Nuprl Lemma : Accum-class-invariant

[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.
    ((∀s:B. SqStable(P[s]))
     (∀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 ∈ Accum-class(f;init;X)(e)
     P[v])


Proof




Definitions occuring in Statement :  Accum-class: Accum-class(f;init;X) 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 apply: a function: x:A ─→ B[x] universe: Type bag-member: x ↓∈ bs bag: bag(T)
Lemmas :  Accum-classrel-Memory Memory-class-invariant es-le_weakening classrel_wf es-locl_wf es-le-self Accum-class_wf all_wf bag-member_wf es-loc_wf event-ordering+_subtype es-E_wf es-le_wf sq_stable_wf event-ordering+_wf eclass_wf Id_wf bag_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.
        ((\mforall{}s:B.  SqStable(P[s]))
        {}\mRightarrow{}  (\mforall{}a:A.  \mforall{}e':E.    (e'  \mleq{}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{}  Accum-class(f;init;X)(e)
        {}\mRightarrow{}  P[v])



Date html generated: 2015_07_22-PM-00_18_14
Last ObjectModification: 2015_01_28-AM-10_43_08

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