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

[Info,A,B:Type]. ∀[f:Id ─→ A ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
(v ∈ f@(Loc, X)(e) ⇐⇒ ↓∃a:A. (a ∈ X(e) ∧ v ↓∈ 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 uall: [x:A]. B[x] exists: x:A. B[x] iff: ⇐⇒ Q squash: T and: P ∧ Q apply: a function: x:A ─→ B[x] universe: Type bag-member: x ↓∈ bs bag: bag(T)
Lemmas :  simple-loc-comb-1-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].
(v  \mmember{}  f@(Loc,  X)(e)  \mLeftarrow{}{}\mRightarrow{}  \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_53
Last ObjectModification: 2015_01_28-AM-11_40_45

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