Nuprl Lemma : hdf-parallel-compose-eq
∀[A,B,C:Type]. ∀[X1,X2:hdataflow(A;B ⟶ bag(C))]. ∀[X:hdataflow(A;B)].
(X1 o X || X2 o X = (X1 || X2 o X) ∈ hdataflow(A;C)) supposing (valueall-type(C) and valueall-type(B) and (↓B))
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
hdf-compose2: X o Y,
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
squash: ↓T,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
parallel-class-program: X || Y,
eclass2-program: Xpr o Ypr,
mkid: "$x",
Id: Id,
prop: ℙ
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[X1,X2:hdataflow(A;B {}\mrightarrow{} bag(C))]. \mforall{}[X:hdataflow(A;B)].
(X1 o X || X2 o X = (X1 || X2 o X)) supposing (valueall-type(C) and valueall-type(B) and (\mdownarrow{}B))
Date html generated:
2016_05_17-AM-09_12_22
Last ObjectModification:
2016_01_17-PM-09_11_51
Theory : local!classes
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