Nuprl Lemma : consensus-state3-cases
∀[V:Type]
∀x:consensus-state3(V)
(((x = INITIAL ∈ consensus-state3(V)) ∨ (x = WITHDRAWN ∈ consensus-state3(V)))
∨ (∃v:V. ((x = CONSIDERING[v] ∈ consensus-state3(V)) ∨ (x = COMMITED[v] ∈ consensus-state3(V)))))
Proof
Definitions occuring in Statement :
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
cs-withdrawn: WITHDRAWN,
cs-initial: INITIAL,
consensus-state3: consensus-state3(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
cs-commited_wf,
equal_wf,
cs-considering_wf,
or_wf,
equal-wf-T-base,
bool_wf,
eqtt_to_assert,
cs-withdrawn_wf,
equal-wf-base,
exists_wf,
equal-wf-base-T,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
cs-initial_wf,
consensus-state3_wf
\mforall{}[V:Type]
\mforall{}x:consensus-state3(V)
(((x = INITIAL) \mvee{} (x = WITHDRAWN)) \mvee{} (\mexists{}v:V. ((x = CONSIDERING[v]) \mvee{} (x = COMMITED[v]))))
Date html generated:
2015_07_17-AM-11_23_46
Last ObjectModification:
2015_01_28-AM-07_30_21
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