{ [Info,T:Type].
    S:Id List. G:Graph(S). F:information-flow(T;S). es:EO+(Info).
    X:EClass(T). e:E(X). i:Id.
      ((i  S)
       es-interface-locs-list(es;X;S)
       flow-graph(S;T;F;G)
       (loc(e)i)G supposing information-flow-relation(es;X;F;e;i)) }

{ Proof }



Definitions occuring in Statement :  information-flow-relation: information-flow-relation(es;X;F;e;i),  es-interface-locs-list: es-interface-locs-list(es;X;S),  es-E-interface: E(X),  eclass: EClass(A[eo; e]),  event-ordering+: EO+(Info),  flow-graph: flow-graph(S;T;F;G),  information-flow: information-flow(T;S),  es-loc: loc(e),  id-graph-edge: (ij)G,  id-graph: Graph(S),  Id: Id,  uimplies: b supposing a,  uall: [x:A]. B[x],  all: x:A. B[x],  implies: P  Q,  list: type List,  universe: Type,  l_member: (x  l)
Definitions :  lambda: x.A[x],  axiom: Ax,  int: ,  unit: Unit,  fpf: a:A fp-> B[a],  le: A  B,  ge: i  j ,  event_ordering: EO,  es-E: E,  es-loc: loc(e),  es-interface-predecessors: (X)(e),  strong-subtype: strong-subtype(A;B),  eq_atom: x =a y,  eq_atom: eq_atom$n(x;y),  atom: Atom$n,  dep-isect: Error :dep-isect,  record+: record+,  null: null(as),  not: A,  and: P  Q,  uiff: uiff(P;Q),  subtype_rel: A r B,  subtype: S  T,  suptype: suptype(S; T),  length: ||as||,  natural_number: $n,  less_than: a < b,  union: left + right,  apply: f a,  eclass-vals: X(L),  bool: ,  can-apply: can-apply(f;x),  void: Void,  false: False,  true: True,  decide: case b of inl(x) => s[x] | inr(y) => t[y],  ifthenelse: if b then t else f fi ,  assert: b,  nat: ,  product: x:A  B[x],  exists: x:A. B[x],  id-graph-edge: (ij)G,  set: {x:A| B[x]} ,  information-flow-relation: information-flow-relation(es;X;F;e;i),  isect: x:A. B[x],  uimplies: b supposing a,  flow-graph: flow-graph(S;T;F;G),  uall: [x:A]. B[x],  equal: s = t,  member: t  T,  universe: Type,  list: type List,  id-graph: Graph(S),  information-flow: information-flow(T;S),  event-ordering+: EO+(Info),  eclass: EClass(A[eo; e]),  so_lambda: x y.t[x; y],  es-E-interface: E(X),  top: Top,  all: x:A. B[x],  l_member: (x  l),  Id: Id,  prop: ,  implies: P  Q,  function: x:A  B[x],  es-interface-locs-list: es-interface-locs-list(es;X;S),  Auto: Error :Auto,  Complete: Error :Complete,  Try: Error :Try,  CollapseTHENA: Error :CollapseTHENA,  CollapseTHEN: Error :CollapseTHEN,  tactic: Error :tactic,  isl: isl(x),  fpf-dom: x  dom(f),  rcv: rcv(l,tg),  locl: locl(a),  Knd: Knd,  proper-iseg: L1 < L2,  iseg: l1  l2,  add: n + m,  l_exists: (xL. P[x]),  multiply: n * m,  gt: i > j,  map: map(f;as),  nil: [],  tag-by: zT,  rev_implies: P  Q,  or: P  Q,  iff: P  Q,  record: record(x.T[x]),  fset: FSet{T},  isect2: T1  T2,  b-union: A  B,  fpf-sub: f  g,  deq: EqDecider(T),  ma-state: State(ds),  real: ,  grp_car: |g|,  class-program: ClassProgram(T),  fpf-cap: f(x)?z,  sqequal: s ~ t,  sq_type: SQType(T),  pair: <a, b>,  guard: {T},  atom: Atom,  es-base-E: es-base-E(es),  token: "$token",  record-select: r.x,  cand: A c B,  MaAuto: Error :MaAuto,  Unfold: Error :Unfold
Lemmas :  length-es-interface-vals,  es-interface-predecessors-nonempty,  nat_wf,  length_wf1,  es-base-E_wf,  subtype_rel_self,  subtype_rel_function,  length_wf_nat,  pos-length,  not_wf,  equal-nil-sq-nil,  l_member_length,  non_neg_length,  subtype_rel_sum,  isl_wf,  top_wf,  member_wf,  member_null,  Id_wf,  pos_length2,  can-apply_wf,  eclass-vals_wf,  bool_wf,  information-flow-relation_wf,  flow-graph_wf,  es-interface-locs-list_wf,  l_member_wf,  es-E-interface_wf,  eclass_wf,  event-ordering+_wf,  information-flow_wf,  id-graph_wf,  es-interface-predecessors_wf,  es-loc_wf,  event-ordering+_inc,  subtype_rel_wf,  es-interface-top,  es-E_wf,  true_wf,  false_wf

\mforall{}[Info,T:Type].
    \mforall{}S:Id  List.  \mforall{}G:Graph(S).  \mforall{}F:information-flow(T;S).  \mforall{}es:EO+(Info).  \mforall{}X:EClass(T).  \mforall{}e:E(X).  \mforall{}i:Id.
        ((i  \mmember{}  S)
        {}\mRightarrow{}  es-interface-locs-list(es;X;S)
        {}\mRightarrow{}  flow-graph(S;T;F;G)
        {}\mRightarrow{}  (loc(e){}\mrightarrow{}i)\mmember{}G  supposing  information-flow-relation(es;X;F;e;i))


Date html generated: 2011_08_16-PM-04_38_24
Last ObjectModification: 2011_06_20-AM-01_00_50

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