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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
local-simulation-eo: local-simulation-eo(es;e;hdr;locs),
top: Top,
local-simulation-inputs: local-simulation-inputs(es;e;hdr;locs),
local-simulation-event: local-simulation-event(es;e;hdr;locs),
mapfilter: mapfilter(f;P;L),
es-le-before: ≤loc(e),
subtype_rel: A ⊆r B,
encodes-msg-type: hdr encodes T,
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
select: L[n],
cons: [a / b],
iff: P ⇐⇒ Q,
msg-type: msg-type(msg;f),
name: Name
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:
2016_05_17-AM-08_53_48
Last ObjectModification:
2016_01_17-PM-08_33_28
Theory : messages
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