Nuprl Lemma : nysiad_QueueState-classrel
∀[add2baghdr,addwaitinghdr,adeliverhdr,inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom List].
∀[mf:nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr)].
∀es:EO+(Message(mf)). ∀e:E. ∀x:Id. ∀v:(Message(mf) × Id? × Id) List × 𝔹.
(v ∈ nysiad_QueueState(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr;mf) x(e)
⇐⇒ v
= nysiad_QueueStateFun(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;...;mf;x;es;e)
∈ ((Message(mf) × Id? × Id) List × 𝔹))
Proof
Definitions occuring in Statement :
nysiad_QueueStateFun: nysiad_QueueStateFun(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr;mf;x;es;e),
nysiad_QueueState: nysiad_QueueState(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr;mf),
nysiad_headers_type: nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
unit: Unit,
apply: f a,
product: x:A × B[x],
union: left + right,
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
nysiad_headers_type: nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
name: Name,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
nysiad_headers: nysiad_headers(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
nysiad_headers_fun: nysiad_headers_fun(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr;mf),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
nysiad_headers_no_rep: nysiad_headers_no_rep(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
squash: ↓T,
no_repeats: no_repeats(T;l),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
less_than: a < b,
true: True,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
select: L[n],
subtract: n - m,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
Id: Id,
nysiad_QueueStateFun: nysiad_QueueStateFun(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr;mf;x;es;e),
rev_uimplies: rev_uimplies(P;Q),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
vatype: ValueAllType
Latex:
\mforall{}[add2baghdr,addwaitinghdr,adeliverhdr,inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom List].
\mforall{}[...
Date html generated:
2016_05_17-PM-01_28_28
Last ObjectModification:
2016_01_18-AM-07_27_46
Theory : event-logic-applications
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