Nuprl Lemma : fresh-inning-reachable
∀[V:Type]
∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀ws:{a:Id| (a ∈ A)} List. ∀x:ConsensusState. ∀i:ℤ.
((ws ∈ W)
⇒ x ((λx,y. CR(in ws)[x, y] )^*) (λa.<if a ∈b ws) then i else Inning(x;a) fi , Estimate(x;a)>)
supposing (∀a∈ws.Inning(x;a) < i))
Proof
Definitions occuring in Statement :
consensus-rel-mod: CR(in ws)[x, y] ,
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
consensus-state4: ConsensusState,
id-deq: IdDeq,
Id: Id,
deq-member: x ∈b L),
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
list: T List,
rel_star: R^*,
ifthenelse: if b then t else f fi ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
lambda: λx.A[x],
pair: <a, b>,
int: ℤ,
universe: Type
Lemmas :
set_wf,
less_than_wf,
primrec-wf2,
nat_wf,
first0,
subtype_rel_list,
Id_wf,
top_wf,
reduce_nil_lemma,
rel_star_weakening,
consensus-state4_wf,
l_member_wf,
cs-inning_wf,
cs-estimate_wf,
fpf_wf,
consensus-rel-mod_wf,
pair_eta_rw,
iff_weakening_equal,
rel_star_transitivity,
deq-member_wf,
id-deq_wf,
firstn_wf,
subtract_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
iff_transitivity,
assert_wf,
iff_weakening_uiff,
assert_of_band,
decidable__cand,
length_wf,
select_wf,
decidable__le,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
not_wf,
decidable__lt,
decidable__l_member,
decidable__equal_Id,
decidable__not,
infix_ap_wf,
rel_star_wf,
eq_id_wf,
le-add-cancel-alt,
assert-eq-id,
list-subtype,
equal-wf-T-base,
bor_wf,
bnot_wf,
or_wf,
bnot_thru_band,
assert_of_bor,
assert_of_bnot,
atom2_subtype_base,
member_firstn,
le_weakening2,
le_wf,
subtract-is-less,
sq_stable__le,
squash_wf,
true_wf,
list_wf,
ifthenelse_wf,
band_wf,
firstn_decomp,
iff_imp_equal_bool,
append_wf,
cons_wf,
nil_wf,
member_append,
member_singleton,
iff_wf,
lelt_wf,
select_member,
trivial-int-eq1,
uiff_transitivity,
rel_rel_star,
l_member-settype,
all_wf,
fpf-domain_wf,
consensus-state4-subtype,
exists_wf,
cs-precondition_wf,
fpf-join_wf,
fpf-single_wf,
int-deq_wf,
bfalse_wf,
le-add-cancel2,
decidable__equal_int,
less_than_transitivity2,
le_weakening,
not-equal-2,
int_subtype_base,
and_wf,
length_wf_nat,
firstn_all
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}ws:\{a:Id| (a \mmember{} A)\} List. \mforall{}x:ConsensusState. \mforall{}i:\mBbbZ{}.
((ws \mmember{} W)
{}\mRightarrow{} x
((\mlambda{}x,y. CR(in ws)[x, y] )\^{}*)
(\mlambda{}a.<if a \mmember{}\msubb{} ws) then i else Inning(x;a) fi , Estimate(x;a)>)
supposing (\mforall{}a\mmember{}ws.Inning(x;a) < i))
Date html generated:
2015_07_17-AM-11_38_10
Last ObjectModification:
2015_02_04-PM-05_47_36
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