Nuprl Lemma : pv11_p1_ScoutState-functional
∀[Cmd:ValueAllType]. ∀[accpts:bag(Id)]. ∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))].
∀[x:pv11_p1_Ballot_Num()].
  pv11_p1_ScoutState(Cmd;accpts;mf) x is functional
Proof
Definitions occuring in Statement : 
pv11_p1_ScoutState: pv11_p1_ScoutState(Cmd;accpts;mf)
, 
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd)
, 
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num()
, 
Message: Message(f)
, 
es-functional-class: X is functional
, 
event-ordering+: EO+(Info)
, 
Id: Id
, 
list: T List
, 
vatype: ValueAllType
, 
uall: ∀[x:A]. B[x]
, 
apply: f a
, 
product: x:A × B[x]
, 
int: ℤ
, 
bag: bag(T)
Definitions unfolded in proof : 
vatype: ValueAllType
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd)
, 
subtype_rel: A ⊆r B
, 
listp: A List+
, 
name: Name
, 
prop: ℙ
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
sq_stable: SqStable(P)
, 
l_all: (∀x∈L.P[x])
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
iff: P 
⇐⇒ Q
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
less_than: a < b
, 
squash: ↓T
, 
length: ||as||
, 
list_ind: list_ind, 
pv11_p1_headers: pv11_p1_headers()
, 
cons: [a / b]
, 
nil: []
, 
it: ⋅
, 
true: True
, 
select: L[n]
, 
subtract: n - m
, 
uimplies: b supposing a
, 
guard: {T}
, 
rev_implies: P 
⇐ Q
, 
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd)
, 
name_eq: name_eq(x;y)
, 
name-deq: NameDeq
, 
list-deq: list-deq(eq)
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
atom-deq: AtomDeq
, 
eq_atom: x =a y
, 
bfalse: ff
, 
btrue: tt
, 
null: null(as)
, 
pv11_p1_ScoutState: pv11_p1_ScoutState(Cmd;accpts;mf)
, 
state-class1: state-class1(init;tr;X)
, 
top: Top
, 
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num()
, 
pv11_p1_p1b'base: pv11_p1_p1b'base(Cmd;mf)
, 
encodes-msg-type: hdr encodes T
, 
es-functional-class: X is functional
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
es-total-class: es-total-class(es;X)
, 
nat: ℕ
Latex:
\mforall{}[Cmd:ValueAllType].  \mforall{}[accpts:bag(Id)].  \mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)].
\mforall{}[es:EO+(Message(mf))].  \mforall{}[x:pv11\_p1\_Ballot\_Num()].
    pv11\_p1\_ScoutState(Cmd;accpts;mf)  x  is  functional
Date html generated:
2016_05_17-PM-02_54_55
Last ObjectModification:
2016_01_18-AM-11_21_56
Theory : paxos!synod
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