Nuprl Lemma : consensus-ts4-archived-invariant
∀[V:Type]
∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[x:ts-reachable(consensus-ts4(V;A;W))]. ∀[i:ℤ]. ∀[v:V]. ∀[a:{a:Id|
(a ∈ A)} ]\000C.
∀[j:ℕi]. ∀[v':V]. v' = v ∈ V supposing in state x, inning j could commit v'
supposing by state x, a archived v in inning i
supposing ∀v1,v2:V. Dec(v1 = v2 ∈ V)
Proof
Definitions occuring in Statement :
cs-inning-committable: in state s, inning i could commit v ,
cs-archived: by state s, a archived v in inning i,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
ts-reachable-induction,
consensus-ts4_wf,
all_wf,
l_member_wf,
cs-archived_wf,
int_seg_wf,
cs-inning-committable_wf,
subtype_rel_set,
ts-type_wf,
consensus-state4_wf,
infix_ap_wf,
rel_star_wf,
ts-rel_wf,
ts-init_wf,
subtype_rel_self,
ts-reachable_wf,
subtype_rel_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
ts-init_wf_reachable,
subtype_rel_dep_function,
set_wf,
list_wf,
Id_wf,
decidable_wf,
equal_wf,
sq_stable__all,
sq_stable__equal,
decidable__cs-archived,
cs-inning-committable-step,
fpf_wf,
int_seg_subtype-nat,
false_wf,
decidable__equal_Id,
cs-estimate_wf,
member_wf,
fpf-domain_wf,
subtype-fpf2,
top_wf,
fpf-ap_wf,
int-deq_wf,
member-fpf-dom,
subtype_base_sq,
atom2_subtype_base,
assert_wf,
fpf-dom_wf,
fpf-join-ap-sq,
consensus-state4-subtype,
fpf-domain-join,
fpf-single_wf,
bool_cases,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
member-fpf-domain,
eqff_to_assert,
assert_of_bnot,
fpf_ap_single_lemma,
member_singleton,
int_subtype_base,
cs-precondition_wf,
squash_wf,
true_wf,
and_wf,
fpf-join_wf,
not_wf,
iff_weakening_equal,
sq_stable__le,
le_wf,
less_than_wf,
exists_wf,
int_seg_properties,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
lelt_wf,
or_wf,
cs-not-completed_wf,
cs-inning_wf
\mforall{}[V:Type]
\mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[x:ts-reachable(consensus-ts4(V;A;W))]. \mforall{}[i:\mBbbZ{}].
\mforall{}[v:V]. \mforall{}[a:\{a:Id| (a \mmember{} A)\} ].
\mforall{}[j:\mBbbN{}i]. \mforall{}[v':V]. v' = v supposing in state x, inning j could commit v'
supposing by state x, a archived v in inning i
supposing \mforall{}v1,v2:V. Dec(v1 = v2)
Date html generated:
2015_07_17-AM-11_34_06
Last ObjectModification:
2015_07_16-AM-10_17_05
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