### Nuprl Lemma : Accum-loc-class-exists

`∀[Info,B,A:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)].`
`  ((↓∃x:B. x ↓∈ init loc(e)) `` (↓∃u:A. u ∈ X(e)) `` (↓∃v:B. v ∈ Accum-loc-class(f;init;X)(e)))`

Proof

Definitions occuring in Statement :  Accum-loc-class: `Accum-loc-class(f;init;X)` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-loc: `loc(e)` es-E: `E` Id: `Id` uall: `∀[x:A]. B[x]` exists: `∃x:A. B[x]` squash: `↓T` implies: `P `` Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` bag-member: `x ↓∈ bs` bag: `bag(T)`
Lemmas :  primed-class-opt-exists Accum-loc-class_wf rec-combined-loc-class-opt-1-classrel simple-loc-comb-2-classrel primed-class-opt_wf rec-combined-loc-class-opt-1_wf lifting-loc-2_wf classrel_wf exists_wf squash_wf bag-member_wf es-loc_wf event-ordering+_subtype eclass_wf es-E_wf event-ordering+_wf Id_wf bag_wf

Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
\mforall{}[X:EClass(A)].
((\mdownarrow{}\mexists{}x:B.  x  \mdownarrow{}\mmember{}  init  loc(e))  {}\mRightarrow{}  (\mdownarrow{}\mexists{}u:A.  u  \mmember{}  X(e))  {}\mRightarrow{}  (\mdownarrow{}\mexists{}v:B.  v  \mmember{}  Accum-loc-class(f;init;X)(e)))

Date html generated: 2015_07_22-PM-00_18_06
Last ObjectModification: 2015_01_28-AM-10_42_55

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