Y*(inputs))
supposing valueall-type(B)
Date html generated:
2016_05_16-AM-10_41_50
Last ObjectModification:
2016_01_17-AM-11_11_40
Theory : halting!dataflow
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