Nuprl Lemma : new_23_sig_rounds_mem
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e1,e2:E. ∀n,round1,round2:ℤ. ∀z:ℤ × ℤ × Cmd.
  ((e1 <loc e2)
  
⇒ z ∈ new_23_sig_RoundInfo(Cmd;notify;propose;f)(e1)
  
⇒ round1 ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) n(e1)
  
⇒ round2 ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) n(e2)
  
⇒ let z,cmd = z 
     in let n',round' = z 
        in (n = n' ∈ ℤ) 
⇒ (round' ≤ round2))
Proof
Definitions occuring in Statement : 
new_23_sig_NewRoundsState: new_23_sig_NewRoundsState(Cmd;notify;propose;f)
, 
new_23_sig_RoundInfo: new_23_sig_RoundInfo(Cmd;notify;propose;f)
, 
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose)
, 
Message: Message(f)
, 
classrel: v ∈ X(e)
, 
event-ordering+: EO+(Info)
, 
es-locl: (e <loc e')
, 
es-E: E
, 
list: T List
, 
vatype: ValueAllType
, 
le: A ≤ B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
apply: f a
, 
spread: spread def, 
product: x:A × B[x]
, 
int: ℤ
, 
atom: Atom
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
vatype: ValueAllType
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose)
, 
l_all: (∀x∈L.P[x])
, 
and: P ∧ Q
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
so_apply: x[s]
, 
iff: P 
⇐⇒ Q
, 
name: Name
, 
new_23_sig_headers: new_23_sig_headers(notify;propose)
, 
listp: A List+
, 
rev_implies: P 
⇐ Q
, 
guard: {T}
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
new_23_sig_headers_fun: new_23_sig_headers_fun(Cmd;notify;propose)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
ifthenelse: if b then t else f fi 
, 
sq_stable: SqStable(P)
, 
cand: A c∧ B
, 
new_23_sig_headers_no_rep: new_23_sig_headers_no_rep(notify;propose)
, 
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
, 
name_eq: name_eq(x;y)
, 
name-deq: NameDeq
, 
list-deq: list-deq(eq)
, 
band: p ∧b q
, 
atom-deq: AtomDeq
, 
eq_atom: x =a y
, 
null: null(as)
, 
new_23_sig_NewRoundsState: new_23_sig_NewRoundsState(Cmd;notify;propose;f)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
Memory1: Memory1(init;tr;X)
, 
so_apply: x[s1;s2;s3]
, 
new_23_sig_update_round: new_23_sig_update_round(Cmd)
, 
decidable: Dec(P)
, 
nequal: a ≠ b ∈ T 
, 
new_23_sig_RoundInfo: new_23_sig_RoundInfo(Cmd;notify;propose;f)
, 
new_23_sig_vote'base: new_23_sig_vote'base(Cmd;notify;propose;f)
, 
new_23_sig_retry'base: new_23_sig_retry'base(Cmd;notify;propose;f)
, 
encodes-msg-type: hdr encodes T
, 
new_23_sig_vote2retry: new_23_sig_vote2retry(Cmd)
Latex:
\mforall{}Cmd:ValueAllType.  \mforall{}notify,propose:Atom  List.  \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)).  \mforall{}e1,e2:E.  \mforall{}n,round1,round2:\mBbbZ{}.  \mforall{}z:\mBbbZ{}  \mtimes{}  \mBbbZ{}  \mtimes{}  Cmd.
    ((e1  <loc  e2)
    {}\mRightarrow{}  z  \mmember{}  new\_23\_sig\_RoundInfo(Cmd;notify;propose;f)(e1)
    {}\mRightarrow{}  round1  \mmember{}  new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f)  n(e1)
    {}\mRightarrow{}  round2  \mmember{}  new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f)  n(e2)
    {}\mRightarrow{}  let  z,cmd  =  z 
          in  let  n',round'  =  z 
                in  (n  =  n')  {}\mRightarrow{}  (round'  \mleq{}  round2))
Date html generated:
2016_05_17-PM-02_05_11
Last ObjectModification:
2016_01_18-AM-09_34_21
Theory : 2!3!consensus!with!signatures
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