Nuprl Lemma : State-loc-comb-invariant-or

[Info,A,S:Type]. ∀[P:S ─→ ℙ].
  ∀init:Id ─→ bag(S). ∀f:Id ─→ A ─→ S ─→ S. ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:S.
    (((single-valued-bag(init loc(e);S) ∧ single-valued-classrel(es;X;A)) ∨ (∀s:S. SqStable(P[s])))
     (∀s:S. (s ↓∈ init loc(e)  P[s]))
     (∀a:A. ∀e':E.
          (e' ≤loc e   a ∈ X(e')  (∀s:S. (s ∈ Memory-loc-class(f;init;X)(e')  P[s]  P[f loc(e') s]))))
     v ∈ State-loc-comb(init;f;X)(e)
     P[v])


Proof




Definitions occuring in Statement :  State-loc-comb: State-loc-comb(init;f;X) Memory-loc-class: Memory-loc-class(f;init;X) single-valued-classrel: single-valued-classrel(es;X;T) classrel: v ∈ X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-le: e ≤loc e'  es-loc: loc(e) es-E: E Id: Id sq_stable: SqStable(P) uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] implies:  Q or: P ∨ Q and: P ∧ Q apply: a function: x:A ─→ B[x] universe: Type single-valued-bag: single-valued-bag(b;T) bag-member: x ↓∈ bs bag: bag(T)
Lemmas :  State-loc-comb-invariant-sv State-loc-comb-invariant classrel_wf State-loc-comb_wf all_wf es-E_wf event-ordering+_subtype es-le_wf Memory-loc-class_wf es-loc_wf bag-member_wf or_wf single-valued-bag_wf single-valued-classrel_wf sq_stable_wf event-ordering+_wf eclass_wf Id_wf bag_wf

Latex:
\mforall{}[Info,A,S:Type].  \mforall{}[P:S  {}\mrightarrow{}  \mBbbP{}].
    \mforall{}init:Id  {}\mrightarrow{}  bag(S).  \mforall{}f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  S  {}\mrightarrow{}  S.  \mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.  \mforall{}v:S.
        (((single-valued-bag(init  loc(e);S)  \mwedge{}  single-valued-classrel(es;X;A))  \mvee{}  (\mforall{}s:S.  SqStable(P[s])))
        {}\mRightarrow{}  (\mforall{}s:S.  (s  \mdownarrow{}\mmember{}  init  loc(e)  {}\mRightarrow{}  P[s]))
        {}\mRightarrow{}  (\mforall{}a:A.  \mforall{}e':E.
                    (e'  \mleq{}loc  e 
                    {}\mRightarrow{}  a  \mmember{}  X(e')
                    {}\mRightarrow{}  (\mforall{}s:S.  (s  \mmember{}  Memory-loc-class(f;init;X)(e')  {}\mRightarrow{}  P[s]  {}\mRightarrow{}  P[f  loc(e')  a  s]))))
        {}\mRightarrow{}  v  \mmember{}  State-loc-comb(init;f;X)(e)
        {}\mRightarrow{}  P[v])



Date html generated: 2015_07_22-PM-00_24_40
Last ObjectModification: 2015_01_28-AM-10_09_28

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