Nuprl Lemma : consensus-ts5-archive-invariant
∀[V:Type]
((∀v1,v2:V. Dec(v1 = v2 ∈ V))
⇒ (∃v,v':V. (¬(v = v' ∈ V)))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀x:ts-reachable(consensus-ts5(V;A;W)). ∀v:V. ∀b:{a:Id| (a ∈ A)} . ∀i:ℤ.
(state fst(x) may consider v in inning i) supposing
((Estimate(fst(x);b)(i) = v ∈ V) and
(↑i ∈ dom(Estimate(fst(x);b))))))
Proof
Definitions occuring in Statement :
consensus-ts5: consensus-ts5(V;A;W),
cs-precondition: state s may consider v in inning i,
cs-estimate: Estimate(s;a),
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
Id: Id,
int-deq: IntDeq,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
sq_stable__all,
all_wf,
Id_wf,
l_member_wf,
isect_wf,
assert_wf,
fpf-dom_wf,
int-deq_wf,
cs-estimate_wf,
top_wf,
consensus-state4-subtype,
fpf-ap_wf,
cs-precondition_wf,
sq_stable__uall,
assert_witness,
sq_stable_from_decidable,
decidable__cs-precondition,
equal_wf,
set_wf,
ts-reachable_wf,
consensus-ts5_wf,
subtype_rel_wf,
ts-type_wf,
deq_member_nil_lemma,
false_wf,
infix_ap_wf,
consensus-state4_wf,
consensus-state5_wf,
ts-rel_wf,
subtype_rel-equal,
decidable__equal_Id,
squash_wf,
true_wf,
list_wf,
member_wf,
and_wf,
fpf_wf,
subtype-fpf2,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_functionality_wrt_uiff,
deq_wf,
subtype_top,
iff_weakening_equal,
le_wf,
cs-inning_wf,
not_wf,
cs-archive-blocked_wf,
less_than_wf,
exists_wf,
cs-knowledge-precondition_wf,
fpf-single_wf,
fpf-join_wf,
decidable__equal_int,
int_subtype_base,
rel_star_wf,
ts-init_wf,
consensus-ts5-true-knowledge,
id-deq_wf,
subtype_rel_sum,
equal-wf-T-base,
decide_bfalse_lemma,
decidable__lt,
not-equal-2,
add_functionality_wrt_le,
add-associates,
add-commutes,
le-add-cancel,
add-swap,
equal-wf-base-T,
atom2_subtype_base,
fpf-join-single-property,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
fpf-join-dom,
fpf-join-ap-sq,
bool_cases,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
member-fpf-domain,
fpf_ap_single_lemma
\mforall{}[V:Type]
((\mforall{}v1,v2:V. Dec(v1 = v2))
{}\mRightarrow{} (\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}x:ts-reachable(consensus-ts5(V;A;W)). \mforall{}v:V.
\mforall{}b:\{a:Id| (a \mmember{} A)\} . \mforall{}i:\mBbbZ{}.
(state fst(x) may consider v in inning i) supposing
((Estimate(fst(x);b)(i) = v) and
(\muparrow{}i \mmember{} dom(Estimate(fst(x);b))))))
Date html generated:
2015_07_17-AM-11_42_36
Last ObjectModification:
2015_07_16-AM-10_20_48
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