---

{ [M:Type  Type]
    [A:pEnvType(P.M[P])  pRunType(P.M[P])  ]
      n2m:  pMsg(P.M[P]). l2m:Id  pMsg(P.M[P]).
      S1,S2:InitialSystem(P.M[P]).
        [B1,B2:EO+(pMsg(P.M[P]))  ].
          (assuming(env,r.A[env;r])
            S1 |= eo.B1[eo]
           assuming(env,r.A[env;r])
              S2 |= eo.B2[eo]
           (S:InitialSystem(P.M[P])
                (sub-system(P.M[P];S1;S)
                 sub-system(P.M[P];S2;S)
                 assuming(env,r.A[env;r])
                    S |= eo.B1[eo]  B2[eo]))) 
    supposing Continuous+(P.M[P]) }

{ Proof }

---

Definitions occuring in Statement :  system-strongly-realizes: system-strongly-realizes,  sub-system: sub-system(P.M[P];S1;S2),  InitialSystem: InitialSystem(P.M[P]),  pEnvType: pEnvType(T.M[T]),  pRunType: pRunType(T.M[T]),  pMsg: pMsg(P.M[P]),  event-ordering+: EO+(Info),  Id: Id,  strong-type-continuous: Continuous+(T.F[T]),  nat: ,  uimplies: b supposing a,  uall: [x:A]. B[x],  prop: ,  so_apply: x[s1;s2],  so_apply: x[s],  all: x:A. B[x],  implies: P  Q,  and: P  Q,  function: x:A  B[x],  universe: Type
Definitions :  uall: [x:A]. B[x],  uimplies: b supposing a,  strong-type-continuous: Continuous+(T.F[T]),  so_apply: x[s],  prop: ,  all: x:A. B[x],  implies: P  Q,  system-strongly-realizes: system-strongly-realizes,  so_apply: x[s1;s2],  and: P  Q,  member: t  T,  ext-eq: A  B,  so_lambda: x.t[x],  so_lambda: x y.t[x; y],  system-realizes: system-realizes,  let: let,  InitialSystem: InitialSystem(P.M[P])
Lemmas :  nat_wf,  sub-system_wf,  InitialSystem_wf,  system-strongly-realizes_wf,  pRunType_wf,  pEnvType_wf,  event-ordering+_wf,  pMsg_wf,  Id_wf,  strong-type-continuous_wf,  sub-system_transitivity,  pRun_wf2

---

\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}[A:pEnvType(P.M[P])  {}\mrightarrow{}  pRunType(P.M[P])  {}\mrightarrow{}  \mBbbP{}]
        \mforall{}n2m:\mBbbN{}  {}\mrightarrow{}  pMsg(P.M[P]).  \mforall{}l2m:Id  {}\mrightarrow{}  pMsg(P.M[P]).  \mforall{}S1,S2:InitialSystem(P.M[P]).
            \mforall{}[B1,B2:EO+(pMsg(P.M[P]))  {}\mrightarrow{}  \mBbbP{}].
                (assuming(env,r.A[env;r])
                    S1  |=  eo.B1[eo]
                {}\mRightarrow{}  assuming(env,r.A[env;r])
                        S2  |=  eo.B2[eo]
                {}\mRightarrow{}  (\mforall{}S:InitialSystem(P.M[P])
                            (sub-system(P.M[P];S1;S)
                            {}\mRightarrow{}  sub-system(P.M[P];S2;S)
                            {}\mRightarrow{}  assuming(env,r.A[env;r])
                                    S  |=  eo.B1[eo]  \mwedge{}  B2[eo]))) 
    supposing  Continuous+(P.M[P])


Date html generated: 2011_08_17-PM-03_55_50
Last ObjectModification: 2011_06_18-AM-11_28_06

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