Nuprl Lemma : consensus-ts3-invariant1
∀[V:Type]. ∀[L:ts-reachable(consensus-ts3(V))]. ∀[v:V].
∀[v':V]. v' = v ∈ V supposing (CONSIDERING[v'] ∈ L) ∨ (COMMITED[v'] ∈ L)
supposing (CONSIDERING[v] ∈ L) ∨ (COMMITED[v] ∈ L)
Proof
Definitions occuring in Statement :
consensus-ts3: consensus-ts3(T),
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
ts-reachable-induction,
consensus-ts3_wf,
all_wf,
or_wf,
l_member_wf,
consensus-state3_wf,
cs-considering_wf,
subtype_rel_set,
ts-type_wf,
list_wf,
infix_ap_wf,
rel_star_wf,
ts-rel_wf,
ts-init_wf,
subtype_rel_self,
cs-commited_wf,
ts-reachable_wf,
subtype_rel_wf,
sq_stable__all,
equal_wf,
sq_stable__equal,
nil_wf,
subtype_rel_dep_function,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
length_wf_nat,
nat_wf,
member_append,
cons_wf,
cs-initial_wf,
member_singleton,
equal-wf-T-base,
consensus-state3-unequal,
consensus-ts3-invariant0,
less_than_transitivity1,
length_wf,
le_weakening,
lelt_wf,
select_wf,
squash_wf,
le_wf,
less_than_wf,
sq_stable__le,
iff_weakening_equal,
int_seg_wf,
decidable__equal_int,
cs-considering-equal,
and_wf,
decidable__lt,
cs-commited-equal,
false_wf,
le_antisymmetry_iff,
less-iff-le,
add_functionality_wrt_le,
add-associates,
add-swap,
add-commutes,
le-add-cancel,
subtype_base_sq,
int_subtype_base,
int_seg_subtype-nat,
less_than_transitivity2,
bool_wf,
outl_wf,
assert_wf,
isl_wf,
bfalse_wf
\mforall{}[V:Type]. \mforall{}[L:ts-reachable(consensus-ts3(V))]. \mforall{}[v:V].
\mforall{}[v':V]. v' = v supposing (CONSIDERING[v'] \mmember{} L) \mvee{} (COMMITED[v'] \mmember{} L)
supposing (CONSIDERING[v] \mmember{} L) \mvee{} (COMMITED[v] \mmember{} L)
Date html generated:
2015_07_17-AM-11_24_18
Last ObjectModification:
2015_07_16-AM-10_17_19
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