### Nuprl Lemma : rec-process_wf_pi

`∀[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])` uimplies: `b supposing a` subtype_rel: `A ⊆r B` 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`
Lemmas :  rec-process_wf_Process piM_wf piM-continuous ldag_wf Id_wf Com_wf subtype_rel_wf Process_wf strong-type-continuous_wf

Latex:
\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: 2015_07_23-AM-11_36_21
Last ObjectModification: 2015_01_29-AM-07_39_49

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