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

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

Proof

Definitions occuring in Statement :  concat-lifting-loc-2: `f@Loc` simple-loc-comb-2: `F o (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` 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-comb2-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].
uiff(v  \mmember{}  f@Loc  o  (Loc,X,  Y)(e);\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_49
Last ObjectModification: 2015_01_28-AM-11_41_08

Home Index