Nuprl Lemma : new_23_sig_replica_state_mem_fun
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀slots:set-sig{i:l}(ℤ).
∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀n:ℤ. ∀c:Cmd.
((e1 <loc e2)
⇒ <n, c> ∈ 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))))
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-locl: (e <loc e'),
es-E: E,
list: T List,
vatype: ValueAllType,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
set-sig-member: set-sig-member(s),
record-select: r.x,
prop: ℙ,
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose: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{}e1,e2:E. \mforall{}n:\mBbbZ{}. \mforall{}c:Cmd.
((e1 <loc e2)
{}\mRightarrow{} <n, c> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e1)
{}\mRightarrow{} (\muparrow{}(set-sig-member(slots) n new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e2))))
Date html generated:
2016_05_17-PM-02_14_32
Last ObjectModification:
2015_12_29-PM-08_06_54
Theory : 2!3!consensus!with!signatures
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