Nuprl Lemma : new_23_sig_voter_start_unique
∀Cmd:ValueAllType. ∀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)). ∀n:ℤ. ∀e1,e2:E. ∀c1,c2:Cmd.
((¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e1)))
⇒ <n, c1> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e1)
⇒ (¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e2)))
⇒ <n, c2> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e2)
⇒ (loc(e1) = loc(e2) ∈ Id)
⇒ (e1 = e2 ∈ E))
Proof
Definitions occuring in Statement :
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_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
assert: ↑b,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ T,
set-sig-member: set-sig-member(s),
set-sig: set-sig{i:l}(Item)
Lemmas :
es-locl-trichotomy,
new_23_sig_replica_state_mem_fun,
equal_wf,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
Message_wf,
subtype_rel_dep_function,
name_wf,
vatype_wf,
classrel_wf,
new_23_sig_Proposal_wf,
not_wf,
assert_wf,
set-sig-member_wf,
new_23_sig_ReplicaStateFun_wf,
es-E_wf,
event-ordering+_wf,
new_23_sig_headers_type_wf,
set-sig_wf,
list_wf,
valueall-type_wf
Latex:
\mforall{}Cmd:ValueAllType. \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{}n:\mBbbZ{}. \mforall{}e1,e2:E.
\mforall{}c1,c2:Cmd.
((\mneg{}\muparrow{}(set-sig-member(slots) n new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e1)))
{}\mRightarrow{} <n, c1> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e1)
{}\mRightarrow{} (\mneg{}\muparrow{}(set-sig-member(slots) n new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e2)))
{}\mRightarrow{} <n, c2> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e2)
{}\mRightarrow{} (loc(e1) = loc(e2))
{}\mRightarrow{} (e1 = e2))
Date html generated:
2015_07_23-PM-03_57_23
Last ObjectModification:
2015_01_29-AM-08_49_15
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