Nuprl Lemma : nysiad_MessageBagState-classrel
∀[M:ValueAllType]. ∀[add2baghdr,addwaitinghdr,adeliverhdr:Atom List]. ∀[deqM:EqDecider(M)].
∀[inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom List]. ∀[waitingmap:map-sig{i:l}(Id;M)].
∀[mf:nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr)].
∀[msg2m:Message(mf) ⟶ M].
  ∀es:EO+(Message(mf)). ∀e:E. ∀v:(M × Id? × Id) List × map-sig-map(waitingmap).
    (v ∈
      nysiad_MessageBagState(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m)(
      e)
    
⇐⇒ v
        = nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;...;...;...;...;mf;...;es;e)
        ∈ ((M × Id? × Id) List × map-sig-map(waitingmap)))
Proof
Definitions occuring in Statement : 
nysiad_MessageBagStateFun: nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m;es;e)
, 
nysiad_MessageBagState: nysiad_MessageBagState(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;readyhdr;...;...;mf;msg2m)
, 
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
, 
deq: EqDecider(T)
, 
vatype: ValueAllType
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
unit: Unit
, 
function: x:A ⟶ B[x]
, 
product: x:A × B[x]
, 
union: left + right
, 
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
, 
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_MessageBagStateFun: nysiad_MessageBagStateFun(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;mf;msg2m;es;e)
, 
rev_uimplies: rev_uimplies(P;Q)
, 
classrel: v ∈ X(e)
, 
bag-member: x ↓∈ bs
Latex:
\mforall{}[M:ValueAllType].  \mforall{}[add2baghdr,addwaitinghdr,adeliverhdr:Atom  List].  \mforall{}[deqM:EqDecider(M)].
\mforall{}[inputmsghdr,kdeliverhdr,readyhdr,tooarcasthdr:Atom  List].  \mforall{}[waitingmap:map-sig\{i:l\}(Id;M)].
\mforall{}[...
Date html generated:
2016_05_17-PM-01_24_50
Last ObjectModification:
2016_01_18-AM-07_30_49
Theory : event-logic-applications
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