Nuprl Lemma : assert-cs-is-considering
∀[V:Type]. ∀x:consensus-state3(V). (↑cs-is-considering(x) ⇐⇒ ∃v:V. (x = CONSIDERING[v] ∈ consensus-state3(V)))
Proof
Definitions occuring in Statement :
cs-is-considering: cs-is-considering(x),
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
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 :
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
cs-is-considering: cs-is-considering(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
isl: isl(x),
not: ¬A,
uimplies: b supposing a,
btrue: tt,
true: True,
sq_type: SQType(T),
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[V:Type]. \mforall{}x:consensus-state3(V). (\muparrow{}cs-is-considering(x) \mLeftarrow{}{}\mRightarrow{} \mexists{}v:V. (x = CONSIDERING[v]))
Date html generated:
2016_05_16-AM-11_50_52
Last ObjectModification:
2015_12_29-PM-01_18_23
Theory : event-ordering
Home
Index