Nuprl Lemma : simple-loc-comb-1-concat-classrel-weak
∀[Info,A,B:Type]. ∀[f:Id ⟶ A ⟶ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
(v ∈ f@(Loc, X)(e) ⇐⇒ ↓∃a:A. (a ∈ X(e) ∧ v ↓∈ f loc(e) a))
Proof
Definitions occuring in Statement :
concat-lifting-loc-1: f@,
simple-loc-comb-1: F(Loc, 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],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
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,
uiff: uiff(P;Q),
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:B].
(v \mmember{} f@(Loc, X)(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}a:A. (a \mmember{} X(e) \mwedge{} v \mdownarrow{}\mmember{} f loc(e) a))
Date html generated:
2016_05_17-AM-09_20_33
Last ObjectModification:
2015_12_29-PM-04_07_13
Theory : classrel!lemmas
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