Nuprl Lemma : simple-loc-comb-2-concat-classrel-weak

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


Proof




Definitions occuring in Statement :  concat-lifting-loc-2: f@Loc simple-loc-comb-2: (Loc,X, Y) 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-2-concat-classrel classrel_wf simple-loc-comb-2_wf concat-lifting-loc-2_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,C:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  bag(C)].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].
\mforall{}[e:E].  \mforall{}[v:C].
    (v  \mmember{}  f@Loc  o  (Loc,X,  Y)(e)  \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}\mexists{}a:A.  \mexists{}b:B.  (a  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Y(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  loc(e)  a  b))



Date html generated: 2015_07_22-PM-00_10_51
Last ObjectModification: 2015_01_28-AM-11_40_33

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