Nuprl Lemma : pRun-invariant2
∀[M:Type ⟶ Type]
∀n2m:ℕ ⟶ pMsg(P.M[P]). ∀l2m:Id ⟶ pMsg(P.M[P]). ∀S0:System(P.M[P]). ∀env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
∀e1,e2:runEvents(r).
(∀P:Process(P.M[P])
((P ∈ run-prior-state(S0;r;e1))
⇒ (iterate-Process(P;map(λe.run-event-msg(r;e);run-event-interval(r;e1;e2)))
∈ run-event-state(r;e2)))) supposing
((run-event-step(e1) ≤ run-event-step(e2)) and
(run-event-loc(e1) = run-event-loc(e2) ∈ Id))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
run-prior-state: run-prior-state(S0;r;e),
run-event-interval: run-event-interval(r;e1;e2),
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
run-event-state: run-event-state(r;e),
run-event-msg: run-event-msg(r;e),
runEvents: runEvents(r),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
iterate-Process: iterate-Process(P;msgs),
pMsg: pMsg(P.M[P]),
Process: Process(P.M[P]),
Id: Id,
l_member: (x ∈ l),
map: map(f;as),
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
let: let,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
let: let,
prop: ℙ,
top: Top,
runEvents: runEvents(r),
nat: ℕ,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
l_contains: A ⊆ B,
iff: P ⇐⇒ Q,
or: P ∨ Q,
Id: Id,
sq_type: SQType(T),
iterate-Process: iterate-Process(P;msgs),
dataflow-ap: df(a),
Process-apply: Process-apply(P;m),
cand: A c∧ B,
squash: ↓T,
true: True,
rev_implies: P ⇐ Q,
decidable: Dec(P),
less_than: a < b,
le: A ≤ B,
less_than': less_than'(a;b)
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}S0:System(P.M[P]). \mforall{}env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
\mforall{}e1,e2:runEvents(r).
(\mforall{}P:Process(P.M[P])
((P \mmember{} run-prior-state(S0;r;e1))
{}\mRightarrow{} (iterate-Process(P;map(\mlambda{}e.run-event-msg(r;e);run-event-interval(r;e1;e2)))
\mmember{} run-event-state(r;e2)))) supposing
((run-event-step(e1) \mleq{} run-event-step(e2)) and
(run-event-loc(e1) = run-event-loc(e2)))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_48_36
Last ObjectModification:
2016_01_18-AM-00_13_58
Theory : process-model
Home
Index