Nuprl Lemma : parallel-class-program-eq-hdf
∀[Info,B:Type].
∀[Xpr1,Xpr2,Ypr1,Ypr2:Id ⟶ hdataflow(Info;B)].
(Xpr1 || Ypr1 = Xpr2 || Ypr2 ∈ (Id ⟶ hdataflow(Info;B))) supposing
((Xpr1 = Xpr2 ∈ (Id ⟶ hdataflow(Info;B))) and
(Ypr1 = Ypr2 ∈ (Id ⟶ hdataflow(Info;B))))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
parallel-class-program: X || Y,
hdataflow: hdataflow(A;B),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
parallel-class-program: X || Y,
squash: ↓T,
prop: ℙ
Latex:
\mforall{}[Info,B:Type].
\mforall{}[Xpr1,Xpr2,Ypr1,Ypr2:Id {}\mrightarrow{} hdataflow(Info;B)].
(Xpr1 || Ypr1 = Xpr2 || Ypr2) supposing ((Xpr1 = Xpr2) and (Ypr1 = Ypr2))
supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_08_54
Last ObjectModification:
2016_01_17-PM-09_12_25
Theory : local!classes
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