### Nuprl Lemma : State-comb-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 ∈ State-comb(init;f;X)(e) and `
`     v2 ∈ State-comb(init;f;X)(e) and `
`     single-valued-bag(init loc(e);B) and `
`     single-valued-classrel(es;X;A))`

Proof

Definitions occuring in Statement :  State-comb: `State-comb(init;f;X)` 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` single-valued-bag: `single-valued-bag(b;T)` bag: `bag(T)`
Lemmas :  State-comb-classrel iterated_classrel-single-val classrel_wf State-comb_wf single-valued-bag_wf es-loc_wf event-ordering+_subtype single-valued-classrel_wf es-E_wf Id_wf bag_wf eclass_wf event-ordering+_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{}  State-comb(init;f;X)(e)  and
v2  \mmember{}  State-comb(init;f;X)(e)  and
single-valued-bag(init  loc(e);B)  and
single-valued-classrel(es;X;A))

Date html generated: 2015_07_22-PM-00_21_34
Last ObjectModification: 2015_01_28-AM-10_13_03

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