Nuprl Lemma : three-cs-vote-invariant
∀V:Type. ∀A:Id List. ∀t:ℕ+. ∀f:(V List) ─→ V. ∀s:ts-type(three-consensus-ts(V;A;t;f)).
((ts-init(three-consensus-ts(V;A;t;f)) (ts-rel(three-consensus-ts(V;A;t;f))^*) s)
⇒ (∀a:{a:Id| (a ∈ A)} . ∀n:ℕ. ∀b:{a:Id| (a ∈ A)} . ∀v1:V.
((Vote[b;n;v1] ∈ s a) ⇒ (∃L:consensus-rcv(V;A) List. (L ≤ s b ∧ archive-condition(V;A;t;f;n;v1;L))))))
Proof
Definitions occuring in Statement :
three-consensus-ts: three-consensus-ts(V;A;t;f),
archive-condition: archive-condition(V;A;t;f;n;v;L),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
iseg: l1 ≤ l2,
l_member: (x ∈ l),
list: T List,
rel_star: R^*,
nat_plus: ℕ+,
nat: ℕ,
infix_ap: x f y,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
ts-rel: ts-rel(ts),
ts-init: ts-init(ts),
ts-type: ts-type(ts)
Lemmas :
ts-reachable-induction2,
three-consensus-ts_wf,
nat_plus_subtype_nat,
all_wf,
l_member_wf,
nat_wf,
consensus-rcv_wf,
cs-rcv-vote_wf,
subtype_rel_set,
ts-type_wf,
list_wf,
infix_ap_wf,
rel_star_wf,
ts-rel_wf,
ts-init_wf,
subtype_rel_self,
exists_wf,
iseg_wf,
archive-condition_wf,
ts-reachable_wf,
subtype_rel_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
set_wf,
not_wf,
equal_wf,
append_wf,
cons_wf,
nat_plus_wf,
Id_wf,
decidable__equal_Id,
or_wf,
member_singleton,
member_append,
and_wf,
member_wf,
true_wf,
squash_wf,
iff_weakening_equal,
atom2_subtype_base,
subtype_base_sq,
iseg_append
\mforall{}V:Type. \mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}s:ts-type(three-consensus-ts(V;A;t;f)).
((ts-init(three-consensus-ts(V;A;t;f)) (ts-rel(three-consensus-ts(V;A;t;f))\^{}*) s)
{}\mRightarrow{} (\mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}n:\mBbbN{}. \mforall{}b:\{a:Id| (a \mmember{} A)\} . \mforall{}v1:V.
((Vote[b;n;v1] \mmember{} s a)
{}\mRightarrow{} (\mexists{}L:consensus-rcv(V;A) List. (L \mleq{} s b \mwedge{} archive-condition(V;A;t;f;n;v1;L))))))
Date html generated:
2015_07_17-AM-11_52_30
Last ObjectModification:
2015_07_16-AM-09_46_31
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