Nuprl Lemma : local-simulation-classrel
∀[f:Name ─→ Type]. ∀[Info,T:Type]. ∀[X:EClass(T)].
∀locs:bag(Id). ∀hdr:Name.
∀es:EO+(Message(f)). ∀e:E.
∀[v:T]
uiff(v ∈ local-simulation-class(X;locs;hdr)(e);(↑has-header-and-in-locs(info(e);hdr;locs))
∧ v ∈ X(local-simulation-event(es;e;hdr;locs)))
supposing LocalClass(X)
supposing hdr encodes Id × Info
Proof
Definitions occuring in Statement :
local-simulation-event: local-simulation-event(es;e;hdr;locs),
local-simulation-eo: local-simulation-eo(es;e;hdr;locs),
has-header-and-in-locs: has-header-and-in-locs(msg;hdr;locs),
local-simulation-class: local-simulation-class(X;locs;hdr),
encodes-msg-type: hdr encodes T,
Message: Message(f),
local-class: LocalClass(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
es-info: info(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
name: Name,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
bag: bag(T)
Lemmas :
local-simulation-eo_wf,
local-simulation-event_wf,
es-E_wf,
event-ordering+_subtype,
iff_weakening_uiff,
classrel_wf,
Message_wf,
parallel-bag-class_wf,
Id_wf,
base-process-class_wf,
squash_wf,
exists_wf,
bag-member_wf,
parallel-bag-classrel,
true_wf,
uiff_wf,
assert-has-header-and-in-locs,
es-info_wf,
subtype_rel_product,
top_wf,
subtype_rel_transitivity,
test-msg-header-and-loc_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
bag_wf,
atom2_subtype_base,
equal_wf,
es-loc_wf,
assert-test-msg-header-and-loc,
local-simulation-event-loc,
iff_weakening_equal,
msg-body_wf2,
subtype_rel-equal,
msg-type_wf,
base-process-inputs_wf,
base-process-inputs-non-null,
local-class-output-agree2,
list-eo_wf,
assert_of_lt_int,
length_wf,
assert_wf,
lt_int_wf,
list-eo-E,
subtype_rel_list,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtract-is-less,
lelt_wf,
list-eo-loc,
list-eo-info-le-before,
global-eo-info-le-before,
local-simulation-inputs_wf,
set_wf,
map_cons_lemma,
map_nil_lemma,
filter_cons_lemma,
filter_nil_lemma,
has-header-and-in-locs_wf,
bool_cases_sqequal,
assert-bnot,
map_append_sq,
filter_append_sq,
map_wf,
es-before_wf,
list_wf,
firstn_all,
length-append,
length-map,
length_of_cons_lemma,
length_of_nil_lemma,
le_weakening,
filter_wf5,
append_wf,
l_member_wf,
nil_wf,
add-mul-special,
zero-mul,
le-add-cancel2,
cons_wf,
filter-map,
filter-filter,
map-map,
filter-sq,
eq_id_wf,
bfalse_wf,
assert-eq-id,
filter_type,
bag-member-empty-iff,
local-simulation-eo-loc
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)].
\mforall{}locs:bag(Id). \mforall{}hdr:Name.
\mforall{}es:EO+(Message(f)). \mforall{}e:E.
\mforall{}[v:T]
uiff(v \mmember{} local-simulation-class(X;locs;hdr)(e);(\muparrow{}has-header-and-in-locs(info(e);hdr;locs))
\mwedge{} v \mmember{} X(local-simulation-event(es;e;hdr;locs)))
supposing LocalClass(X)
supposing hdr encodes Id \mtimes{} Info
Date html generated:
2015_07_22-PM-00_06_50
Last ObjectModification:
2015_02_04-PM-04_50_23
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