Nuprl Lemma : eclass0-classrel

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

Proof

Definitions occuring in Statement :  eclass0: `(f o 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 :  squash_wf exists_wf bag-member_wf es-loc_wf iff_weakening_uiff bag-combine_wf bag-member-combine uiff_wf classrel_wf eclass0_wf event-ordering+_subtype es-E_wf event-ordering+_wf Id_wf bag_wf eclass_wf
\mforall{}[Info,B,C:Type].  \mforall{}[X:EClass(B)].  \mforall{}[f:Id  {}\mrightarrow{}  B  {}\mrightarrow{}  bag(C)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:C].
uiff(v  \mmember{}  (f  o  X)(e);\mdownarrow{}\mexists{}b:B.  (b  \mmember{}  X(e)  \mwedge{}  v  \mdownarrow{}\mmember{}  f  loc(e)  b))

Date html generated: 2015_07_17-PM-00_35_32
Last ObjectModification: 2015_01_27-PM-11_29_55

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