Nuprl Lemma : Memory-class-invariant-sv

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


Proof




Definitions occuring in Statement :  Memory-class: Memory-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-locl: (e <loc e') es-loc: loc(e) es-E: E Id: Id uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] implies:  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 :  Memory-classrel2 decidable__assert es-first_wf2 sq_stable__bag-member iterated-classrel-invariant es-pred_wf bag-member_wf es-loc_wf es-pred-locl es-locl_transitivity1 prior-iterated-classrel_wf classrel_wf es-le_wf sq_stable__single-valued-iterated-classrel single-valued-bag_wf squash_wf true_wf bag_wf es-pred-loc-base iff_weakening_equal Memory-class_wf all_wf event-ordering+_subtype es-E_wf es-locl_wf single-valued-classrel_wf event-ordering+_wf eclass_wf Id_wf es-loc-pred and_wf equal_wf

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



Date html generated: 2015_07_22-PM-00_13_10
Last ObjectModification: 2015_07_16-AM-09_39_46

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