Nuprl Lemma : decidable__cs-archive-blocked
∀[V:Type]
((∀v1,v2:V. Dec(v1 = v2 ∈ V))
⇒ (∃v,v':V. (¬(v = v' ∈ V)))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀ws,ws':{a:Id| (a ∈ A)} List. ∀s:ConsensusState. ∀i:ℤ. ∀v:V.
Dec(in state s, ws' blocks ws from archiving v in inning i)))
Proof
Definitions occuring in Statement :
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
consensus-state4: ConsensusState,
Id: Id,
l_member: (x ∈ l),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
Id_wf,
l_member_wf,
set_wf,
decidable__l_exists_better-extract,
decidable__l_member,
decidable__equal_set,
decidable__equal_Id,
l_exists_iff,
subtype_rel_list,
l_member-set2,
l_member-settype,
lelt_wf,
decidable__lt,
length_wf,
false_wf,
less-iff-le,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
equal_wf,
select_wf,
sq_stable__le,
int_seg_wf,
select_member,
int_seg_properties,
assert_wf,
fpf-dom_wf,
int-deq_wf,
cs-estimate_wf,
top_wf,
consensus-state4-subtype,
condition-implies-le,
minus-add,
minus-one-mul,
and_wf,
not_wf,
fpf_wf,
l_all_wf2,
fpf-ap_wf,
all_wf,
l_exists_wf,
subtype-fpf2,
cs-archive-blocked_wf,
le_wf,
less_than_wf,
exists_wf,
l_all_iff,
decidable__le,
not-le-2,
add-associates,
zero-add,
le-add-cancel2,
iff_weakening_equal,
decidable_functionality,
decidable__exists_int_seg,
decidable__l_exists,
decidable__and,
decidable__not,
decidable__l_all,
decidable__implies,
decidable__cand,
decidable__assert,
decidable__all_int_seg
\mforall{}[V:Type]
((\mforall{}v1,v2:V. Dec(v1 = v2))
{}\mRightarrow{} (\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}ws,ws':\{a:Id| (a \mmember{} A)\} List. \mforall{}s:ConsensusState.
\mforall{}i:\mBbbZ{}. \mforall{}v:V.
Dec(in state s, ws' blocks ws from archiving v in inning i)))
Date html generated:
2015_07_17-AM-11_30_32
Last ObjectModification:
2015_07_16-AM-10_19_46
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