Nuprl Lemma : pi-guarded-trans_wf
∀[compList:(pi_prefix() × pi_term()) List]. ∀[g:{Q:pi_term()| (∃C∈compList. pi-rank(Q) ≤ pi-rank(snd(C)))}
⟶ Id
⟶ Name
⟶ (Name List)
⟶ pi-process()].
(pi-guarded-trans(compList;g) ∈ Id ⟶ Name ⟶ (Name List) ⟶ pi-process())
Proof
Definitions occuring in Statement :
pi-guarded-trans: pi-guarded-trans(compList;g),
pi-process: pi-process(),
pi-rank: pi-rank(p),
pi_term: pi_term(),
pi_prefix: pi_prefix(),
Id: Id,
name: Name,
l_exists: (∃x∈L. P[x]),
list: T List,
uall: ∀[x:A]. B[x],
pi2: snd(t),
le: A ≤ B,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ,
pi-guarded-trans: pi-guarded-trans(compList;g),
pi-process: pi-process(),
Process: Process(P.M[P]),
process: process(P.M[P];P.E[P]),
uimplies: b supposing a,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
piM: piM(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
sq_stable: SqStable(P),
squash: ↓T,
PiDataVal: PiDataVal(),
pMsg: pMsg(P.M[P]),
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[compList:(pi\_prefix() \mtimes{} pi\_term()) List]. \mforall{}[g:\{Q:pi\_term()|
(\mexists{}C\mmember{}compList. pi-rank(Q) \mleq{} pi-rank(snd(C)))\}
{}\mrightarrow{} Id
{}\mrightarrow{} Name
{}\mrightarrow{} (Name List)
{}\mrightarrow{} pi-process()].
(pi-guarded-trans(compList;g) \mmember{} Id {}\mrightarrow{} Name {}\mrightarrow{} (Name List) {}\mrightarrow{} pi-process())
Date html generated:
2016_05_17-AM-11_35_03
Last ObjectModification:
2016_01_18-AM-07_46_33
Theory : event-logic-applications
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