Nuprl Lemma : cs-inning-committable-step
∀V:Type
((∀v,v':V. Dec(v = v' ∈ V))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀x,y:ts-reachable(consensus-ts4(V;A;W)). ∀i:ℕ. ∀v:V.
((x ts-rel(consensus-ts4(V;A;W)) y)
⇒ in state y, inning i could commit v
⇒ in state x, inning i could commit v )))
Proof
Definitions occuring in Statement :
cs-inning-committable: in state s, inning i could commit v ,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
l_member: (x ∈ l),
list: T List,
nat: ℕ,
decidable: Dec(P),
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts)
Lemmas :
consensus-ts4-estimate-domain,
set_wf,
l_member_wf,
cs-inning-committable_wf,
subtype_rel_set,
ts-type_wf,
consensus-ts4_wf,
consensus-state4_wf,
infix_ap_wf,
rel_star_wf,
ts-rel_wf,
ts-init_wf,
subtype_rel_self,
ts-reachable_wf,
subtype_rel_wf,
subtype_rel_dep_function,
nat_wf,
list_wf,
Id_wf,
all_wf,
decidable_wf,
equal_wf,
or_wf,
cs-archived_wf,
cs-not-completed_wf,
decidable__cs-archived,
decidable__cs-not-completed,
decidable__equal_Id,
subtype_base_sq,
atom2_subtype_base,
nat_properties,
fpf_wf,
fpf-domain_wf,
subtype-fpf2,
top_wf,
fpf-ap_wf,
int-deq_wf,
member-fpf-dom,
fpf-domain-join,
cs-estimate_wf,
consensus-state4-subtype,
fpf-single_wf,
assert_wf,
fpf-dom_wf,
fpf-join-ap-sq,
bool_cases,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
member-fpf-domain,
member_singleton,
le_weakening,
cs-inning_wf,
consensus-ts4-inning-rel,
rel_rel_star,
consensus-rel_wf,
consensus-ts4-estimate-rel,
le_transitivity
\mforall{}V:Type
((\mforall{}v,v':V. Dec(v = v'))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}x,y:ts-reachable(consensus-ts4(V;A;W)). \mforall{}i:\mBbbN{}. \mforall{}v:V\000C.
((x ts-rel(consensus-ts4(V;A;W)) y)
{}\mRightarrow{} in state y, inning i could commit v
{}\mRightarrow{} in state x, inning i could commit v )))
Date html generated:
2015_07_17-AM-11_33_00
Last ObjectModification:
2015_07_16-AM-10_15_14
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