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

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


Proof not projected




Definitions occuring in Statement :  rec-combined-class-opt-1: F|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: b supposing a uall: [x:A]. B[x] apply: f a function: x:A  B[x] universe: Type equal: s = t lifting-2: lifting-2(f) single-valued-bag: single-valued-bag(b;T) bag: bag(T)
Definitions :  so_lambda: x y.t[x; y] top: Top true: True squash: T false: False not: A le: A  B ge: i  j  nat: member: t  T all: x:A. B[x] implies: P  Q iff: P  Q rev_implies: P  Q and: P  Q exists: x:A. B[x] so_apply: x[s1;s2] or: P  Q uiff: uiff(P;Q) uimplies: b supposing a prop: uall: [x:A]. B[x] strongwellfounded: SWellFounded(R[x; y]) single-valued-classrel: single-valued-classrel(es;X;T) es-locl: (e <loc e') es-p-local-pred: es-p-local-pred(es;P) single-valued-bag: single-valued-bag(b;T) subtype: S  T guard: {T}
Lemmas :  event-ordering+_wf eclass_wf bag_wf Id_wf es-E_wf event-ordering+_inc es-loc_wf single-valued-bag_wf single-valued-classrel_wf lifting-2_wf rec-combined-class-opt-1_wf classrel_wf equal_wf primed-class-opt-classrel primed-class-opt_wf simple-comb-2-classrel rec-combined-class-opt-1-classrel es-causl_wf le_wf nat_wf less_than_wf ge_wf nat_properties es-causl-swellfnd and_wf es-locl-trichotomy

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


Date html generated: 2012_02_20-PM-02_56_43
Last ObjectModification: 2012_02_06-AM-00_10_32

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