Nuprl Lemma : pv11_p1-ilf
(∀[loc:Id]. ∀[accpts:bag(Id)]. ∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[mf:pv11_p1_headers_type{i:l}(Cmd)].
∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ ((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc) o pv11_p1_p1b'base(Cmd;mf)) o
pv11_p1_ScoutState(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc))(e)
⇐⇒ ((header(e) = ``pv11_p1 p1b`` ∈ Name)
∧ has-es-info-type(es;e;mf;Id
× pv11_p1_Ballot_Num()
× pv11_p1_Ballot_Num()
× ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
∧ ((pv11_p1_init_ballot_num() loc) = (fst(snd(msgval(e)))) ∈ pv11_p1_Ballot_Num())
∧ (d = 0 ∈ ℤ)
∧ (i = loc(e) ∈ Id)
∧ (↓(((pv11_p1_init_ballot_num() loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ #(fst(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_init_ballot_num() loc;es;e))) < pv11_p1_threshold(accpts)
∧ (m
= make-Msg(``pv11_p1 adopted``;<pv11_p1_init_ballot_num() loc
, snd(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_init_ballot_num()
loc;es;e))
>)
∈ Message(mf)))
∨ ((¬((pv11_p1_init_ballot_num() loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num()))
∧ (m = make-Msg(``pv11_p1 preempted``;fst(snd(snd(msgval(e))))) ∈ Message(mf))))})
∧ (∀[z3:ℤ]. ∀[z1:pv11_p1_Ballot_Num()]. ∀[reps,accpts:bag(Id)]. ∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[z4:Cmd].
∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ ((pv11_p1_commander_output(Cmd;accpts;reps;mf) <z1, z3, z4> o pv11_p1_p2b'base(Cmd;mf)) o pv11_p1_Comm\000CanderState(Cmd;accpts;mf) z1 z3)(e)
⇐⇒ ((header(e) = ``pv11_p1 p2b`` ∈ Name)
∧ has-es-info-type(es;e;mf;Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()))
∧ ((z1 = (fst(snd(msgval(e)))) ∈ pv11_p1_Ballot_Num()) ∧ (z3 = (fst(snd(snd(msgval(e))))) ∈ ℤ))
∧ (d = 0 ∈ ℤ)
∧ (↓((z1 = (snd(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ #(pv11_p1_CommanderStateFun(Cmd;accpts;mf;z1;z3;es;e)) < pv11_p1_threshold(accpts)
∧ i ↓∈ reps
∧ (m = make-Msg([decision];<z3, z4>) ∈ Message(mf)))
∨ ((¬(z1 = (snd(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num()))
∧ (i = loc(e) ∈ Id)
∧ (m = make-Msg(``pv11_p1 preempted``;snd(snd(snd(msgval(e))))) ∈ Message(mf))))})
∧ (∀[loc:Id]. ∀[param:pv11_p1_Ballot_Num()]. ∀[accpts:bag(Id)]. ∀[Cmd:{T:Type| valueall-type(T)} ].
∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ ((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_upd_bnum() param loc) o pv11_p1_p1b'base(Cmd;mf)) o
pv11_p1_ScoutState(Cmd;accpts;mf) (pv11_p1_upd_bnum() param loc))(e)
⇐⇒ ((header(e) = ``pv11_p1 p1b`` ∈ Name)
∧ has-es-info-type(es;e;mf;Id
× pv11_p1_Ballot_Num()
× pv11_p1_Ballot_Num()
× ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
∧ ((pv11_p1_upd_bnum() param loc) = (fst(snd(msgval(e)))) ∈ pv11_p1_Ballot_Num())
∧ (d = 0 ∈ ℤ)
∧ (i = loc(e) ∈ Id)
∧ (↓(((pv11_p1_upd_bnum() param loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ #(fst(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_upd_bnum() param
loc;es;e))) < pv11_p1_threshold(accpts)
∧ (m
= make-Msg(``pv11_p1 adopted``;<pv11_p1_upd_bnum() param loc
, snd(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_upd_bnum() param
loc;es;e))
>)
∈ Message(mf)))
∨ ((¬((pv11_p1_upd_bnum() param loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num()))
∧ (m = make-Msg(``pv11_p1 preempted``;fst(snd(snd(msgval(e))))) ∈ Message(mf))))})
∧ (∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[accpts,ldrs:bag(Id)]. ∀[ldrs_uid:Id ⟶ ℤ]. ∀[reps:bag(Id)].
∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf)(e)
⇐⇒ ↓(loc(e) ↓∈ ldrs
∧ ((((((d = 0 ∈ ℤ) ∧ (m = make-Msg(``pv11_p1 p1a``;<loc(e), pv11_p1_init_ballot_num() loc(e)>) ∈ Message(mf)) \000C∧ i ↓∈ accpts)
∧ (↑first(e)))
∨ ((no ((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc(e)) o
pv11_p1_p1b'base(Cmd;mf)) o pv11_p1_ScoutState(Cmd;accpts;mf)
(pv11_p1_init_ballot_num() loc(e))) prior to e)
∧ <d, i, m> ∈ {((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc(e)) o
pv11_p1_p1b'base(Cmd;mf)) o pv11_p1_ScoutState(Cmd;accpts;mf)
(pv11_p1_init_ballot_num() loc(e)))}(e)))
∨ (∃e':{e':E| e' ≤loc e }
∃z1:pv11_p1_Ballot_Num()
∃z3:ℤ
∃z4:Cmd
(((((header(e') = [propose] ∈ Name) ∧ has-es-info-type(es;e';mf;ℤ × Cmd))
∧ ((↑(fst(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e')))))
∧ (¬↑(pv11_p1_in_domain(Cmd) (fst(msgval(e')))
(snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e')))))))
∧ (z1 = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e'))) ∈ pv11_p1_Ballot_Num())
∧ (<z3, z4> = msgval(e') ∈ (ℤ × Cmd)))
∨ (((header(e') = ``pv11_p1 adopted`` ∈ Name)
∧ has-es-info-type(es;e';mf;pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
∧ ((fst(msgval(e'))) = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e'))) ∈ pv11_p1_Ballot_Num())
∧ ((<z3, z4> ↓∈ snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;...;...;...))) ∧ ...) ∨ ...)
∧ ...))
∧ ...)))
∨ ...))
∨ ...})
Proof
Definitions occuring in Statement :
pv11_p1_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
pv11_p1_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_scout_output: pv11_p1_scout_output(Cmd;accpts;mf),
pv11_p1_ScoutStateFun: pv11_p1_ScoutStateFun(Cmd;accpts;mf;x;es;e),
pv11_p1_ScoutState: pv11_p1_ScoutState(Cmd;accpts;mf),
pv11_p1_commander_output: pv11_p1_commander_output(Cmd;accpts;reps;mf),
pv11_p1_CommanderStateFun: pv11_p1_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e),
pv11_p1_CommanderState: pv11_p1_CommanderState(Cmd;accpts;mf),
pv11_p1_AcceptorStateFun: pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_init_ballot_num: pv11_p1_init_ballot_num(),
pv11_p1_p2b'base: pv11_p1_p2b'base(Cmd;mf),
pv11_p1_p1b'base: pv11_p1_p1b'base(Cmd;mf),
pv11_p1_threshold: pv11_p1_threshold(accpts),
pv11_p1_in_domain: pv11_p1_in_domain(Cmd),
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_upd_bnum: pv11_p1_upd_bnum(),
pv11_p1_is_bnum: pv11_p1_is_bnum(),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
msg-interface: Interface,
make-Msg: make-Msg(hdr;val),
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
eclass2: (X o Y),
eclass1: (f o X),
no-classrel-in-interval: (no X between start and e),
no-prior-classrel: (no X prior to e),
classrel: v ∈ X(e),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
l_member: (x ∈ l),
cons: [a / b],
nil: [],
list: T List,
valueall-type: valueall-type(T),
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
guard: {T},
pi1: fst(t),
pi2: snd(t),
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
squash: ↓T,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
token: "$token",
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
and: P ∧ Q,
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,
implies: P ⇒ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
vatype: ValueAllType,
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),
cand: A c∧ B,
has-es-info-type: has-es-info-type(es;e;f;T),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
make-msg-interface: make-msg-interface(i;l;m),
equal-info-body: v = body(e),
pv11_p1_p1b'base: pv11_p1_p1b'base(Cmd;mf),
encodes-msg-type: hdr encodes T,
uiff: uiff(P;Q),
pv11_p1_scout_output: pv11_p1_scout_output(Cmd;accpts;mf),
spreadn: spread4,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
pi2: snd(t),
pi1: fst(t),
bool: 𝔹,
unit: Unit,
nat: ℕ,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
msg-interface: Interface,
pv11_p1_preempted'send: pv11_p1_preempted'send(Cmd;mf),
mk-msg-interface: mk-msg-interface(l;m),
pv11_p1_adopted'send: pv11_p1_adopted'send(Cmd;mf),
pv11_p1_p2b'base: pv11_p1_p2b'base(Cmd;mf),
pv11_p1_commander_output: pv11_p1_commander_output(Cmd;accpts;reps;mf),
spreadn: spread3,
pv11_p1_decision'broadcast: pv11_p1_decision'broadcast(Cmd;mf),
pv11_p1_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
sq_or: a ↓∨ b,
pv11_p1_Leader: pv11_p1_Leader(Cmd;accpts;ldrs_uid;reps;mf),
pv11_p1_SpawnFirstScout: pv11_p1_SpawnFirstScout(Cmd;accpts;mf),
pv11_p1_LeaderPropose: pv11_p1_LeaderPropose(Cmd;ldrs_uid;mf),
pv11_p1_propose'base: pv11_p1_propose'base(Cmd;mf),
pv11_p1_LeaderAdopted: pv11_p1_LeaderAdopted(Cmd;ldrs_uid;mf),
pv11_p1_adopted'base: pv11_p1_adopted'base(Cmd;mf),
pv11_p1_Commander: pv11_p1_Commander(Cmd;accpts;reps;mf),
pv11_p1_CommanderNotify: pv11_p1_CommanderNotify(Cmd;accpts;mf),
pv11_p1_CommanderOutput: pv11_p1_CommanderOutput(Cmd;accpts;reps;mf),
pv11_p1_LeaderPreempted: pv11_p1_LeaderPreempted(Cmd;ldrs_uid;mf),
pv11_p1_preempted'base: pv11_p1_preempted'base(Cmd;mf),
pv11_p1_Scout: pv11_p1_Scout(Cmd;accpts;mf),
pv11_p1_ScoutNotify: pv11_p1_ScoutNotify(Cmd;accpts;mf),
pv11_p1_ScoutOutput: pv11_p1_ScoutOutput(Cmd;accpts;mf),
pv11_p1_Acceptor: pv11_p1_Acceptor(Cmd;ldrs_uid;mf),
pv11_p1_AcceptorsP1a: pv11_p1_AcceptorsP1a(Cmd;ldrs_uid;mf),
let: let,
pv11_p1_p1a'base: pv11_p1_p1a'base(Cmd;mf),
pv11_p1_AcceptorsP2a: pv11_p1_AcceptorsP2a(Cmd;ldrs_uid;mf),
pv11_p1_p2a'base: pv11_p1_p2a'base(Cmd;mf),
pv11_p1_leader_propose: pv11_p1_leader_propose(Cmd),
pv11_p1_leader_adopted: pv11_p1_leader_adopted(Cmd;ldrs_uid),
bag-map: bag-map(f;bs),
pv11_p1_update_proposals: pv11_p1_update_proposals(Cmd),
bag-append: as + bs,
bag-filter: [x∈b|p[x]],
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
mapfilter: mapfilter(f;P;L),
pv11_p1_p2a'broadcast: pv11_p1_p2a'broadcast(Cmd;mf),
pv11_p1_leader_preempted: pv11_p1_leader_preempted(Cmd;ldrs_uid),
pv11_p1_p1a'broadcast: pv11_p1_p1a'broadcast(Cmd;mf),
empty-bag: {},
hint: hint(t),
pv11_p1_p1b'send: pv11_p1_p1b'send(Cmd;mf),
pv11_p1_p2b'send: pv11_p1_p2b'send(Cmd;mf),
decidable: Dec(P),
pv11_p1_init_ballot_num: pv11_p1_init_ballot_num(),
pv11_p1_mk_bnum: pv11_p1_mk_bnum()
Latex:
(\mforall{}[loc:Id]. \mforall{}[accpts:bag(Id)]. \mforall{}[Cmd:\{T:Type| valueall-type(T)\} ].
\mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} ((pv11\_p1\_scout\_output(Cmd;accpts;mf) (pv11\_p1\_init\_ballot\_num() loc) o
pv11\_p1\_p1b'base(Cmd;mf)) o pv11\_p1\_ScoutState(Cmd;accpts;mf)
(pv11\_p1\_init\_ballot\_num() loc))(e)
\mLeftarrow{}{}\mRightarrow{} ((header(e) = ``pv11\_p1 p1b``)
\mwedge{} has-es-info-type(es;e;mf;Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((pv11\_p1\_init\_ballot\_num() loc) = (fst(snd(msgval(e)))))
\mwedge{} (d = 0)
\mwedge{} (i = loc(e))
\mwedge{} (\mdownarrow{}(((pv11\_p1\_init\_ballot\_num() loc) = (fst(snd(snd(msgval(e))))))
\mwedge{} \#(fst(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;pv11\_p1\_init\_ballot\_num()
loc;es;e))) < pv11\_p1\_threshold(accpts)
\mwedge{} (m
= make-Msg(``pv11\_p1 adopted``;<pv11\_p1\_init\_ballot\_num() loc
, snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;...
loc;es;e))
>)))
\mvee{} ((\mneg{}((pv11\_p1\_init\_ballot\_num() loc) = (fst(snd(snd(msgval(e)))))))
\mwedge{} (m = make-Msg(``pv11\_p1 preempted``;fst(snd(snd(msgval(e))))))))\})
\mwedge{} (\mforall{}[z3:\mBbbZ{}]. \mforall{}[z1:pv11\_p1\_Ballot\_Num()]. \mforall{}[reps,accpts:bag(Id)]. \mforall{}[Cmd:\{T:Type| valueall-type(T)\} ].
\mforall{}[z4:Cmd]. \mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} ((pv11\_p1\_commander\_output(Cmd;accpts;reps;mf)
<z1, z3, z4> o pv11\_p1\_p2b'base(Cmd;mf)) o
pv11\_p1\_CommanderState(Cmd;accpts;mf) z1 z3)(e)
\mLeftarrow{}{}\mRightarrow{} ((header(e) = ``pv11\_p1 p2b``)
\mwedge{} has-es-info-type(es;e;mf;Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num()))
\mwedge{} ((z1 = (fst(snd(msgval(e))))) \mwedge{} (z3 = (fst(snd(snd(msgval(e)))))))
\mwedge{} (d = 0)
\mwedge{} (\mdownarrow{}((z1 = (snd(snd(snd(msgval(e))))))
\mwedge{} \#(pv11\_p1\_CommanderStateFun(Cmd;accpts;mf;z1;z3;es;e)) < pv11\_p1\_threshold(accpts)
\mwedge{} i \mdownarrow{}\mmember{} reps
\mwedge{} (m = make-Msg([decision];<z3, z4>)))
\mvee{} ((\mneg{}(z1 = (snd(snd(snd(msgval(e)))))))
\mwedge{} (i = loc(e))
\mwedge{} (m = make-Msg(``pv11\_p1 preempted``;snd(snd(snd(msgval(e))))))))\})
\mwedge{} (\mforall{}[loc:Id]. \mforall{}[param:pv11\_p1\_Ballot\_Num()]. \mforall{}[accpts:bag(Id)]. \mforall{}[Cmd:\{T:Type| valueall-type(T)\} ].
\mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} ((pv11\_p1\_scout\_output(Cmd;accpts;mf) (pv11\_p1\_upd\_bnum() param loc) o
pv11\_p1\_p1b'base(Cmd;mf)) o pv11\_p1\_ScoutState(Cmd;accpts;mf)
(pv11\_p1\_upd\_bnum() param loc))(e)
\mLeftarrow{}{}\mRightarrow{} ((header(e) = ``pv11\_p1 p1b``)
\mwedge{} has-es-info-type(es;e;mf;Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((pv11\_p1\_upd\_bnum() param loc) = (fst(snd(msgval(e)))))
\mwedge{} (d = 0)
\mwedge{} (i = loc(e))
\mwedge{} (\mdownarrow{}(((pv11\_p1\_upd\_bnum() param loc) = (fst(snd(snd(msgval(e))))))
\mwedge{} \#(fst(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;pv11\_p1\_upd\_bnum() param
loc;es;e))) < pv11\_p1\_threshold(accpts)
\mwedge{} (m
= make-Msg(``pv11\_p1 adopted``;<pv11\_p1\_upd\_bnum() param loc
, snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;...
param
loc;es;e))
>)))
\mvee{} ((\mneg{}((pv11\_p1\_upd\_bnum() param loc) = (fst(snd(snd(msgval(e)))))))
\mwedge{} (m = make-Msg(``pv11\_p1 preempted``;fst(snd(snd(msgval(e))))))))\})
\mwedge{} (\mforall{}[Cmd:\{T:Type| valueall-type(T)\} ]. \mforall{}[accpts,ldrs:bag(Id)]. \mforall{}[ldrs$_{uid}$:Id\000C {}\mrightarrow{} \mBbbZ{}]. \mforall{}[reps:bag(Id)].
\mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid}$;reps;mf)(e)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}(loc(e) \mdownarrow{}\mmember{} ldrs
\mwedge{} ((((((d = 0) \mwedge{} (m = make-Msg(``pv11\_p1 p1a``;<loc(e), pv11\_p1\_init\_ballot\_num() loc(e)>)\000C) \mwedge{} i \mdownarrow{}\mmember{} accpts)
\mwedge{} (\muparrow{}first(e)))
\mvee{} ((no ((pv11\_p1\_scout\_output(Cmd;accpts;mf) (pv11\_p1\_init\_ballot\_num() loc(e)) o
pv11\_p1\_p1b'base(Cmd;mf)) o pv11\_p1\_ScoutState(Cmd;accpts;mf)
(pv11\_p1\_init\_ballot\_num() loc(e))) prior to e)
\mwedge{} <d, i, m> \mmember{} \{((pv11\_p1\_scout\_output(Cmd;accpts;mf)
(pv11\_p1\_init\_ballot\_num() loc(e)) o pv11\_p1\_p1b'base(Cmd;mf)) o
pv11\_p1\_ScoutState(Cmd;accpts;mf) (pv11\_p1\_init\_ballot\_num() loc(e)))\}(
e)))
\mvee{} (\mexists{}e':\{e':E| e' \mleq{}loc e \}
\mexists{}z1:pv11\_p1\_Ballot\_Num()
\mexists{}z3:\mBbbZ{}
\mexists{}z4:Cmd
(((((header(e') = [propose]) \mwedge{} has-es-info-type(es;e';mf;\mBbbZ{} \mtimes{} Cmd))
\mwedge{} ((\muparrow{}(fst(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;mf;es;e\000C')))))
\mwedge{} (\mneg{}\muparrow{}(pv11\_p1\_in\_domain(Cmd) (fst(msgval(e')))
(snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;mf;e\000Cs;e')))))))
\mwedge{} (z1 = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;mf;es;e'\000C))))
\mwedge{} (<z3, z4> = msgval(e')))
\mvee{} (((header(e') = ``pv11\_p1 adopted``)
\mwedge{} has-es-info-type(es;e';mf;pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num()
\mtimes{} \mBbbZ{}
\mtimes{} Cmd) List)))
\mwedge{} ((fst(msgval(e'))) = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid\mbackslash{}f\000Cf7d$;mf;es;e'))))
\mwedge{} ((<z3, z4> \mdownarrow{}\mmember{} snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}\mbackslash{}\000Cff24;mf;es;e')))
\mwedge{} (\mneg{}(\mexists{}p2:Cmd. (<z3, p2> \mmember{} pv11\_p1\_pmax(Cmd;ldrs$_{uid}$) \000C(snd(msgval(e')))))))
\mvee{} (\mexists{}v2:pv11\_p1\_Ballot\_Num()
(<v2, z3, z4> \mdownarrow{}\mmember{} snd(msgval(e'))
\mwedge{} (\mneg{}(\mexists{}z5:pv11\_p1\_Ballot\_Num(). \mexists{}z8:Cmd. ((\muparrow{}(v2 ... ...)) \mwedge{} ...))))))
\mwedge{} ...))
\mwedge{} ...)))
\mvee{} ...))
\mvee{} ...\})
Date html generated:
2016_05_17-PM-03_08_39
Last ObjectModification:
2016_04_03-PM-09_39_05
Theory : paxos!synod
Home
Index