{ 
[S,M:Type 
Type].
([s0:S[Process(T.M[T])]]. [next:
T:{T:Type| Process(T.M[T]) 
r T}
(S[M[T] (T 
LabeledDAG(Id
(Com(T.M[T]) T)))]
M[T]
(S[T] LabeledDAG(Id (Com(T.M[T])
T))))].
(RecProcess(s0;s,m.next[s;m]) 
Process(T.M[T]))) supposing
(Continuous+(T.M[T]) and
Continuous+(T.S[T])) }
{ Proof }
Definitions occuring in Statement :
Process: Process(P.M[P]),
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],
member: t T,
so_lambda: 
x.t[x],
Com: Com(P.M[P]),
tagged+: T |+ z:B,
Process: Process(P.M[P]),
prop: 
Lemmas :
rec-process_wf,
ldag_wf,
Id_wf,
Com_wf,
Process_wf,
strong-type-continuous_wf,
continuous-ldag,
isect2_wf,
tag-case_wf,
unit_wf,
strong-continuous-product,
continuous-constant,
strong-continuous-isect2,
strong-continuous-tag-case,
continuous-id
\mforall{}[S,M:Type {}\mrightarrow{} Type].
(\mforall{}[s0:S[Process(T.M[T])]]. \mforall{}[next:\mcap{}T:\{T:Type| Process(T.M[T]) \msubseteq{}r T\}
(S[M[T] {}\mrightarrow{} (T \mtimes{} LabeledDAG(Id \mtimes{} (Com(T.M[T]) T)))]
{}\mrightarrow{} M[T]
{}\mrightarrow{} (S[T] \mtimes{} LabeledDAG(Id \mtimes{} (Com(T.M[T]) T))))].
(RecProcess(s0;s,m.next[s;m]) \mmember{} Process(T.M[T]))) supposing
(Continuous+(T.M[T]) and
Continuous+(T.S[T]))
Date html generated:
2011_08_16-PM-06_49_09
Last ObjectModification:
2011_06_18-AM-11_03_30
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