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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