Nuprl Lemma : max_exch_inc_nax

es:EO'. e1,e2:E. n1,n2:.
  ((n,s:. e:E. (e1 loc e   (e <loc e2)  n  max_exch_Input()(e)  s  max_exch_Maximum()(e)  (s < n)))
   (e1 <loc e2)
   n1  max_exch_Maximum()(e1)
   n2  max_exch_Maximum()(e2)
   (n1 < n2))


Proof not projected




Definitions occuring in Statement :  max_exch_Maximum: max_exch_Maximum() max_exch_Input: max_exch_Input() Message: Message classrel: v  X(e) event-ordering+: EO+(Info) es-le: e loc e'  es-locl: (e <loc e') es-E: E all: x:A. B[x] exists: x:A. B[x] implies: P  Q and: P  Q less_than: a < b int:
Definitions :  all: x:A. B[x] implies: P  Q exists: x:A. B[x] and: P  Q max_exch_Input: max_exch_Input() imax: imax(a;b) prop: trans: Trans(T;x,y.E[x; y]) not: A member: t  T so_lambda: x.t[x] cand: A c B ifthenelse: if b then t else f fi  btrue: tt uiff: uiff(P;Q) assert: b false: False bfalse: ff max_exch_int'base: max_exch_int'base() max_exch_exchange'base: max_exch_exchange'base() name: Name name_eq: name_eq(x;y) name-deq: NameDeq list-deq: list-deq(eq) band: p  q atom-deq: AtomDeq eq_atom: x =a y max_exch_Maximum: max_exch_Maximum() uall: [x:A]. B[x] so_apply: x[s1;s2] bool: unit: Unit uimplies: b supposing a le: A  B guard: {T} so_apply: x[s] it: subtype: S  T
Lemmas :  Memory-class-progress Message_wf imax_wf single-bag_wf Id_wf max_exch_Input_wf decidable__lt less_than_wf sq_stable_from_decidable le_int_wf bool_wf uiff_transitivity equal_wf assert_wf le_wf eqtt_to_assert assert_of_le_int lt_int_wf bnot_wf eqff_to_assert assert_functionality_wrt_uiff bnot_of_le_int assert_of_lt_int not_wf classrel_wf Memory-class_wf es-locl_wf event-ordering+_inc es-le_wf parallel-class-single-val max_exch_int'base_wf simple-loc-comb-1_wf concat-lifting-loc-1_wf max_exch_exchange'base_wf disjoint-classrel-symm simple-loc-comb-1-concat-disjoint-classrel base-disjoint-classrel assert-name_eq name_wf simple-loc-comb-1-concat-single-val single-valued-classrel-base single-valued-bag-single es-E_wf exists_wf max_exch_Maximum_wf event-ordering+_wf

\mforall{}es:EO'.  \mforall{}e1,e2:E.  \mforall{}n1,n2:\mBbbZ{}.
    ((\mexists{}n,s:\mBbbZ{}
          \mexists{}e:E
            (e1  \mleq{}loc  e    \mwedge{}  (e  <loc  e2)  \mwedge{}  n  \mmember{}  max\_exch\_Input()(e)  \mwedge{}  s  \mmember{}  max\_exch\_Maximum()(e)  \mwedge{}  (s  <  n)))
    {}\mRightarrow{}  (e1  <loc  e2)
    {}\mRightarrow{}  n1  \mmember{}  max\_exch\_Maximum()(e1)
    {}\mRightarrow{}  n2  \mmember{}  max\_exch\_Maximum()(e2)
    {}\mRightarrow{}  (n1  <  n2))


Date html generated: 2012_02_20-PM-05_17_10
Last ObjectModification: 2012_02_17-PM-03_08_11

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