Nuprl Lemma : member-local-simulation-inputs
∀f:Name ⟶ Type
∀[Info:Type]
∀es:EO+(Message(f)). ∀hdr:Name. ∀locs:bag(Id).
∀e:E. ∀v:Id × Info.
((v ∈ local-simulation-inputs(es;e;hdr;locs))
⇐⇒ ∃e':E
(e' ≤loc e
∧ (msg-header(info(e')) = hdr ∈ Name)
∧ fst(v) ↓∈ locs
∧ (v = msg-body(info(e')) ∈ (Id × Info))))
supposing hdr encodes Id × Info
Proof
Definitions occuring in Statement :
local-simulation-inputs: local-simulation-inputs(es;e;hdr;locs),
encodes-msg-type: hdr encodes T,
msg-body: msg-body(msg),
msg-header: msg-header(m),
Message: Message(f),
es-info: info(e),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
Id: Id,
name: Name,
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
encodes-msg-type: hdr encodes T,
subtype_rel: A ⊆r B,
local-simulation-inputs: local-simulation-inputs(es;e;hdr;locs),
prop: ℙ,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
cand: A c∧ B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
msg-type: msg-type(msg;f),
name: Name,
sq_type: SQType(T),
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
sq_stable: SqStable(P),
squash: ↓T,
pi1: fst(t),
true: True
Latex:
\mforall{}f:Name {}\mrightarrow{} Type
\mforall{}[Info:Type]
\mforall{}es:EO+(Message(f)). \mforall{}hdr:Name. \mforall{}locs:bag(Id).
\mforall{}e:E. \mforall{}v:Id \mtimes{} Info.
((v \mmember{} local-simulation-inputs(es;e;hdr;locs))
\mLeftarrow{}{}\mRightarrow{} \mexists{}e':E
(e' \mleq{}loc e
\mwedge{} (msg-header(info(e')) = hdr)
\mwedge{} fst(v) \mdownarrow{}\mmember{} locs
\mwedge{} (v = msg-body(info(e')))))
supposing hdr encodes Id \mtimes{} Info
Date html generated:
2016_05_17-AM-08_53_17
Last ObjectModification:
2016_01_17-PM-08_34_14
Theory : messages
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