Nuprl Lemma : pRun-invariant3
∀[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-event-state-when(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-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-when: run-event-state-when(r;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)
, 
le: A ≤ B
, 
less_than: a < b
, 
squash: ↓T
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
or: P ∨ Q
, 
nat_plus: ℕ+
, 
nat: ℕ
, 
run-event-step: run-event-step(e)
, 
pi1: fst(t)
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
true: True
, 
cand: A c∧ B
, 
Id: Id
, 
sq_type: SQType(T)
, 
decidable: Dec(P)
, 
label: ...$L... t
, 
iterate-Process: iterate-Process(P;msgs)
, 
dataflow-ap: df(a)
, 
Process-apply: Process-apply(P;m)
, 
l_contains: 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-event-state-when(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_49_00
Last ObjectModification:
2016_01_18-AM-00_21_31
Theory : process-model
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