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

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

Proof

Definitions occuring in Statement :  simple-comb-1: `F|X|` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-E: `E` uall: `∀[x:A]. B[x]` exists: `∃x:A. B[x]` iff: `P `⇐⇒` Q` squash: `↓T` and: `P ∧ Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` concat-lifting-1: `f@` bag-member: `x ↓∈ bs` bag: `bag(T)`
Lemmas :  simple-comb-1-concat-classrel classrel_wf simple-comb-1_wf concat-lifting-1_wf squash_wf exists_wf bag-member_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf bag_wf

Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[f:B  {}\mrightarrow{}  bag(C)].  \mforall{}[X:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:C].
(v  \mmember{}  f@|X|(e)  \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}\mexists{}b:B.  (v  \mdownarrow{}\mmember{}  f  b  \mwedge{}  b  \mmember{}  X(e)))

Date html generated: 2015_07_22-PM-00_10_57
Last ObjectModification: 2015_01_28-AM-11_40_27

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