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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