Nuprl Lemma : decidable__equal_consensus-rcv
∀[V:Type]. ((∀v,w:V. Dec(v = w ∈ V)) ⇒ (∀A:Id List. ∀x,y:consensus-rcv(V;A). Dec(x = y ∈ consensus-rcv(V;A))))
Proof
Definitions occuring in Statement :
consensus-rcv: consensus-rcv(V;A),
Id: Id,
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[V:Type]. ((\mforall{}v,w:V. Dec(v = w)) {}\mRightarrow{} (\mforall{}A:Id List. \mforall{}x,y:consensus-rcv(V;A). Dec(x = y)))
Date html generated:
2016_05_16-PM-00_32_40
Last ObjectModification:
2015_12_29-PM-01_32_01
Theory : event-ordering
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