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
Lemmas :
nat_wf,
pRun_wf,
fulpRunType-subtype,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
le_wf,
nat_properties,
nequal-le-implies,
zero-add,
do-chosen-command_wf,
fulpRunType_wf,
subtract_wf,
decidable__le,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-one-mul,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
pMsg_wf,
unit_wf2,
assert-eq-id,
Id_wf,
atom2_subtype_base,
assert_wf,
eq_id_wf,
is-run-event_wf,
runEvents_wf,
pEnvType_wf,
System_wf,
strong-type-continuous_wf,
lg-is-source_wf,
pInTransit_wf,
btrue_wf,
and_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top,
it_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
list_wf,
component_wf,
ldag_wf,
lg-label_wf,
lelt_wf,
lg-size_wf,
eq_atom_wf,
com-kind_wf,
assert_of_eq_atom,
comm-msg_wf,
outl_wf,
pi2_wf,
deliver-msg_wf,
squash_wf,
neg_assert_of_eq_atom,
create-component_wf,
comm-create_wf,
lg-remove_wf_dag,
lt_int_wf,
bnot_wf,
not_wf,
less_than_wf,
assert_elim,
bool_cases,
assert_of_lt_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
member_wf,
int_upper_wf,
reverse_nil_lemma,
filter_nil_lemma,
map_nil_lemma,
list_ind_nil_lemma,
nil_wf,
list_induction,
all_wf,
Process_wf,
mapfilter_wf,
list_accum_wf,
deliver-msg-to-comp_wf,
reverse_wf,
append_wf,
Process-apply_wf,
pExt_wf,
list_accum_nil_lemma,
mapfilter_nil_lemma,
list_accum_cons_lemma,
append-nil,
map_wf,
filter_wf5,
subtype_rel_dep_function,
l_member_wf,
subtype_rel_self,
set_wf,
subtype_rel_list,
mapfilter-reverse,
reverse-reverse,
filter_cons_lemma,
map_cons_lemma,
cons_wf,
lg-append_wf_dag,
add-cause_wf,
iff_weakening_equal,
reverse-cons,
mapfilter-append,
mapfilter-singleton,
append_assoc_sq,
list_ind_cons_lemma,
append_back_nil,
true_wf,
map-map
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:
2015_07_23-AM-11_13_34
Last ObjectModification:
2015_02_04-PM-04_52_53
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