Nuprl Lemma : State-loc-comb-fun-eq-non-loc

[Info,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
  (State-loc-comb(init;f;X)(e) State-comb(init;f loc(e);X)(e) ∈ B) supposing 
     (single-valued-classrel(es;X;A) and 
     (∀l:Id. single-valued-bag(init l;B)) and 
     (∀l:Id. (1 ≤ #(init l))))


Definitions occuring in Statement :  State-loc-comb: State-loc-comb(init;f;X) State-comb: State-comb(init;f;X) classfun: X(e) single-valued-classrel: single-valued-classrel(es;X;T) 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] le: A ≤ B all: x:A. B[x] apply: a function: x:A ─→ B[x] natural_number: $n universe: Type equal: t ∈ T single-valued-bag: single-valued-bag(b;T) bag-size: #(bs) bag: bag(T)
Lemmas :  classrel-classfun State-comb_wf es-loc_wf State-comb-functional classfun_wf State-loc-comb_wf State-loc-comb-functional State-loc-comb-classrel-non-loc single-valued-classrel_wf all_wf Id_wf single-valued-bag_wf le_wf bag-size_wf nat_wf es-E_wf event-ordering+_subtype eclass_wf bag_wf

\mforall{}[Info,B,A:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].
    (State-loc-comb(init;f;X)(e)  =  State-comb(init;f  loc(e);X)(e))  supposing 
          (single-valued-classrel(es;X;A)  and 
          (\mforall{}l:Id.  single-valued-bag(init  l;B))  and 
          (\mforall{}l:Id.  (1  \mleq{}  \#(init  l))))

Date html generated: 2015_07_22-PM-00_24_12
Last ObjectModification: 2015_01_28-AM-10_09_54

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