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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