Nuprl Lemma : eclass-union-classrel
∀[Info,A:Type]. ∀[X:EClass(bag(A))]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A].
uiff(v ∈ eclass-union(X)(e);↓∃b:bag(A). (v ↓∈ b ∧ b ∈ X(e)))
Proof
Definitions occuring in Statement :
eclass-union: eclass-union(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
eclass-union: eclass-union(X),
squash: ↓T,
prop: ℙ,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
class-ap: X(e),
eclass: EClass(A[eo; e]),
sq_stable: SqStable(P),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(bag(A))]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A].
uiff(v \mmember{} eclass-union(X)(e);\mdownarrow{}\mexists{}b:bag(A). (v \mdownarrow{}\mmember{} b \mwedge{} b \mmember{} X(e)))
Date html generated:
2016_05_16-PM-02_08_30
Last ObjectModification:
2016_01_17-PM-07_38_10
Theory : event-ordering
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