Nuprl Lemma : new_23_sig_quorum_state_eq1-forward
∀Cmd:ValueAllType. ∀notify,propose: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_QuorumStateFun(Cmd;notify;propose;f;<n, r>;es.start;e)
= <rev(mapfilter(λe.(snd(fst(msgval(e))));
λe.new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es.start;e;n;r);
[start;e)))
, rev(mapfilter(λe.(snd(msgval(e)));
λe.new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es.start;e;n;r);
[start;e)))
>
∈ (Cmd List × (Id List))))
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_QuorumStateFun: new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e),
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,
Id: Id,
mapfilter: mapfilter(f;P;L),
reverse: rev(as),
list: T List,
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
lambda: λx.A[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Lemmas :
new_23_sig_quorum_state_eq1,
eo-forward_wf,
Message_wf,
member-eo-forward-E,
equal_wf,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
reverse_wf,
squash_wf,
true_wf,
list_wf,
mapfilter_wf,
set_wf,
assert_wf,
bool_wf,
es-E_wf,
l_member_wf,
es-closed-open-interval_wf,
new_23_sig_vote_with_ballot_first_wf,
member-es-closed-open-interval,
es-closed-open-interval-forward,
es-init_wf,
eo-forward-E-subtype,
es-le_wf,
event_ordering_wf,
es-init-forward,
iff_weakening_equal,
es-le-self,
list-eq-subtype,
eo-forward-info-body,
new_23_sig_vote_with_ballot_first-assert-forward,
valueall-type_wf,
new_23_sig_vote_with_ballot-assert-type,
es-info-body_wf,
mapfilter-wf2
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose: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{} (new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;<n, r>es.start;e)
= <rev(mapfilter(\mlambda{}e.(snd(fst(msgval(e))));
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es.start;e;n;r);
[start;e)))
, rev(mapfilter(\mlambda{}e.(snd(msgval(e)));
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es.start;e;n;r);
[start;e)))
>))
Date html generated:
2015_07_23-PM-04_03_06
Last ObjectModification:
2015_02_04-PM-03_55_59
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