Nuprl Lemma : rec-combined-loc-class-opt-1-single-val0

[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[F:Id ─→ A ─→ B ─→ B]. ∀[X:EClass(A)]. ∀[init:Id ─→ bag(B)]. ∀[e:E]. ∀[v1,v2:B].
  (v1 v2 ∈ B) supposing 
     (v1 ∈ lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and 
     v2 ∈ lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and 
     single-valued-classrel(es;X;A) and 
     single-valued-bag(init loc(e);B))


Proof




Definitions occuring in Statement :  lifting-loc-2: lifting-loc-2(f) rec-combined-loc-class-opt-1: F|Loc, X, Prior(self)?init| single-valued-classrel: single-valued-classrel(es;X;T) classrel: v ∈ X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id uimplies: supposing a uall: [x:A]. B[x] apply: a function: x:A ─→ B[x] universe: Type equal: t ∈ T single-valued-bag: single-valued-bag(b;T) bag: bag(T)
Lemmas :  es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf classrel_wf rec-combined-loc-class-opt-1_wf lifting-loc-2_wf single-valued-classrel_wf single-valued-bag_wf es-loc_wf nat_wf decidable__le subtract_wf false_wf not-ge-2 less-iff-le condition-implies-le minus-one-mul zero-add minus-add minus-minus add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel decidable__lt es-causl_wf rec-combined-loc-class-opt-1-classrel simple-loc-comb-2-classrel primed-class-opt_wf primed-class-opt-classrel es-locl-trichotomy equal_wf zero-le-nat le_wf add-mul-special zero-mul event-ordering+_subtype es-E_wf Id_wf bag_wf eclass_wf event-ordering+_wf and_wf

Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[F:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[X:EClass(A)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
\mforall{}[e:E].  \mforall{}[v1,v2:B].
    (v1  =  v2)  supposing 
          (v1  \mmember{}  lifting-loc-2(F)|Loc,  X,  Prior(self)?init|(e)  and 
          v2  \mmember{}  lifting-loc-2(F)|Loc,  X,  Prior(self)?init|(e)  and 
          single-valued-classrel(es;X;A)  and 
          single-valued-bag(init  loc(e);B))



Date html generated: 2015_07_22-PM-00_16_52
Last ObjectModification: 2015_01_28-AM-10_44_52

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