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 :
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),
hdf-parallel: X || Y,
hdf-compose2: X o Y,
hdataflow: hdataflow(A;B)
Lemmas :
parallel-compose2-program-eq,
Id_wf,
hdataflow_wf,
valueall-type_wf,
squash_wf,
bag_wf
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:
2015_07_22-PM-00_05_57
Last ObjectModification:
2015_01_28-AM-09_52_16
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