Nuprl Lemma : consensus-accum-num-property3
∀[V:Type]
∀A:Id List. ∀t:ℕ+. ∀f:(V List) ─→ V. ∀v0:V. ∀L:consensus-rcv(V;A) List.
let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in if b
then archive-condition(V;A;t;f;i - 1;v;L)
else ∀v:V. (¬archive-condition(V;A;t;f;i;v;L))
fi
Proof
Definitions occuring in Statement :
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
list: T List,
nat_plus: ℕ+,
ifthenelse: if b then t else f fi ,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
function: x:A ─→ B[x],
subtract: n - m,
natural_number: $n,
universe: Type
Lemmas :
consensus-rcv_wf,
list-cases,
list_ind_nil_lemma,
product_subtype_list,
list_ind_cons_lemma,
list_wf,
not_wf,
less_than_wf,
archive-condition_wf,
nat_plus_subtype_nat,
nil_wf,
id-deq_wf,
subtype_rel-deq,
Id_wf,
l_member_wf,
sq_stable__l_member,
decidable__equal_Id,
equal_wf,
set_wf,
consensus-accum-num-property1,
append_wf,
cons_wf,
consensus-accum-num-state_wf,
bool_wf,
eqtt_to_assert,
subtract_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
all_wf,
subtype_rel_list,
top_wf,
list_accum_cons_lemma,
list_accum_nil_lemma,
eq_int_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
length_of_nil_lemma,
zip_nil_lemma,
equal-wf-T-base,
filter_wf5,
rcvd-inning-gt_wf,
length_wf,
equal-wf-base-T,
votes-from-inning_wf,
le_wf,
null_wf3,
values-for-distinct_wf,
zip_wf,
bnot_wf,
archive-condition-append-init,
lt_int_wf,
archive-condition-append-vote,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-commutes,
le-add-cancel2,
cs-rcv-vote_wf,
mul-associates,
le-add-cancel,
le_int_wf,
length_of_cons_lemma,
zip_cons_cons_lemma,
remove-repeats_wf,
le-add-cancel-alt,
list_accum_append,
uiff_transitivity,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
null_cons_lemma,
filter_cons_lemma,
filter_nil_lemma,
null_nil_lemma,
false_wf,
decidable__assert,
assert_of_null,
zero-add,
or_wf,
member_wf,
decidable__lt,
minus-minus,
trivial-int-eq1,
decidable__equal_int,
votes-from-inning-is-nil,
not-equal-2,
map_nil_lemma,
remove_repeats_nil_lemma,
rcvd-innings-nil,
add-zero,
mapfilter-append,
zip-append,
map_cons_lemma,
le_antisymmetry,
length_wf_nat,
nat_wf,
and_wf,
length-map,
map_wf,
length-append,
unzip_zip,
sq_stable__le,
le_weakening
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}v0:V. \mforall{}L:consensus-rcv(V;A) List.
let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in if b
then archive-condition(V;A;t;f;i - 1;v;L)
else \mforall{}v:V. (\mneg{}archive-condition(V;A;t;f;i;v;L))
fi
Date html generated:
2015_07_17-AM-11_51_52
Last ObjectModification:
2015_07_16-AM-10_08_23
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