Nuprl Lemma : rec-process_wf_Process
∀[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]),
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,
ldag_wf,
Id_wf,
Com_wf,
continuous-ldag,
strong-continuous-product,
continuous-constant,
subtype_rel_wf,
Process_wf,
strong-type-continuous_wf,
strong-continuous-isect2,
isect2_wf,
tag-case_wf,
unit_wf2,
strong-continuous-tag-case,
continuous-id
Latex:
\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:
2015_07_23-AM-11_07_14
Last ObjectModification:
2015_01_29-AM-00_10_14
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