Nuprl Lemma : consensus-ts3-invariant0
∀[V:Type]
∀L:ts-reachable(consensus-ts3(V)). ∀i:ℕ||L||.
∀j:ℕ||L||. (L[j] = INITIAL ∈ consensus-state3(V)) ∨ (L[j] = WITHDRAWN ∈ consensus-state3(V)) supposing i < j
supposing L[i] = INITIAL ∈ consensus-state3(V)
Proof
Definitions occuring in Statement :
consensus-ts3: consensus-ts3(T),
cs-withdrawn: WITHDRAWN,
cs-initial: INITIAL,
consensus-state3: consensus-state3(T),
select: L[n],
length: ||as||,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
or: P ∨ Q,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
consensus-state3-unequal,
ts-reachable-induction,
consensus-ts3_wf,
member-less_than,
length_of_nil_lemma,
stuck-spread,
base_wf,
less_than_transitivity1,
less_than_irreflexivity,
less_than_wf,
int_seg_wf,
equal-wf-T-base,
consensus-state3_wf,
select_wf,
nil_wf,
sq_stable__le,
length_wf,
le_weakening,
lelt_wf,
squash_wf,
le_wf,
list_wf,
equal_wf,
all_wf,
isect_wf,
subtype_rel_set,
ts-type_wf,
infix_ap_wf,
rel_star_wf,
ts-rel_wf,
ts-init_wf,
subtype_rel_self,
or_wf,
ts-reachable_wf,
subtype_rel_wf,
sq_stable__all,
sq_stable__uall,
sq_stable_from_decidable,
decidable__or,
decidable__equal_cs-initial,
decidable__equal_cs-withdrawn,
subtype_rel_dep_function,
length_wf_nat,
nat_wf,
member_wf,
decidable__equal_int,
set_wf,
int_subtype_base,
subtype_base_sq,
minus-zero,
zero-add,
not-le-2,
decidable__le,
subtract_wf,
select-cons-hd,
iff_weakening_equal,
le-add-cancel,
add-commutes,
add-associates,
add-zero,
zero-mul,
add-mul-special,
add-swap,
minus-one-mul,
minus-add,
condition-implies-le,
false_wf,
decidable__lt,
length_of_cons_lemma,
cons_wf,
select_append_back,
length_append,
cs-initial_wf,
top_wf,
subtype_rel_list,
true_wf,
select_append_front,
le-add-cancel2,
add_functionality_wrt_le,
le_antisymmetry_iff,
less-iff-le,
cs-withdrawn_wf,
less_than_transitivity2
\mforall{}[V:Type]
\mforall{}L:ts-reachable(consensus-ts3(V)). \mforall{}i:\mBbbN{}||L||.
\mforall{}j:\mBbbN{}||L||. (L[j] = INITIAL) \mvee{} (L[j] = WITHDRAWN) supposing i < j supposing L[i] = INITIAL
Date html generated:
2015_07_17-AM-11_24_01
Last ObjectModification:
2015_07_16-AM-09_51_16
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