Nuprl Lemma : eclass0-bag-classrel
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ⟶ bag(B) ⟶ bag(C)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ eclass0-bag(f;X)(e);v ↓∈ f loc(e) X(e))
Proof
Definitions occuring in Statement :
eclass0-bag: eclass0-bag(f;X),
classrel: v ∈ X(e),
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
eclass0-bag: eclass0-bag(f;X),
classrel: v ∈ X(e),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[f:Id {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(C)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} eclass0-bag(f;X)(e);v \mdownarrow{}\mmember{} f loc(e) X(e))
Date html generated:
2016_05_16-PM-02_15_21
Last ObjectModification:
2016_01_17-PM-07_35_34
Theory : event-ordering
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