### Nuprl Lemma : State-loc-comb-exists

`∀[Info,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].`
`  ↓∃v:B. v ∈ State-loc-comb(init;f;X)(e) supposing #(init loc(e)) > 0`

Proof

Definitions occuring in Statement :  State-loc-comb: `State-loc-comb(init;f;X)` 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]` gt: `i > j` exists: `∃x:A. B[x]` squash: `↓T` apply: `f a` function: `x:A ─→ B[x]` natural_number: `\$n` universe: `Type` bag-size: `#(bs)` bag: `bag(T)`
Lemmas :  State-comb-exists State-loc-comb-classrel-non-loc classrel_wf State-loc-comb_wf gt_wf bag-size_wf es-loc_wf event-ordering+_subtype nat_wf es-E_wf event-ordering+_wf eclass_wf Id_wf bag_wf

Latex:
\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)].
\mforall{}[e:E].
\mdownarrow{}\mexists{}v:B.  v  \mmember{}  State-loc-comb(init;f;X)(e)  supposing  \#(init  loc(e))  >  0

Date html generated: 2015_07_22-PM-00_23_53
Last ObjectModification: 2015_01_28-AM-10_10_52

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