Nuprl Lemma : loop-classrel
∀[Info,B:Type]. ∀[X:EClass(B ⟶ bag(B))]. ∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
  uiff(v ∈ loop-class(X;init)(e);↓∃f:B ⟶ bag(B). ∃b:B. (f ∈ X(e) ∧ b ∈ Prior(loop-class(X;init))?init(e) ∧ v ↓∈ f b))
Proof
Definitions occuring in Statement : 
loop-class: loop-class(X;init)
, 
primed-class-opt: Prior(X)?b
, 
classrel: v ∈ X(e)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-E: E
, 
Id: Id
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
exists: ∃x:A. B[x]
, 
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 : 
loop-class: loop-class(X;init)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
squash: ↓T
, 
classrel: v ∈ X(e)
, 
bag-member: x ↓∈ bs
Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  bag(B))].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:B].
    uiff(v  \mmember{}  loop-class(X;init)(e);\mdownarrow{}\mexists{}f:B  {}\mrightarrow{}  bag(B)
                                                                      \mexists{}b:B
                                                                        (f  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Prior(loop-class(X;init))?init(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  b))
Date html generated:
2016_05_16-PM-11_33_24
Last ObjectModification:
2016_01_17-PM-07_08_05
Theory : event-ordering
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