{ [M:Type  Type]
    [m,n:]. [Ps:n  lvprocess(lp.M[lp];m)].
    [F:n  ((Id  process-input'(lp.M[lp];m)) List)
         ((Id  process-input'(lp.M[lp];m)) List)].
      (parallel-process(Ps;F)  lvprocess(lp.M[lp];m)) 
    supposing A,B:Type.  ((A r B)  (M[A] r M[B])) }

{ Proof }



Definitions occuring in Statement :  parallel-process: parallel-process(Ps;F) process-input': process-input'(lp.M[lp];n) lvprocess: lvprocess(lp.M[lp];n) Id: Id subtype_rel: A r B int_seg: {i..j} nat: uimplies: b supposing a uall: [x:A]. B[x] so_apply: x[s] all: x:A. B[x] implies: P  Q member: t  T function: x:A  B[x] product: x:A  B[x] list: type List natural_number: $n universe: Type
Definitions :  uall: [x:A]. B[x] uimplies: b supposing a all: x:A. B[x] implies: P  Q so_apply: x[s] nat: lvprocess: lvprocess(lp.M[lp];n) process-input': process-input'(lp.M[lp];n) member: t  T parallel-process: parallel-process(Ps;F) ycomb: Y so_lambda: x.t[x] subtype: S  T suptype: suptype(S; T) int_seg: {i..j} lelt: i  j < k and: P  Q prop:
Lemmas :  parallel-dataflow_wf nat_wf ifthenelse_wf le_int_wf top_wf lvprocess_wf Id_wf int_seg_wf le_wf process-input'_wf dataflow_wf nat_properties subtype_rel_self subtype_rel_list subtype_rel_simple_product dataflow_subtype

\mforall{}[M:Type  {}\mrightarrow{}  Type]
    \mforall{}[m,n:\mBbbN{}].  \mforall{}[Ps:\mBbbN{}n  {}\mrightarrow{}  lvprocess(lp.M[lp];m)].  \mforall{}[F:\mBbbN{}n  {}\mrightarrow{}  ((Id  \mtimes{}  process-input'(lp.M[lp];m))  List)
                                                                                                      {}\mrightarrow{}  ((Id  \mtimes{}  process-input'(lp.M[lp];m))  List)].
        (parallel-process(Ps;F)  \mmember{}  lvprocess(lp.M[lp];m)) 
    supposing  \mforall{}A,B:Type.    ((A  \msubseteq{}r  B)  {}\mRightarrow{}  (M[A]  \msubseteq{}r  M[B]))


Date html generated: 2011_08_17-PM-06_38_48
Last ObjectModification: 2011_06_18-PM-12_04_34

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