Nuprl Lemma : local-simulation-msg-constraint
∀[f,g:Name ─→ Type]. ∀[X:EClass(Interface)].
∀[es:EO+(Message(f))]. ∀[hdr:Name]. ∀[locs:bag(Id)].
∀[hdrs:Name List]. ∀[i:Id].
(local-simulation-input-validity(g;X;hdr;locs;hdrs;es;i)
⇒ (∀e:E. ((loc(e) = i ∈ Id) ⇒ eo-msg-interface-constraint(local-simulation-eo(es;e;hdr;locs);X;hdrs;g))))
supposing hdr encodes Id × Message(g)
supposing LocalClass(X)
Proof
Definitions occuring in Statement :
local-simulation-input-validity: local-simulation-input-validity(g;X;hdr;locs;hdrs;es;i),
eo-msg-interface-constraint: eo-msg-interface-constraint(es;X;hdrs;f),
msg-interface: Interface,
local-simulation-eo: local-simulation-eo(es;e;hdr;locs),
encodes-msg-type: hdr encodes T,
Message: Message(f),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
es-le-before_wf2,
event-ordering+_subtype,
Message_wf,
list_wf,
es-E_wf,
es-le_wf,
filter_type,
has-header-and-in-locs_wf,
es-info_wf,
subtype_rel_product,
Id_wf,
top_wf,
subtype_top,
subtype_rel_transitivity,
assert_wf,
select_wf,
sq_stable__le,
set_wf,
decidable__es-le,
sq_stable__assert,
equal_wf,
int_seg_wf,
length_wf,
filter_wf5,
subtype_rel_list,
l_member_wf,
es-le-loc,
global-eo-info,
select-map,
map_wf,
es-loc_wf,
es-le-before_wf,
lelt_wf,
filter-map,
compose_wf,
bool_wf,
length-map,
assert-has-header-and-in-locs,
es-info-body_wf,
subtype_rel_wf,
squash_wf,
true_wf,
iff_weakening_equal,
local-simulation-classrel,
msg-interface_wf,
es-locl_transitivity2,
local-simulation-E-subtype,
es-le_weakening,
local-simulation-eo_wf,
local-simulation-event_wf,
es-causl_wf,
classrel_wf,
make-msg-interface_wf,
exists_wf,
global-eo-causl,
mapfilter_wf,
map-length,
iseg-es-le-before,
es-locl_wf,
subtype_rel_dep_function,
subtype_rel_self,
less_than_wf,
filter_append_sq,
select-append,
int_seg_subtype-nat,
false_wf,
lt_int_wf,
bnot_wf,
not_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
select_member,
member_filter,
member-es-le-before,
es-locl_irreflexivity,
filter_cons_lemma,
filter_nil_lemma,
es-before_wf,
length_nil,
non_neg_length,
nil_wf,
length_wf_nil,
length_cons,
cons_wf,
length_wf_nat,
append_wf,
length_append,
global-eo-loc,
embedding-preserves-local-class,
local-simulation-embedding
Latex:
\mforall{}[f,g:Name {}\mrightarrow{} Type]. \mforall{}[X:EClass(Interface)].
\mforall{}[es:EO+(Message(f))]. \mforall{}[hdr:Name]. \mforall{}[locs:bag(Id)].
\mforall{}[hdrs:Name List]. \mforall{}[i:Id].
(local-simulation-input-validity(g;X;hdr;locs;hdrs;es;i)
{}\mRightarrow{} (\mforall{}e:E
((loc(e) = i)
{}\mRightarrow{} eo-msg-interface-constraint(local-simulation-eo(es;e;hdr;locs);X;hdrs;g))))
supposing hdr encodes Id \mtimes{} Message(g)
supposing LocalClass(X)
Date html generated:
2015_07_22-PM-00_07_03
Last ObjectModification:
2015_02_04-PM-04_46_45
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