Nuprl Lemma : rec-process_wf_pi_simple_state
∀[S:Type]. ∀[s0:S]. ∀[next:⋂T:{T:Type| pi-process() ⊆r T} . (S ⟶ piM(T) ⟶ (S × LabeledDAG(Id × (Com(T.piM(T)) T))))].
(RecProcess(s0;s,m.next[s;m]) ∈ pi-process())
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,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
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 unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B
Latex:
\mforall{}[S:Type]. \mforall{}[s0:S]. \mforall{}[next:\mcap{}T:\{T:Type| pi-process() \msubseteq{}r T\}
(S {}\mrightarrow{} piM(T) {}\mrightarrow{} (S \mtimes{} LabeledDAG(Id \mtimes{} (Com(T.piM(T)) T))))].
(RecProcess(s0;s,m.next[s;m]) \mmember{} pi-process())
Date html generated:
2016_05_17-AM-11_30_36
Last ObjectModification:
2015_12_29-PM-06_50_23
Theory : event-logic-applications
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