Nuprl Lemma : new_23_sig_vote_with_ballot_first-assert-forward
∀Cmd:ValueAllType. ∀propose,notify:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e,start:E. ∀n,r:ℤ.
(start ≤loc e
⇒ (↑new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es.start;e;n;r)
⇐⇒ (↑new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;r))
∧ (↑(∀e'∈[start;e).¬bnew_23_sig_vote_with_ballot_and_id(Cmd;notify;propose;f;es;e';n;r;snd(msgval(e))))_b)))
Proof
Definitions occuring in Statement :
new_23_sig_vote_with_ballot_first: new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r),
new_23_sig_vote_with_ballot_and_id: new_23_sig_vote_with_ballot_and_id(Cmd;notify;propose;f;es;e;n;r;i),
new_23_sig_vote_with_ballot: new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;r),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
es-info-body: msgval(e),
Message: Message(f),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-closed-open-interval: [e;e'),
es-le: e ≤loc e' ,
es-E: E,
bl-all: (∀x∈L.P[x])_b,
list: T List,
vatype: ValueAllType,
bnot: ¬bb,
assert: ↑b,
pi2: snd(t),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
int: ℤ,
atom: Atom
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
true: True,
bfalse: ff,
false: False,
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
has-es-info-type: has-es-info-type(es;e;f;T),
pi2: snd(t),
so_apply: x[s],
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
guard: {T}
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}propose,notify:Atom List. \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)). \mforall{}e,start:E. \mforall{}n,r:\mBbbZ{}.
(start \mleq{}loc e
{}\mRightarrow{} (\muparrow{}new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es.start;e;n;r)
\mLeftarrow{}{}\mRightarrow{} (\muparrow{}new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;r))
\mwedge{} (\muparrow{}...)))
Date html generated:
2016_05_17-PM-02_33_24
Last ObjectModification:
2015_12_29-PM-08_04_37
Theory : 2!3!consensus!with!signatures
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