Nuprl Lemma : run-prior-state_wf
∀[M:Type ⟶ Type]. ∀[S0:System(P.M[P])]. ∀[r:fulpRunType(P.M[P])]. ∀[e:ℕ × Id].
(run-prior-state(S0;r;e) ∈ Process(P.M[P]) List)
Proof
Definitions occuring in Statement :
run-prior-state: run-prior-state(S0;r;e),
fulpRunType: fulpRunType(T.M[T]),
System: System(P.M[P]),
Process: Process(P.M[P]),
Id: Id,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
run-prior-state: run-prior-state(S0;r;e),
run-event-local-pred: run-event-local-pred(r;e),
run-event-history: run-event-history(r;e),
run-event-loc: run-event-loc(e),
run-event-state: run-event-state(r;e),
run-event-step: run-event-step(e),
let: let,
pi2: snd(t),
pi1: fst(t),
and: P ∧ Q,
prop: ℙ,
nat: ℕ,
all: ∀x:A. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
cand: A c∧ B,
component: component(P.M[P]),
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
System: System(P.M[P]),
bfalse: ff,
top: Top,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
fulpRunType: fulpRunType(T.M[T]),
spreadn: spread3
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[S0:System(P.M[P])]. \mforall{}[r:fulpRunType(P.M[P])]. \mforall{}[e:\mBbbN{} \mtimes{} Id].
(run-prior-state(S0;r;e) \mmember{} Process(P.M[P]) List)
Date html generated:
2016_05_17-AM-10_44_19
Last ObjectModification:
2015_12_29-PM-05_23_09
Theory : process-model
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