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
Lemmas :
all_wf,
runEvents_wf,
Id_wf,
run-event-loc_wf,
not_wf,
le_wf,
run-event-step_wf,
less_than_wf,
nat_plus_wf,
nat_wf,
subtract_wf,
l_contains_wf,
Process_wf,
run-event-state-when_wf,
pRun_wf,
set_wf,
primrec-wf2,
add-zero,
l_contains_weakening,
l_contains_transitivity,
decidable__lt,
false_wf,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
equal_wf,
assert_wf,
eq_id_wf,
strong-type-continuous_wf,
ldag_wf,
pInTransit_wf,
pMsg_wf,
list_wf,
component_wf,
nil_wf,
list_ind_nil_lemma,
mapfilter_wf,
mapfilter_nil_lemma,
list_induction,
append_wf,
list_accum_wf,
System_wf,
deliver-msg-to-comp_wf,
list_accum_cons_lemma,
append_back_nil,
filter_cons_lemma,
bool_wf,
eqtt_to_assert,
assert-eq-id,
map_cons_lemma,
eq_id_self,
btrue_wf,
not_assert_elim,
and_wf,
btrue_neq_bfalse,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
cons_wf,
l_all_iff,
l_member_wf,
map_wf,
filter_wf5,
subtype_rel_dep_function,
subtype_rel_self,
member_append,
member_singleton,
or_wf,
cons_member,
append_assoc_sq,
list_ind_cons_lemma,
Process-apply_wf,
pExt_wf,
lg-append_wf_dag,
add-cause_wf,
zero-le-nat,
is-run-event_wf,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int,
int_subtype_base,
fulpRunType_wf,
unit_wf2,
pRun_wf2,
top_wf,
int_seg_wf,
int_seg_subtype-nat,
lg-is-source_wf,
lg-label_wf,
eq_atom_wf,
com-kind_wf,
assert_of_eq_atom,
comm-msg_wf,
lg-remove_wf_dag,
neg_assert_of_eq_atom,
mapfilter-contains,
comm-create_wf,
select_wf,
sq_stable__le,
select_member,
length_wf,
lt_int_wf,
lg-size_wf,
bnot_wf,
assert_elim,
bfalse_wf,
bool_cases,
assert_of_lt_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
nat_plus_properties,
trivial-int-eq1,
isect_wf,
add-mul-special,
zero-mul
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:
2015_07_23-AM-11_13_46
Last ObjectModification:
2015_01_29-AM-00_12_44
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