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),
set-sig-member: set-sig-member(s),
set-sig: set-sig{i:l}(Item),
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
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
not: ¬A,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x],
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
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:
2016_05_17-PM-02_25_13
Last ObjectModification:
2015_12_29-PM-08_06_19
Theory : 2!3!consensus!with!signatures
Home
Index