Nuprl Lemma : hdf-parallel-bag-iterate
∀[A,B:Type]. ∀[Xs:bag(hdataflow(A;B))]. ∀[inputs:A List].
  hdf-parallel-bag(Xs)*(inputs) = hdf-parallel-bag(bag-map(λx.x*(inputs);Xs)) ∈ hdataflow(A;B) 
  supposing valueall-type(B)
Proof
Definitions occuring in Statement : 
hdf-parallel-bag: hdf-parallel-bag(Xs)
, 
iterate-hdataflow: P*(inputs)
, 
hdataflow: hdataflow(A;B)
, 
list: T List
, 
valueall-type: valueall-type(T)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
lambda: λx.A[x]
, 
universe: Type
, 
equal: s = t ∈ T
, 
bag-map: bag-map(f;bs)
, 
bag: bag(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
, 
squash: ↓T
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
hdf-parallel-bag: hdf-parallel-bag(Xs)
, 
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
ifthenelse: if b then t else f fi 
, 
pi1: fst(t)
, 
subtype_rel: A ⊆r B
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
compose: f o g
, 
true: True
, 
has-value: (a)↓
, 
callbyvalueall: callbyvalueall, 
has-valueall: has-valueall(a)
Latex:
\mforall{}[A,B:Type].  \mforall{}[Xs:bag(hdataflow(A;B))].  \mforall{}[inputs:A  List].
    hdf-parallel-bag(Xs)*(inputs)  =  hdf-parallel-bag(bag-map(\mlambda{}x.x*(inputs);Xs)) 
    supposing  valueall-type(B)
Date html generated:
2016_05_16-AM-10_41_58
Last ObjectModification:
2016_01_17-AM-11_12_07
Theory : halting!dataflow
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