Nuprl Lemma : run-event-state-next2
∀[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
∀e:runEvents(r)
(run-event-state(r;e)
= rev(map(λP.(fst(Process-apply(P;run-event-msg(r;e))));run-event-state-when(r;e)))
∈ (Process(P.M[P]) List))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
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]),
Process-apply: Process-apply(P;m),
pMsg: pMsg(P.M[P]),
Process: Process(P.M[P]),
Id: Id,
reverse: rev(as),
map: map(f;as),
list: T List,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
let: let,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
all: ∀x:A. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
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],
let: let,
runEvents: runEvents(r),
pi1: fst(t),
pi2: snd(t),
implies: P ⇒ Q,
run-event-state: run-event-state(r;e),
run-event-msg: run-event-msg(r;e),
is-run-event: is-run-event(r;t;x),
run-info: run-info(r;e),
pRun: pRun(S0;env;nat2msg;loc2msg),
ycomb: Y,
nat: ℕ,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
spreadn: spread3,
isl: isl(x),
outl: outl(x),
bfalse: ff,
band: p ∧b q,
assert: ↑b,
false: False,
prop: ℙ,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
ge: i ≥ j ,
int_upper: {i...},
fulpRunType: fulpRunType(T.M[T]),
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
System: System(P.M[P]),
run-event-state-when: run-event-state-when(r;e),
Id: Id,
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]),
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
component: component(P.M[P]),
mapfilter: mapfilter(f;P;L),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
deliver-msg: deliver-msg(t;m;x;Cs;L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
compose: f o g
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{}e:runEvents(r)
(run-event-state(r;e)
= rev(map(\mlambda{}P.(fst(Process-apply(P;run-event-msg(r;e))));run-event-state-when(r;e))))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_46_46
Last ObjectModification:
2016_01_18-AM-00_23_30
Theory : process-model
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