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
Lemmas :
l_member_wf,
Process_wf,
run-event-state-when_wf,
less_than_transitivity1,
run-event-step_wf,
less_than_transitivity2,
le_weakening2,
less_than_irreflexivity,
less_than_wf,
le_wf,
equal_wf,
Id_wf,
run-event-loc_wf,
runEvents_wf,
run-event-interval-cases,
all_wf,
nat_wf,
subtract_wf,
iterate-Process_wf,
map_wf,
pMsg_wf,
run-event-msg_wf,
run-event-interval_wf,
run-event-state_wf,
set_wf,
primrec-wf2,
squash_wf,
true_wf,
pRunType_wf,
fulpRunType-subtype,
iff_weakening_equal,
fulpRunType_wf,
run-event-state-next2,
Process-apply_wf,
subtype_rel_weakening,
ext-eq_weakening,
pExt_wf,
exists_wf,
member_map,
member-reverse,
subtype_base_sq,
set_subtype_base,
assert_wf,
is-run-event_wf,
product_subtype_base,
int_subtype_base,
atom2_subtype_base,
le_weakening,
member-run-event-interval,
list_wf,
list_subtype_base,
member_singleton,
map_cons_lemma,
map_nil_lemma,
iter_df_cons_lemma,
iter_df_nil_lemma,
subtype_rel_wf,
sub-mset-contains,
l_all_iff,
map_append_sq,
iterate-dataflow-append,
subtype_rel_list,
top_wf,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
less-iff-le,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
run-event-step-positive,
add-mul-special,
zero-mul,
add-zero
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:
2015_07_23-AM-11_14_48
Last ObjectModification:
2015_02_04-PM-04_50_43
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