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: ⇐⇒ Q squash: T and: P ∧ Q apply: a function: x:A ─→ B[x] universe: Type equal: 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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