### 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 ∈ B) 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

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 ∈ T` lifting-2: `lifting-2(f)` 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-class-opt-1_wf lifting-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-class-opt-1-classrel simple-comb-2-classrel primed-class-opt_wf primed-class-opt-classrel 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 es-locl-trichotomy and_wf

Latex:
\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: 2015_07_22-PM-00_16_26
Last ObjectModification: 2015_01_28-AM-10_45_20

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