Nuprl Lemma : hdf-halted-compose2
∀[A,B,C:Type]. ∀[X1:hdataflow(A;B ⟶ bag(C))]. ∀[X2:hdataflow(A;B)].
uiff(↑hdf-halted(X1 o X2);↑(hdf-halted(X1) ∨bhdf-halted(X2))) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-compose2: X o Y,
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
bor: p ∨bq,
valueall-type: valueall-type(T),
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
all: ∀x:A. B[x],
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q,
prop: ℙ,
hdf-compose2: X o Y,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-halted: hdf-halted(P),
or: P ∨ Q,
hdf-run: hdf-run(P),
isr: isr(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
sq_type: SQType(T),
guard: {T},
btrue: tt,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
bor: p ∨bq,
true: True,
exists: ∃x:A. B[x],
bnot: ¬bb,
top: Top
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X1:hdataflow(A;B {}\mrightarrow{} bag(C))]. \mforall{}[X2:hdataflow(A;B)].
uiff(\muparrow{}hdf-halted(X1 o X2);\muparrow{}(hdf-halted(X1) \mvee{}\msubb{}hdf-halted(X2))) supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_39_46
Last ObjectModification:
2015_12_28-PM-07_44_38
Theory : halting!dataflow
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