Nuprl Lemma : decidable__classrel
∀[Info,T:Type]. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ (∀X:EClass(T). ∀es:EO+(Info). ∀e:E. ∀v:T. Dec(v ∈ X(e))))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
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],
classrel: v ∈ X(e),
member: t ∈ T,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info,T:Type].
((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} (\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:T. Dec(v \mmember{} X(e))))
Date html generated:
2016_05_16-PM-01_38_37
Last ObjectModification:
2015_12_29-PM-02_09_16
Theory : event-ordering
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