Nuprl Lemma : consensus-ts4-estimate-domain
∀V:Type. ∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀a:{a:Id| (a ∈ A)} . ∀x:ts-reachable(consensus-ts4(V;A;W)). ∀i:ℤ.
((i ∈ fpf-domain(Estimate(x;a))) ⇒ (i ≤ Inning(x;a)))
Proof
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
fpf-domain: fpf-domain(f),
Id: Id,
l_member: (x ∈ l),
list: T List,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
ts-reachable: ts-reachable(ts)
Lemmas :
all_wf,
l_member_wf,
fpf-domain_wf,
cs-estimate_wf,
top_wf,
consensus-state4-subtype,
le_wf,
cs-inning_wf,
ts-reachable_wf,
consensus-ts4_wf,
subtype_rel_wf,
ts-type_wf,
sq_stable__all,
sq_stable__le,
less_than_wf,
squash_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
infix_ap_wf,
consensus-state4_wf,
ts-rel_wf,
subtype_rel_dep_function,
subtype_rel_self,
Id_wf,
fpf_wf,
decidable__equal_Id,
subtype_base_sq,
atom2_subtype_base,
true_wf,
list_wf,
subtype-fpf2,
iff_weakening_equal,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
decidable__l_member,
decidable__equal_int,
le_transitivity,
le_weakening,
fpf-domain-join,
fpf-single_wf,
int-deq_wf,
member_singleton,
and_wf,
equal_wf
\mforall{}V:Type. \mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}a:\{a:Id| (a \mmember{} A)\} .
\mforall{}x:ts-reachable(consensus-ts4(V;A;W)). \mforall{}i:\mBbbZ{}.
((i \mmember{} fpf-domain(Estimate(x;a))) {}\mRightarrow{} (i \mleq{} Inning(x;a)))
Date html generated:
2015_07_17-AM-11_26_51
Last ObjectModification:
2015_07_16-AM-10_17_52
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