Nuprl Lemma : classrel-at
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[locs:bag(Id)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
(v ∈ X@locs(e) ⇐⇒ loc(e) ↓∈ locs ∧ v ∈ X(e))
Proof
Definitions occuring in Statement :
class-at: X@locs,
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,
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
classrel: v ∈ X(e),
class-at: X@locs,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
bag-member: x ↓∈ bs,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
false: False,
not: ¬A,
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[locs:bag(Id)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
(v \mmember{} X@locs(e) \mLeftarrow{}{}\mRightarrow{} loc(e) \mdownarrow{}\mmember{} locs \mwedge{} v \mmember{} X(e))
Date html generated:
2016_05_16-PM-10_53_06
Last ObjectModification:
2016_01_17-PM-07_16_34
Theory : event-ordering
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