{ 
[S:Type 
Type]
[s0:S[pi-process()]]. [next:
T:{T:Type| pi-process() 
r T}
(S[piM(T) (T 
LabeledDAG(Id
(Com(T.piM(T)) T)))]
piM(T)
(S[T] LabeledDAG(Id
(Com(T.piM(T)) T))))].
(RecProcess(s0;s,m.next[s;m]) 
pi-process())
supposing Continuous+(T.S[T]) }
{ Proof }
Definitions occuring in Statement :
pi-process: pi-process(),
piM: piM(T),
Com: Com(P.M[P]),
ldag: LabeledDAG(T),
rec-process: RecProcess(s0;s,m.next[s; m]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
subtype_rel: A r B,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
apply: f a,
isect: x:A. B[x],
function: x:A B[x],
product: x:A B[x],
universe: Type
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s],
pi-process: pi-process(),
member: t T,
so_apply: x[s1;s2],
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
all: x:A. B[x],
implies: P 
Q,
piM: piM(T),
prop: 
Lemmas :
rec-process_wf_Process,
piM_wf,
ldag_wf,
Id_wf,
Com_wf,
Process_wf,
strong-type-continuous_wf,
continuous-constant,
PiDataVal_wf
\mforall{}[S:Type {}\mrightarrow{} Type]
\mforall{}[s0:S[pi-process()]]. \mforall{}[next:\mcap{}T:\{T:Type| pi-process() \msubseteq{}r T\}
(S[piM(T) {}\mrightarrow{} (T \mtimes{} LabeledDAG(Id \mtimes{} (Com(T.piM(T)) T)))]
{}\mrightarrow{} piM(T)
{}\mrightarrow{} (S[T] \mtimes{} LabeledDAG(Id \mtimes{} (Com(T.piM(T)) T))))].
(RecProcess(s0;s,m.next[s;m]) \mmember{} pi-process())
supposing Continuous+(T.S[T])
Date html generated:
2011_08_17-PM-06_57_57
Last ObjectModification:
2011_06_18-PM-12_36_39
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