Nuprl Lemma : parallel-class-program-eq
∀[Info,B:Type].
∀[X,Y:EClass(B)]. ∀[Xpr1,Xpr2:LocalClass(X)]. ∀[Ypr1,Ypr2:LocalClass(Y)].
(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,
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
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,
hdataflow: hdataflow(A;B)
Lemmas :
parallel-class-program_wf,
bag_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
event-ordering+_subtype,
map_wf,
es-E_wf,
es-info_wf,
es-before_wf,
hdataflow_wf,
iff_weakening_equal,
all_wf,
equal_wf,
class-ap_wf,
local-class_wf,
parallel-class_wf,
Id_wf,
valueall-type_wf,
and_wf,
pi2_wf
Latex:
\mforall{}[Info,B:Type].
\mforall{}[X,Y:EClass(B)]. \mforall{}[Xpr1,Xpr2:LocalClass(X)]. \mforall{}[Ypr1,Ypr2:LocalClass(Y)].
(Xpr1 || Ypr1 = Xpr2 || Ypr2) supposing ((Xpr1 = Xpr2) and (Ypr1 = Ypr2))
supposing valueall-type(B)
Date html generated:
2015_07_22-PM-00_03_55
Last ObjectModification:
2015_02_04-PM-05_09_47
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