Nuprl Lemma : decidable__cs-precondition
∀[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. ∀s:ConsensusState. ∀i:ℤ. ∀v:V.
Dec(state s may consider v in inning i)))
Proof
Definitions occuring in Statement :
cs-precondition: state s may consider 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 :
consensus-state4_wf,
list_wf,
Id_wf,
l_member_wf,
exists_wf,
not_wf,
equal_wf,
all_wf,
decidable_wf,
l_all_wf2,
subtype_rel_list,
le_wf,
cs-inning_wf,
l_member-set2,
cs-archive-blocked_wf,
fpf_wf,
subtype_base_sq,
atom2_subtype_base,
select_wf,
sq_stable__le,
set_wf,
sq_stable__l_member,
decidable__equal_Id,
subtype_rel_self,
decidable__l_exists_better-extract,
decidable__cand,
decidable__l_all-better-extract,
decidable__le,
decidable__not,
decidable__cs-archive-blocked,
subtype_rel_dep_function,
subtype_rel_sets,
l_exists_iff,
l_exists_wf,
l_all_iff,
iff_wf,
decidable_functionality
\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{}s:ConsensusState. \mforall{}i:\mBbbZ{}. \mforall{}v:V.
Dec(state s may consider v in inning i)))
Date html generated:
2015_07_17-AM-11_30_39
Last ObjectModification:
2015_01_28-AM-01_37_33
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