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)
Lemmas :
primed-class-opt_wf,
loop-class_wf,
classrel_wf,
squash_wf,
exists_wf,
bag_wf,
bag-member_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Id_wf,
eclass_wf,
eclass2-classrel
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:
2015_07_21-PM-02_31_55
Last ObjectModification:
2015_01_27-PM-09_46_06
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