Nuprl Lemma : max1-ilf

([es:EO']. [e:E].
   v:. {v  max_exch_Input()(e)  v  Base([int];)(e)  (a:Id. <a, v>  Base(``max_exch exchange``;Id  )(e))})
 ([A,B:Id]. [es:EO']. [e:E]. [i:Id]. [m:Message].
     {<i, m>  max_exch_main(A;B)(e)
      ((loc(e) = A)  (loc(e) = B))
          (b1:
              (b1  Memory-class(x,state.imax(x;state);loc.{0};max_exch_Input())(e)
               (m = make-Msg(``max_exch exchange``;Id  ;<loc(e), b1>))))
          (b:. <i, b>  Base(``max_exch exchange``;Id  )(e))})


Proof not projected




Definitions occuring in Statement :  max_exch_main: max_exch_main(A;B),  max_exch_Input: max_exch_Input(),  Memory-class: Memory-class(f;init;X),  make-Msg: make-Msg(hdr;typ;val),  base-headers-msg-val: Base(hdr;typ),  Message: Message,  classrel: v  X(e),  event-ordering+: EO+(Info),  es-loc: loc(e),  es-E: E,  Id: Id,  imax: imax(a;b),  sq_or: a  b,  uall: [x:A]. B[x],  guard: {T},  all: x:A. B[x],  exists: x:A. B[x],  iff: P  Q,  squash: T,  and: P  Q,  lambda: x.A[x],  pair: <a, b>,  product: x:A  B[x],  cons: [car / cdr],  nil: [],  natural_number: $n,  int: ,  token: "$token",  equal: s = t,  single-bag: {x}
Definitions :  and: P  Q,  uall: [x:A]. B[x],  all: x:A. B[x],  guard: {T},  iff: P  Q,  classrel: v  X(e),  sq_or: a  b,  exists: x:A. B[x],  member: t  T,  squash: T,  or: P  Q,  prop: ,  name: Name,  cand: A c B,  implies: P  Q,  rev_implies: P  Q,  true: True,  so_lambda: x.t[x],  bag-member: x  bs,  max_exch_int'base: max_exch_int'base(),  max_exch_exchange'base: max_exch_exchange'base(),  max_exch_Input: max_exch_Input(),  let: let,  subtype: S  T,  top: Top,  label: ...$L... t,  suptype: suptype(S; T),  max_exch_exchange'send: max_exch_exchange'send(),  max_exch_Maximum: max_exch_Maximum(),  max_exch_Exchange: max_exch_Exchange(),  max_exch_main: max_exch_main(A;B),  so_apply: x[s],  rev_uimplies: rev_uimplies(P;Q),  uiff: uiff(P;Q),  uimplies: b supposing a,  pi1: fst(t),  pi2: snd(t)
Lemmas :  classrel_wf,  Message_wf,  base-headers-msg-val_wf,  exists_wf,  Id_wf,  true_wf,  false_wf,  or_wf,  squash_wf,  sq_or_wf,  bag-member_wf,  single-bag_wf,  parallel-class_wf,  max_exch_int'base_wf,  simple-loc-comb-1_wf,  concat-lifting-loc-1_wf,  max_exch_exchange'base_wf,  max_exch_Input_wf,  es-E_wf,  event-ordering+_inc,  event-ordering+_wf,  and_true_l,  exists-elim,  trivial-eq,  sq_or_squash3,  bag-member-single-weak,  parallel-classrel-weak,  simple-loc-comb-1-concat-classrel-weak,  exists-product1,  equal_wf,  es-loc_wf,  product-valueall-type,  Id-valueall-type,  int-valueall-type,  valueall-type_wf,  Memory-class_wf,  imax_wf,  make-Msg_wf,  max_exch_exchange'send_wf,  simple-loc-comb-2_wf,  concat-lifting-loc-2_wf,  max_exch_Maximum_wf,  let_wf,  top_wf,  bag_wf,  eclass_wf2,  class-at_wf,  max_exch_Exchange_wf,  cons-bag_wf,  max_exch_main_wf,  squash_and,  squash_true,  pi1_wf_top,  pi2_wf,  simple-loc-comb-2-concat-classrel-weak,  classrel-at,  bag-member-cons

(\mforall{}[es:EO'].  \mforall{}[e:E].
      \mforall{}v:\mBbbZ{}
          \{v  \mmember{}  max\_exch\_Input()(e)
          \mLeftarrow{}{}\mRightarrow{}  v  \mmember{}  Base([int];\mBbbZ{})(e)  \mdownarrow{}\mvee{}  (\mexists{}a:Id.  <a,  v>  \mmember{}  Base(``max\_exch  exchange``;Id  \mtimes{}  \mBbbZ{})(e))\})
\mwedge{}  (\mforall{}[A,B:Id].  \mforall{}[es:EO'].  \mforall{}[e:E].  \mforall{}[i:Id].  \mforall{}[m:Message].
          \{<i,  m>  \mmember{}  max\_exch\_main(A;B)(e)
          \mLeftarrow{}{}\mRightarrow{}  ((loc(e)  =  A)  \mdownarrow{}\mvee{}  (loc(e)  =  B))
                  \mwedge{}  (\mdownarrow{}\mexists{}b1:\mBbbZ{}
                            (b1  \mmember{}  Memory-class(\mlambda{}x,state.imax(x;state);\mlambda{}loc.\{0\};max\_exch\_Input())(e)
                            \mwedge{}  (m  =  make-Msg(``max\_exch  exchange``;Id  \mtimes{}  \mBbbZ{};<loc(e),  b1>))))
                  \mwedge{}  (\mdownarrow{}\mexists{}b:\mBbbZ{}.  <i,  b>  \mmember{}  Base(``max\_exch  exchange``;Id  \mtimes{}  \mBbbZ{})(e))\})


Date html generated: 2012_02_20-PM-05_18_26
Last ObjectModification: 2012_02_17-PM-03_41_01

Home Index