Nuprl Lemma : parallel-classrel
∀[T,Info:Type]. ∀[X,Y:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].  uiff(v ∈ X || Y(e);v ∈ X(e) ↓∨ v ∈ Y(e))
Proof
Definitions occuring in Statement : 
parallel-class: X || Y
, 
classrel: v ∈ X(e)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-E: E
, 
sq_or: a ↓∨ b
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
sq_or: a ↓∨ b
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
squash: ↓T
, 
prop: ℙ
, 
classrel: v ∈ X(e)
, 
bag-member: x ↓∈ bs
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
parallel-class: X || Y
, 
eclass-compose2: eclass-compose2(f;X;Y)
, 
all: ∀x:A. B[x]
, 
eclass: EClass(A[eo; e])
, 
iff: P 
⇐⇒ Q
, 
implies: P 
⇒ Q
, 
rev_implies: P 
⇐ Q
Latex:
\mforall{}[T,Info:Type].  \mforall{}[X,Y:EClass(T)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:T].
    uiff(v  \mmember{}  X  ||  Y(e);v  \mmember{}  X(e)  \mdownarrow{}\mvee{}  v  \mmember{}  Y(e))
Date html generated:
2016_05_16-PM-02_30_26
Last ObjectModification:
2016_01_17-PM-07_33_27
Theory : event-ordering
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