### Nuprl Lemma : rec-bind-classrel2

`∀[Info,A,B:Type]. ∀[X:A ─→ EClass(B)]. ∀[Y:A ─→ EClass(A)].`
`  ∀[es:EO+(Info)]. ∀[e:E]. ∀[a:A]. ∀[v:B].`
`    uiff(v ∈ rec-bind-class(X;Y) a(e);↓v ∈ X a(e)`
`                                       ∨ (∃a':A. (a' ∈ Y a(e) ∧ v ∈ X a'(e)))`
`                                       ∨ (∃e':E. ∃a':A. ((e' <loc e) ∧ a' ∈ Y a(e') ∧ v ∈ rec-bind-class(X;Y) a'(e)))) `
`  supposing not-self-starting{i:l}(Info;A;Y)`

Proof

Definitions occuring in Statement :  rec-bind-class: `rec-bind-class(X;Y)` not-self-starting: `not-self-starting{i:l}(Info;A;Y)` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` eo-forward: `eo.e` event-ordering+: `EO+(Info)` es-locl: `(e <loc e')` es-E: `E` uiff: `uiff(P;Q)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` exists: `∃x:A. B[x]` squash: `↓T` or: `P ∨ Q` and: `P ∧ Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type`
Lemmas :  sq_stable__uiff classrel_wf rec-bind-class_wf squash_wf or_wf exists_wf eo-forward_wf member-eo-forward-E es-le-self equal_wf Id_wf es-loc_wf es-locl_wf es-le_weakening sq_stable__classrel sq_stable__squash es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf nat_wf decidable__le subtract_wf false_wf not-ge-2 less-iff-le condition-implies-le minus-one-mul zero-add minus-add minus-minus add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel decidable__lt es-causl_wf zero-le-nat le_wf add-mul-special zero-mul es-E_wf event-ordering+_subtype event-ordering+_wf not-self-starting_wf eclass_wf parallel-classrel mbind-class_wf bind-class-rel and_wf es-le_wf true_wf iff_weakening_equal eo-forward-le eo-forward-E-member es-le-loc es-causle_antisymmetry es-causle_weakening_locl equal-eo-forward-E sq_stable__sq_or

Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[X:A  {}\mrightarrow{}  EClass(B)].  \mforall{}[Y:A  {}\mrightarrow{}  EClass(A)].
\mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[a:A].  \mforall{}[v:B].
uiff(v  \mmember{}  rec-bind-class(X;Y)  a(e);\mdownarrow{}v  \mmember{}  X  a(e)
\mvee{}  (\mexists{}a':A.  (a'  \mmember{}  Y  a(e)  \mwedge{}  v  \mmember{}  X  a'(e)))
\mvee{}  (\mexists{}e':E
\mexists{}a':A
((e'  <loc  e)
\mwedge{}  a'  \mmember{}  Y  a(e')
\mwedge{}  v  \mmember{}  rec-bind-class(X;Y)  a'(e))))
supposing  not-self-starting\{i:l\}(Info;A;Y)

Date html generated: 2015_07_22-PM-00_27_06
Last ObjectModification: 2015_02_04-PM-05_13_30

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