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

[Info,B,C:Type]. ∀[f:B ─→ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
(v ∈ lifting-1(f)|X|(e) ⇐⇒ ↓∃b:B. ((v (f b) ∈ C) ∧ 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: ⇐⇒ Q squash: T and: P ∧ Q apply: a function: x:A ─→ B[x] universe: Type equal: t ∈ T lifting-1: lifting-1(f)
Lemmas :  simple-comb-1-classrel classrel_wf simple-comb-1_wf lifting-1_wf squash_wf exists_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf

Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[f:B  {}\mrightarrow{}  C].  \mforall{}[X:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:C].
(v  \mmember{}  lifting-1(f)|X|(e)  \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}\mexists{}b:B.  ((v  =  (f  b))  \mwedge{}  b  \mmember{}  X(e)))

Date html generated: 2015_07_22-PM-00_11_01
Last ObjectModification: 2015_01_28-AM-11_40_24

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