Nuprl Lemma : adjacent-run-states
∀[M:Type ⟶ Type]
  ∀n2m:ℕ ⟶ pMsg(P.M[P]). ∀l2m:Id ⟶ pMsg(P.M[P]). ∀S:System(P.M[P]). ∀env:pEnvType(P.M[P]). ∀x:Id. ∀n,m:ℕ+.
    (run-event-state-when(pRun(S;env;n2m;l2m);<n, x>) ⊆ run-event-state-when(pRun(S;env;n2m;l2m);<m, x>)) supposing 
       ((∀a:runEvents(pRun(S;env;n2m;l2m))
           ¬((n ≤ run-event-step(a)) ∧ run-event-step(a) < m) supposing run-event-loc(a) = x ∈ Id) and 
       (n ≤ m)) 
  supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement : 
run-event-step: run-event-step(e)
, 
run-event-loc: run-event-loc(e)
, 
run-event-state-when: run-event-state-when(r;e)
, 
runEvents: runEvents(r)
, 
pRun: pRun(S0;env;nat2msg;loc2msg)
, 
pEnvType: pEnvType(T.M[T])
, 
System: System(P.M[P])
, 
pMsg: pMsg(P.M[P])
, 
Process: Process(P.M[P])
, 
Id: Id
, 
l_contains: A ⊆ B
, 
strong-type-continuous: Continuous+(T.F[T])
, 
nat_plus: ℕ+
, 
nat: ℕ
, 
less_than: a < b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
le: A ≤ B
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
and: P ∧ Q
, 
function: x:A ⟶ B[x]
, 
pair: <a, b>
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
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]
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
nat_plus: ℕ+
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
, 
nat: ℕ
, 
ge: i ≥ j 
, 
cand: A c∧ B
, 
le: A ≤ B
, 
component: component(P.M[P])
, 
pi1: fst(t)
, 
deliver-msg: deliver-msg(t;m;x;Cs;L)
, 
append: as @ bs
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
so_apply: x[s1;s2;s3]
, 
pi2: snd(t)
, 
System: System(P.M[P])
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
list_accum: list_accum, 
nil: []
, 
it: ⋅
, 
mapfilter: mapfilter(f;P;L)
, 
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C)
, 
bool: 𝔹
, 
unit: Unit
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
l_contains: A ⊆ B
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
run-event-state-when: run-event-state-when(r;e)
, 
pRun: pRun(S0;env;nat2msg;loc2msg)
, 
ycomb: Y
, 
runEvents: runEvents(r)
, 
run-event-loc: run-event-loc(e)
, 
run-event-step: run-event-step(e)
, 
is-run-event: is-run-event(r;t;x)
, 
exposed-bfalse: exposed-bfalse
, 
spreadn: spread3, 
isl: isl(x)
, 
outl: outl(x)
, 
band: p ∧b q
, 
nequal: a ≠ b ∈ T 
, 
fulpRunType: fulpRunType(T.M[T])
, 
pEnvType: pEnvType(T.M[T])
, 
pRunType: pRunType(T.M[T])
, 
less_than': less_than'(a;b)
, 
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm)
, 
ldag: LabeledDAG(T)
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
lg-is-source: lg-is-source(g;i)
, 
pInTransit: pInTransit(P.M[P])
, 
let: let, 
create-component: create-component(t;P;x;Cs;L)
, 
subtract: n - m
Latex:
\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}n2m:\mBbbN{}  {}\mrightarrow{}  pMsg(P.M[P]).  \mforall{}l2m:Id  {}\mrightarrow{}  pMsg(P.M[P]).  \mforall{}S:System(P.M[P]).  \mforall{}env:pEnvType(P.M[P]).  \mforall{}x:Id.
    \mforall{}n,m:\mBbbN{}\msupplus{}.
        (run-event-state-when(pRun(S;env;n2m;l2m);<n,  x>)  \msubseteq{}  run-event-state-when(pRun(S;env;n2m;l2m);<m,\000C  x>))  supposing 
              ((\mforall{}a:runEvents(pRun(S;env;n2m;l2m))
                      \mneg{}((n  \mleq{}  run-event-step(a))  \mwedge{}  run-event-step(a)  <  m)  supposing  run-event-loc(a)  =  x)  and 
              (n  \mleq{}  m)) 
    supposing  Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_47_07
Last ObjectModification:
2016_01_18-AM-00_22_11
Theory : process-model
Home
Index