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

`∀[Info,B,C:Type]. ∀[f:Id ─→ B ─→ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].`
`  (v ∈ lifting-loc-1(f)(Loc, X)(e) `⇐⇒` ↓∃b:B. (b ∈ X(e) ∧ (v = (f loc(e) b) ∈ C)))`

Proof

Definitions occuring in Statement :  lifting-loc-1: `lifting-loc-1(f)` simple-loc-comb-1: `F(Loc, X)` 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: `P `⇐⇒` Q` squash: `↓T` and: `P ∧ Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` equal: `s = t ∈ T`
Lemmas :  simple-loc-comb-1-classrel classrel_wf simple-loc-comb-1_wf lifting-loc-1_wf squash_wf exists_wf es-loc_wf event-ordering+_subtype es-E_wf event-ordering+_wf eclass_wf Id_wf

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

Date html generated: 2015_07_22-PM-00_08_43
Last ObjectModification: 2015_01_28-AM-11_41_23

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