Nuprl Lemma : consensus-state2-cases
∀[V:Type]
∀x:consensus-state2(V)
((x = AMBIVALENT ∈ consensus-state2(V))
∨ (∃v:V. ((x = PREDECIDED[v] ∈ consensus-state2(V)) ∨ (x = Decided[v] ∈ consensus-state2(V)))))
Proof
Definitions occuring in Statement :
cs-predecided: PREDECIDED[v],
cs-ambivalent: AMBIVALENT,
consensus-state2: consensus-state2(T),
cs-decided: Decided[v],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
consensus-state2: consensus-state2(T),
cs-decided: Decided[v],
guard: {T},
or: P ∨ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
cs-predecided: PREDECIDED[v],
so_lambda: λ2x.t[x],
so_apply: x[s],
cs-ambivalent: AMBIVALENT,
top: Top
Latex:
\mforall{}[V:Type]
\mforall{}x:consensus-state2(V). ((x = AMBIVALENT) \mvee{} (\mexists{}v:V. ((x = PREDECIDED[v]) \mvee{} (x = Decided[v]))))
Date html generated:
2016_05_16-AM-11_47_23
Last ObjectModification:
2015_12_29-PM-01_15_12
Theory : event-ordering
Home
Index