Nuprl Lemma : local-simulation-event-loc
∀[f:Name ─→ Type]. ∀[Info:Type]. ∀[es:EO+(Message(f))]. ∀[hdr:Name]. ∀[locs:bag(Id)].
∀[e:E]
loc(local-simulation-event(es;e;hdr;locs)) = (fst(msg-body(info(e)))) ∈ Id
supposing ↑has-header-and-in-locs(info(e);hdr;locs)
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),
encodes-msg-type: hdr encodes T,
msg-body: msg-body(msg),
Message: Message(f),
es-info: info(e),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
global-eo-loc,
map_append_sq,
filter_append_sq,
filter_wf5,
map_wf,
es-info_wf,
es-before_wf,
l_member_wf,
has-header-and-in-locs_wf,
list_wf,
map_cons_lemma,
map_nil_lemma,
filter_cons_lemma,
filter_nil_lemma,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
assert_elim,
bfalse_wf,
and_wf,
equal_wf,
bnot_wf,
btrue_neq_bfalse,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert_wf,
Message_wf,
subtype_rel_product,
Id_wf,
top_wf,
subtype_rel_transitivity,
es-E_wf,
event-ordering+_subtype,
encodes-msg-type_wf,
bag_wf,
name_wf,
event-ordering+_wf,
cons_wf,
msg-type_wf,
msg-body_wf,
nil_wf,
subtype_rel_list,
length_wf_nat,
lt_int_wf,
length_wf,
assert_of_lt_int,
less_than_irreflexivity,
assert-bnot,
less_than_wf,
select-append,
length-map,
int_subtype_base,
minus-one-mul,
add-mul-special,
zero-mul,
assert-has-header-and-in-locs,
pi1_wf_top,
msg-body_wf2,
list_subtype_base,
atom_subtype_base
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[Info:Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[hdr:Name]. \mforall{}[locs:bag(Id)].
\mforall{}[e:E]
loc(local-simulation-event(es;e;hdr;locs)) = (fst(msg-body(info(e))))
supposing \muparrow{}has-header-and-in-locs(info(e);hdr;locs)
supposing hdr encodes Id \mtimes{} Info
Date html generated:
2015_07_21-PM-04_50_33
Last ObjectModification:
2015_01_28-AM-08_47_15
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