Nuprl Lemma : local-simulation-validity2
∀correct:Id ─→ ℙ. ∀g,f:Name ─→ Type. ∀X:EClass(Interface).
(LocalClass(X)
⇒ (∀locs:bag(Id). ∀hdr:Name.
∀hdrs:Name List. ∀es:EO+(Message(f)).
((∀i:Id. ((correct i) ⇒ local-simulation-input-validity(g;X;hdr;locs;hdrs;es;i)))
⇒ (∀R:Interface ─→ Message(g) ─→ ℙ. ∀R':Interface ─→ Message(f) ─→ ℙ.
((∀eo:EO+(Message(g))
(eo-msg-interface-constraint(eo;X;hdrs;g)
⇒ for every v in X there is an
earlier event with info=m such that
R[v;m]))
⇒ (∀e:E. ∀v:Interface.
((correct loc(e))
⇒ (↑has-header-and-in-locs(info(e);hdr;locs))
⇒ R[v;snd(msg-body(info(e)))]
⇒ (↓∃e':E. ((e' < e) ∧ R'[v;info(e')]))))
⇒ for every v in local-simulation-class(X;locs;hdr) at location i s.t. correct i
there is an earlier event with info=m such that R'[v;m])))
supposing hdr encodes Id × Message(g)))
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,
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,
msg-body: msg-body(msg),
Message: Message(f),
local-class: LocalClass(X),
correct-causal-class-relation: for every a in X at location i s.t. Correct[i] there is an earlier event with info=b such that R[a; b],
causal-class-relation: causal-class-relation,
eclass: EClass(A[eo; e]),
es-info: info(e),
event-ordering+: EO+(Info),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
list: T List,
assert: ↑b,
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s1;s2],
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
bag: bag(T)
Lemmas :
local-simulation-validity,
true_wf,
msg-interface_wf,
classrel_wf,
Message_wf,
es-E_wf,
event-ordering+_subtype,
eo-msg-interface-constraint_wf,
event-ordering+_wf,
all_wf,
es-loc_wf,
assert_wf,
has-header-and-in-locs_wf,
es-info_wf,
subtype_rel_product,
Id_wf,
top_wf,
subtype_top,
subtype_rel_transitivity,
assert-has-header-and-in-locs,
msg-body_wf2,
subtype_rel-equal,
msg-type_wf,
iff_weakening_equal,
squash_wf,
exists_wf,
es-causl_wf,
causal-class-relation_wf,
subtype_rel_dep_function,
name_wf,
local-simulation-input-validity_wf,
list_wf,
encodes-msg-type_wf,
bag_wf,
local-class_wf,
eclass_wf3,
local-simulation-class_wf,
and_wf,
equal_wf,
es-causl_transitivity2,
es-causle_weakening_locl,
es-le_weakening
Latex:
\mforall{}correct:Id {}\mrightarrow{} \mBbbP{}. \mforall{}g,f:Name {}\mrightarrow{} Type. \mforall{}X:EClass(Interface).
(LocalClass(X)
{}\mRightarrow{} (\mforall{}locs:bag(Id). \mforall{}hdr:Name.
\mforall{}hdrs:Name List. \mforall{}es:EO+(Message(f)).
((\mforall{}i:Id. ((correct i) {}\mRightarrow{} local-simulation-input-validity(g;X;hdr;locs;hdrs;es;i)))
{}\mRightarrow{} (\mforall{}R:Interface {}\mrightarrow{} Message(g) {}\mrightarrow{} \mBbbP{}. \mforall{}R':Interface {}\mrightarrow{} Message(f) {}\mrightarrow{} \mBbbP{}.
((\mforall{}eo:EO+(Message(g))
(eo-msg-interface-constraint(eo;X;hdrs;g)
{}\mRightarrow{} for every v in X there is an
earlier event with info=m such that
R[v;m]))
{}\mRightarrow{} (\mforall{}e:E. \mforall{}v:Interface.
((correct loc(e))
{}\mRightarrow{} (\muparrow{}has-header-and-in-locs(info(e);hdr;locs))
{}\mRightarrow{} R[v;snd(msg-body(info(e)))]
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E. ((e' < e) \mwedge{} R'[v;info(e')]))))
{}\mRightarrow{} for every v in local-simulation-class(X;locs;hdr) at location i s.t. correct i
there is an earlier event with info=m such that R'[v;m])))
supposing hdr encodes Id \mtimes{} Message(g)))
Date html generated:
2015_07_22-PM-00_07_18
Last ObjectModification:
2015_02_04-PM-04_41_48
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