Nuprl Lemma : OARcast_SenderState-classrel
∀[M:ValueAllType]. ∀[deliverhdr,oarcasthdr,orderedhdr,orderhdr:Atom List].
∀[mf:OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
∀es:EO+(Message(mf)). ∀e:E. ∀v:ℤ.
(v ∈ OARcast_SenderState(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf)(e)
⇐⇒ v = OARcast_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e) ∈ ℤ)
Proof
Definitions occuring in Statement :
OARcast_SenderStateFun: OARcast_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e),
OARcast_SenderState: OARcast_SenderState(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf),
OARcast_headers_type: OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
OARcast_headers_type: OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
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,
OARcast_headers: OARcast_headers(deliverhdr;oarcasthdr;orderedhdr;orderhdr),
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
OARcast_headers_fun: OARcast_headers_fun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
OARcast_headers_no_rep: OARcast_headers_no_rep(deliverhdr;oarcasthdr;orderedhdr;orderhdr),
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,
OARcast_SenderStateFun: OARcast_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e),
rev_uimplies: rev_uimplies(P;Q),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs
Latex:
\mforall{}[M:ValueAllType]. \mforall{}[deliverhdr,oarcasthdr,orderedhdr,orderhdr:Atom List].
\mforall{}[mf:OARcast\_headers\_type\{i:l\}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
\mforall{}es:EO+(Message(mf)). \mforall{}e:E. \mforall{}v:\mBbbZ{}.
(v \mmember{} OARcast\_SenderState(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf)(e)
\mLeftarrow{}{}\mRightarrow{} v = OARcast\_SenderStateFun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr;mf;es;e))
Date html generated:
2016_05_17-PM-01_03_17
Last ObjectModification:
2016_01_18-AM-07_38_44
Theory : event-logic-applications
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