Nuprl Lemma : consensus-state4-cases
∀[V:Type]
∀A:Id List. ∀s:ConsensusState. ∀a:{a:Id| (a ∈ A)} . ∀i:ℤ.
(by state s, a passed inning i without archiving a value
∨ in state s, a has not completed inning i
∨ (∃v:V. by state s, a archived v in inning i))
Proof
Definitions occuring in Statement :
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
consensus-state4: ConsensusState,
Id: Id,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type
Lemmas :
set_wf,
Id_wf,
l_member_wf,
consensus-state4_wf,
list_wf,
fpf-domain_wf,
cs-estimate_wf,
top_wf,
consensus-state4-subtype,
decidable__l_member,
decidable__equal_int,
le_wf,
cs-inning_wf,
not_wf,
less_than_wf,
fpf-ap_wf,
int-deq_wf,
member-fpf-dom,
decidable__lt,
or_wf,
less_than_transitivity1,
less_than_irreflexivity,
exists_wf
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}s:ConsensusState. \mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}i:\mBbbZ{}.
(by state s, a passed inning i without archiving a value
\mvee{} in state s, a has not completed inning i
\mvee{} (\mexists{}v:V. by state s, a archived v in inning i))
Date html generated:
2015_07_17-AM-11_27_34
Last ObjectModification:
2015_07_16-AM-10_17_33
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