### Nuprl Lemma : Accum-classrel-Memory

`∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].`
`  (v ∈ Accum-class(f;init;X)(e) `⇐⇒` ↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Memory-class(f;init;X)(e) ∧ (v = (f a b) ∈ B)))`

Proof

Definitions occuring in Statement :  Memory-class: `Memory-class(f;init;X)` Accum-class: `Accum-class(f;init;X)` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-E: `E` Id: `Id` uall: `∀[x:A]. B[x]` exists: `∃x:A. B[x]` iff: `P `⇐⇒` Q` squash: `↓T` and: `P ∧ Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` equal: `s = t ∈ T` bag: `bag(T)`
Lemmas :  Accum-classrel-Memory-sq squash_wf exists_wf classrel_wf Memory-class_wf eclass_wf es-E_wf event-ordering+_subtype bag-member_wf lifting-2_wf iff_wf Accum-class_wf event-ordering+_wf Id_wf bag_wf bag-member-lifting-2

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

Date html generated: 2015_07_22-PM-00_11_27
Last ObjectModification: 2015_01_28-AM-11_41_06

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