{ es:EO. e1,e2,b:E.
    [Q,P:{e:E| loc(e) = loc(e1)}   {e:E| loc(e) = loc(e1)}   ].
      ((e1 <loc b)
       b loc e2 
       [e1;pred(b)]~([a,b].P[a;b])*[a,b].P[a;b]
       [b;e2]~([a,b].P[a;b])*[a,b].Q[a;b]
       [e1;e2]~([a,b].P[a;b])*[a,b].Q[a;b]) }

{ Proof }



Definitions occuring in Statement :  es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b] es-le: e loc e'  es-locl: (e <loc e') es-pred: pred(e) es-loc: loc(e) es-E: E event_ordering: EO Id: Id uall: [x:A]. B[x] prop: so_apply: x[s1;s2] all: x:A. B[x] implies: P  Q set: {x:A| B[x]}  function: x:A  B[x] equal: s = t
Definitions :  all: x:A. B[x] uall: [x:A]. B[x] prop: implies: P  Q es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b] so_apply: x[s1;s2] exists: x:A. B[x] int_seg: {i..j} and: P  Q member: t  T cand: A c B lelt: i  j < k le: A  B not: A false: False so_lambda: x y.t[x; y] assert: b bfalse: ff ifthenelse: if b then t else f fi  btrue: tt squash: T true: True rev_implies: P  Q iff: P  Q es-locl: (e <loc e') nat_plus: uimplies: b supposing a sq_type: SQType(T) guard: {T} bool: unit: Unit it:
Lemmas :  int_seg_wf le_wf es-le_wf es-locl_wf Id_wf es-loc_wf es-pstar-q_wf es-E_wf es-pred_wf subtype_base_sq bool_subtype_base false_wf event_ordering_wf es-le-loc es-locl-first es-loc-pred bool_wf lt_int_wf assert_wf le_int_wf bnot_wf iff_weakening_uiff uiff_transitivity eqtt_to_assert assert_of_lt_int eqff_to_assert assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int int_subtype_base nat_plus_properties int_seg_properties es-le-trans2 es-pred-locl member_wf es-first_wf squash_wf not_wf

\mforall{}es:EO.  \mforall{}e1,e2,b:E.
    \mforall{}[Q,P:\{e:E|  loc(e)  =  loc(e1)\}    {}\mrightarrow{}  \{e:E|  loc(e)  =  loc(e1)\}    {}\mrightarrow{}  \mBbbP{}].
        ((e1  <loc  b)
        {}\mRightarrow{}  b  \mleq{}loc  e2 
        {}\mRightarrow{}  [e1;pred(b)]\msim{}([a,b].P[a;b])*[a,b].P[a;b]
        {}\mRightarrow{}  [b;e2]\msim{}([a,b].P[a;b])*[a,b].Q[a;b]
        {}\mRightarrow{}  [e1;e2]\msim{}([a,b].P[a;b])*[a,b].Q[a;b])


Date html generated: 2011_08_16-AM-10_57_35
Last ObjectModification: 2011_06_18-AM-09_30_30

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