{ [M:Type  Type]
    n2m:  pMsg(P.M[P]). l2m:Id  pMsg(P.M[P]). S0:System(P.M[P]).
    env:pEnvType(P.M[P]).
      let r = pRun(S0;env;n2m;l2m) in
          e:runEvents(r)
            (((fst(fst(run-info(r;e)))) < run-event-step(e))
             (m:lg-size(snd(S0))
                ((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m)))))) 
    supposing Continuous+(P.M[P]) }

{ Proof }



Definitions occuring in Statement :  run-event-step: run-event-step(e),  runEvents: runEvents(r),  run-info: run-info(r;e),  pRun: pRun(S0;env;nat2msg;loc2msg),  pEnvType: pEnvType(T.M[T]),  System: System(P.M[P]),  pMsg: pMsg(P.M[P]),  lg-label: lg-label(g;x),  lg-size: lg-size(g),  Id: Id,  strong-type-continuous: Continuous+(T.F[T]),  int_seg: {i..j},  nat: ,  let: let,  uimplies: b supposing a,  uall: [x:A]. B[x],  so_apply: x[s],  pi1: fst(t),  pi2: snd(t),  all: x:A. B[x],  exists: x:A. B[x],  or: P  Q,  less_than: a < b,  function: x:A  B[x],  product: x:A  B[x],  natural_number: $n,  int: ,  universe: Type,  equal: s = t
Definitions :  uall: [x:A]. B[x],  uimplies: b supposing a,  strong-type-continuous: Continuous+(T.F[T]),  so_apply: x[s],  all: x:A. B[x],  System: System(P.M[P]),  let: let,  pi1: fst(t),  run-event-step: run-event-step(e),  pi2: snd(t),  member: t  T,  ext-eq: A  B,  and: P  Q,  so_lambda: x.t[x],  top: Top,  subtype: S  T,  squash: T,  true: True,  nat: ,  Id: Id,  ldag: LabeledDAG(T),  spreadn: spread3,  pRun: pRun(S0;env;nat2msg;loc2msg),  or: P  Q,  le: A  B,  exists: x:A. B[x],  int_seg: {i..j},  assert: b,  is-run-event: is-run-event(r;t;x),  run-info: run-info(r;e),  implies: P  Q,  outl: outl(x),  ycomb: Y,  ifthenelse: if b then t else f fi ,  do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),  band: p  q,  isl: isl(x),  btrue: tt,  bfalse: ff,  prop: ,  false: False,  not: A,  fulpRunType: fulpRunType(T.M[T]),  lelt: i  j < k,  guard: {T},  runEvents: runEvents(r),  decidable: Dec(P),  sq_stable: SqStable(P),  pInTransit: pInTransit(P.M[P]),  lg-all: xG.P[x],  lg-is-source: lg-is-source(g;i),  bool: ,  unit: Unit,  iff: P  Q,  sq_type: SQType(T),  it:
Lemmas :  pRun-intransit-invariant,  nat_wf,  pRun_wf2,  decidable__assert,  is-run-event_wf,  pi1_wf_top,  Id_wf,  pi2_wf,  sq_stable__assert,  runEvents_wf,  pEnvType_wf,  System_wf,  pMsg_wf,  strong-type-continuous_wf,  eq_int_wf,  bool_wf,  iff_weakening_uiff,  uiff_transitivity,  assert_wf,  eqtt_to_assert,  assert_of_eq_int,  false_wf,  not_wf,  bnot_wf,  eqff_to_assert,  assert_of_bnot,  not_functionality_wrt_uiff,  pRun_wf,  subtype_rel_function,  unit_wf,  int_seg_wf,  nat_properties,  top_wf,  ldag_wf,  pInTransit_wf,  le_wf,  subtype_rel_simple_product,  subtype_rel_self,  fulpRunType_wf,  lg-is-source_wf_dag,  lt_int_wf,  lg-size_wf_dag,  lg-label_wf_dag,  eq_atom_wf,  com-kind_wf,  assert_of_eq_atom,  assert_witness,  decidable__lt,  lg-size_wf,  is-dag_wf,  subtype_base_sq,  product_subtype_base,  int_subtype_base,  atom2_subtype_base,  subtype_rel-ldag,  component_wf,  lg-all_wf,  le_int_wf,  bool_cases,  bool_subtype_base,  assert_of_lt_int,  assert_functionality_wrt_uiff,  bnot_of_lt_int,  assert_of_le_int,  squash_wf,  true_wf

\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}n2m:\mBbbN{}  {}\mrightarrow{}  pMsg(P.M[P]).  \mforall{}l2m:Id  {}\mrightarrow{}  pMsg(P.M[P]).  \mforall{}S0:System(P.M[P]).  \mforall{}env:pEnvType(P.M[P]).
        let  r  =  pRun(S0;env;n2m;l2m)  in
                \mforall{}e:runEvents(r)
                    (((fst(fst(run-info(r;e))))  <  run-event-step(e))
                    \mvee{}  (\mexists{}m:\mBbbN{}lg-size(snd(S0)).  ((fst(run-info(r;e)))  =  (fst(lg-label(snd(S0);m)))))) 
    supposing  Continuous+(P.M[P])


Date html generated: 2011_08_16-PM-07_03_59
Last ObjectModification: 2011_06_18-AM-11_17_24

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