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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
eo-msg-interface-constraint: eo-msg-interface-constraint(es;X;hdrs;f),
local-simulation-eo: local-simulation-eo(es;e;hdr;locs),
top: Top,
local-simulation-inputs: local-simulation-inputs(es;e;hdr;locs),
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
encodes-msg-type: hdr encodes T,
label: ...$L... t,
so_lambda: λ2x.t[x],
so_apply: x[s],
compose: f o g,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
less_than: a < b,
cand: A c∧ B,
sq_stable: SqStable(P),
local-simulation-input-validity: local-simulation-input-validity(g;X;hdr;locs;hdrs;es;i),
es-header: header(e),
mapfilter: mapfilter(f;P;L),
le: A ≤ B,
es-info-body: msgval(e),
iff: P ⇐⇒ Q,
es-info-type: es-info-type(es;e;f),
msg-type: msg-type(msg;f),
true: True,
rev_implies: P ⇐ Q,
msg-interface: Interface,
uiff: uiff(P;Q),
local-simulation-event: local-simulation-event(es;e;hdr;locs),
iseg: l1 ≤ l2,
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
es-le-before: ≤loc(e),
ge: i ≥ j ,
make-msg-interface: make-msg-interface(i;l;m),
pi1: fst(t),
pi2: snd(t),
es-embedding: (f embeds eo1 into eo2)
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:
2016_05_17-AM-09_14_08
Last ObjectModification:
2016_01_17-PM-11_16_15
Theory : classrel!lemmas
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