Nuprl Lemma : on-loc-classrel
∀[Info,T:Type]. ∀[X:Id ⟶ EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T]. (v ∈ on-loc-class(X)(e) ⇐⇒ v ∈ X loc(e)(e))
Proof
Definitions occuring in Statement :
on-loc-class: on-loc-class(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
classrel: v ∈ X(e),
on-loc-class: on-loc-class(X),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rev_implies: P ⇐ Q,
bag-member: x ↓∈ bs,
squash: ↓T
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:Id {}\mrightarrow{} EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
(v \mmember{} on-loc-class(X)(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} X loc(e)(e))
Date html generated:
2016_05_17-AM-09_16_30
Last ObjectModification:
2016_01_17-PM-11_13_27
Theory : classrel!lemmas
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