### Nuprl Lemma : simple-loc-comb-1-concat-classrel

`∀[Info,A,B:Type]. ∀[f:Id ─→ A ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].`
`  uiff(v ∈ f@(Loc, X)(e);↓∃a:A. (a ∈ X(e) ∧ v ↓∈ f loc(e) a))`

Proof

Definitions occuring in Statement :  concat-lifting-loc-1: `f@` simple-loc-comb-1: `F(Loc, X)` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-loc: `loc(e)` 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 :  simple-loc-comb1-concat-classrel classrel_wf simple-loc-comb-1_wf concat-lifting-loc-1_wf squash_wf exists_wf bag-member_wf es-loc_wf event-ordering+_subtype es-E_wf event-ordering+_wf eclass_wf Id_wf bag_wf

Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:B].
uiff(v  \mmember{}  f@(Loc,  X)(e);\mdownarrow{}\mexists{}a:A.  (a  \mmember{}  X(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  loc(e)  a))

Date html generated: 2015_07_22-PM-00_10_52
Last ObjectModification: 2015_01_28-AM-11_40_55

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