Nuprl Lemma : return-loc-bag-class-classrel
∀[Info,A:Type]. ∀[x:Id ⟶ bag(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A].
(v ∈ return-loc-bag-class(x)(e) ⇐⇒ v ↓∈ x loc(e) ∧ (↑first(e)))
Proof
Definitions occuring in Statement :
return-loc-bag-class: return-loc-bag-class(x),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
return-loc-bag-class: return-loc-bag-class(x),
classrel: v ∈ X(e),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
assert: ↑b,
iff: P ⇐⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
bag-member: x ↓∈ bs,
squash: ↓T
Latex:
\mforall{}[Info,A:Type]. \mforall{}[x:Id {}\mrightarrow{} bag(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A].
(v \mmember{} return-loc-bag-class(x)(e) \mLeftarrow{}{}\mRightarrow{} v \mdownarrow{}\mmember{} x loc(e) \mwedge{} (\muparrow{}first(e)))
Date html generated:
2016_05_17-AM-09_13_08
Last ObjectModification:
2016_01_17-PM-11_15_04
Theory : classrel!lemmas
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