Nuprl Lemma : new_23_sig_progress2-step1
∀[Cmd:ValueAllType]. ∀[eq:EqDecider(Cmd)]. ∀[reps,clients:bag(Id)]. ∀[coeff:{2...}]. ∀[flrs:ℕ].
∀[propose,notify:Atom List]. ∀[slots:set-sig{i:l}(ℤ)]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀[es:EO+(Message(f))]. ∀[e:E]. ∀[n,r:ℤ]. ∀[c:Cmd]. ∀[faulty:bag(Id)]. ∀[e':E]. ∀[c':Cmd].
(msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)
⇒ bag-no-repeats(Id;reps)
⇒ (#(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ)
⇒ loc(e) ↓∈ reps
⇒ (¬loc(e) ↓∈ faulty)
⇒ (e' ≤loc e
∧ <n, c'> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e')
∧ (¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e')))
∧ (no new_23_sig_Notify(Cmd;clients;notify;propose;f) n between e' and e))
⇒ <<n, r>, c> ∈ new_23_sig_RoundInfo(Cmd;notify;propose;f)(e)
⇒ new_23_sig_NewRoundsStateFun(Cmd;notify;propose;f;n;es.e';e) < r
⇒ b_all(Id;reps;i.mk-msg-interface(i;make-Msg(``new_23_sig vote``;<<<n, r>, c>, loc(e)>)) ∈ new_23_sig_main()(e)))
Proof
Definitions occuring in Statement :
new_23_sig_main: new_23_sig_main(),
new_23_sig_ReplicaStateFun: new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e),
new_23_sig_Proposal: new_23_sig_Proposal(Cmd;notify;propose;f),
new_23_sig_Notify: new_23_sig_Notify(Cmd;clients;notify;propose;f),
new_23_sig_NewRoundsStateFun: new_23_sig_NewRoundsStateFun(Cmd;notify;propose;f;x;es;e),
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),
msgs-interface-delivered-with-omissions: msgs-interface-delivered-with-omissions(f;es;X;faulty;failures;ids),
mk-msg-interface: mk-msg-interface(l;m),
msg-interface: Interface,
make-Msg: make-Msg(hdr;val),
Message: Message(f),
no-classrel-in-interval: (no X between start and e),
classrel: v ∈ X(e),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
deq: EqDecider(T),
cons: [a / b],
nil: [],
list: T List,
int_upper: {i...},
nat: ℕ,
vatype: ValueAllType,
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
pair: <a, b>,
product: x:A × B[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
token: "$token",
atom: Atom,
equal: s = t ∈ T,
b_all: b_all(T;b;x.P[x]),
bag-member: x ↓∈ bs,
bag-no-repeats: bag-no-repeats(T;bs),
bag-size: #(bs),
bag: bag(T),
set-sig-member: set-sig-member(s),
set-sig: set-sig{i:l}(Item)
Lemmas :
new_23_sig_round_info_classrel2,
subtype_base_sq,
name_wf,
list_subtype_base,
atom_subtype_base,
subtype_rel_wf,
equal-wf-T-base,
assert-name_eq,
es-info-body_wf,
int_subtype_base,
equal_wf,
equal-wf-base,
es-E_wf,
event-ordering+_subtype,
Message_wf
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[eq:EqDecider(Cmd)]. \mforall{}[reps,clients:bag(Id)]. \mforall{}[coeff:\{2...\}]. \mforall{}[flrs:\mBbbN{}].
\mforall{}[propose,notify:Atom List]. \mforall{}[slots:set-sig\{i:l\}(\mBbbZ{})].
\mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[n,r:\mBbbZ{}].
\mforall{}[c:Cmd]. \mforall{}[faulty:bag(Id)]. \mforall{}[e':E]. \mforall{}[c':Cmd].
(msgs-interface-delivered-with-omissions(f;es;new\_23\_sig\_main();faulty;flrs;reps)
{}\mRightarrow{} bag-no-repeats(Id;reps)
{}\mRightarrow{} (\#(reps) = ((coeff * flrs) + flrs + 1))
{}\mRightarrow{} loc(e) \mdownarrow{}\mmember{} reps
{}\mRightarrow{} (\mneg{}loc(e) \mdownarrow{}\mmember{} faulty)
{}\mRightarrow{} (e' \mleq{}loc e
\mwedge{} <n, c'> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e')
\mwedge{} (\mneg{}\muparrow{}(set-sig-member(slots) n new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e')))
\mwedge{} (no new\_23\_sig\_Notify(Cmd;clients;notify;propose;f) n between e' and e))
{}\mRightarrow{} <<n, r>, c> \mmember{} new\_23\_sig\_RoundInfo(Cmd;notify;propose;f)(e)
{}\mRightarrow{} new\_23\_sig\_NewRoundsStateFun(Cmd;notify;propose;f;n;es.e';e) < r
{}\mRightarrow{} b\_all(Id;reps;i.mk-msg-interface(i;make-Msg(``new\_23\_sig vote``;<<<n, r>, c>, loc(e)>)) \mmember{} new\_2\000C3\_sig\_main()(e)))
Date html generated:
2015_07_23-PM-04_09_18
Last ObjectModification:
2015_01_29-AM-08_47_17
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