Nuprl Lemma : assert-cs-is-decided
∀[V:Type]. ∀x:consensus-state2(V). (↑cs-is-decided(x) 
⇐⇒ ∃v:V. (x = Decided[v] ∈ consensus-state2(V)))
Proof
Definitions occuring in Statement : 
cs-is-decided: cs-is-decided(x)
, 
consensus-state2: consensus-state2(T)
, 
cs-decided: Decided[v]
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
iff: 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]
, 
cs-is-decided: cs-is-decided(x)
, 
isl: isl(x)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
exists: ∃x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
true: True
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
bfalse: ff
, 
false: False
, 
not: ¬A
Latex:
\mforall{}[V:Type].  \mforall{}x:consensus-state2(V).  (\muparrow{}cs-is-decided(x)  \mLeftarrow{}{}\mRightarrow{}  \mexists{}v:V.  (x  =  Decided[v]))
Date html generated:
2016_05_16-AM-11_46_46
Last ObjectModification:
2015_12_29-PM-01_15_05
Theory : event-ordering
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