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Datei: product_finite_measure.prf   Sprache: Lisp

Original von: PVS©

(product_finite_measure
 (x_section_bounded_TCC1 0
  (x_section_bounded_TCC1-1 nil 3450064167
   ("" (skosimp)
    (("" (expand "x_section")
      ((""
        (lemma "x_section_measurable[T1,T2]"
         ("Z" "M!1" "x" "x1!1" "S1" "S1" "S2" "S2"))
        (("" (expand "member") (("" (propax) nil nil)) nil)) nil))
      nil))
    nil)
   ((x_section const-decl "[T1 -> set[T2]]" cross_product "topology/")
    (member const-decl "bool" sets nil)
    (x_section_measurable formula-decl nil product_sigma_def nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (setof type-eq-decl nil defined_types nil)
    (setofsets type-eq-decl nil sets nil)
    (sigma_algebra? const-decl "bool" subset_algebra_def nil)
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def nil)
    (S1 formal-const-decl "sigma_algebra[T1]" product_finite_measure
     nil)
    (S2 formal-const-decl "sigma_algebra[T2]" product_finite_measure
     nil)
    (set type-eq-decl nil sets nil)
    (sigma_times const-decl "sigma_algebra[[T1, T2]]" product_sigma_def
     nil)
    (T1 formal-type-decl nil product_finite_measure nil)
    (T2 formal-type-decl nil product_finite_measure nil))
   nil))
 (x_section_bounded 0
  (x_section_bounded-1 nil 3450064365
   ("" (skosimp)
    (("" (expand "o ")
      (("" (split)
        (("1" (assertnil nil)
         ("2" (expand "x_section")
          (("2"
            (lemma "x_section_measurable[T1,T2]"
             ("Z" "M!1" "x" "x!1" "S1" "S1" "S2" "S2"))
            (("2" (expand "member")
              (("2"
                (lemma "fm_monotone[T2,S2,nu!1]"
                 ("A" "x_section(M!1, x!1)" "B" "fullset[T2]"))
                (("2" (split)
                  (("1" (propax) nil nil)
                   ("2" (expand "subset?")
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                          (("2" (propax) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
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   ((O const-decl "T3" function_props nil)
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    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (subset_algebra_fullset name-judgement "(S)" product_finite_measure
     nil)
    (fm_monotone formula-decl nil finite_measure nil)
    (x_section const-decl "set[T2]" cross_product "topology/")
    (fullset const-decl "set" sets nil)
    (number nonempty-type-decl nil numbers nil)
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     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
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    (>= const-decl "bool" reals nil)
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    (finite_measure nonempty-type-eq-decl nil generalized_measure_def
     nil)
    (x_section_measurable formula-decl nil product_sigma_def nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
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    (setofsets type-eq-decl nil sets nil)
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    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def nil)
    (S1 formal-const-decl "sigma_algebra[T1]" product_finite_measure
     nil)
    (S2 formal-const-decl "sigma_algebra[T2]" product_finite_measure
     nil)
    (set type-eq-decl nil sets nil)
    (sigma_times const-decl "sigma_algebra[[T1, T2]]" product_sigma_def
     nil)
    (T1 formal-type-decl nil product_finite_measure nil)
    (T2 formal-type-decl nil product_finite_measure nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
 (y_section_bounded_TCC1 0
  (y_section_bounded_TCC1-1 nil 3450064167
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      ((""
        (lemma "y_section_measurable[T1,T2]"
         ("Z" "M!1" "y" "x1!1" "S1" "S1" "S2" "S2"))
        (("" (expand "member") (("" (propax) nil nil)) nil)) nil))
      nil))
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    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def nil)
    (S1 formal-const-decl "sigma_algebra[T1]" product_finite_measure
     nil)
    (S2 formal-const-decl "sigma_algebra[T2]" product_finite_measure
     nil)
    (set type-eq-decl nil sets nil)
    (sigma_times const-decl "sigma_algebra[[T1, T2]]" product_sigma_def
     nil)
    (T1 formal-type-decl nil product_finite_measure nil)
    (T2 formal-type-decl nil product_finite_measure nil))
   nil))
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            (("2" (expand "member")
              (("2"
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                 ("a" "y_section(M!1, y!1)" "b" "fullset[T1]"))
                (("1" (split)
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                    (("1" (expand "x_le") (("1" (propax) nil nil))
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                        nil))
                      nil))
                    nil))
                  nil)
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                    (("2" (propax) nil nil)) nil))
                  nil)
                 ("3" (expand "measurable_set?")
                  (("3" (propax) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
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   ((O const-decl "T3" function_props nil)
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    (member const-decl "bool" sets nil)
    (x_le const-decl "bool" extended_nnreal "extended_nnreal/")
    (subset? const-decl "bool" sets nil)
    (subset_algebra_fullset name-judgement "(S)" product_finite_measure
     nil)
    (m_monotone formula-decl nil measure_props nil)
    (measurable_set? const-decl "bool" measure_space_def nil)
    (measurable_set nonempty-type-eq-decl nil measure_space_def nil)
    (y_section const-decl "set[T1]" cross_product "topology/")
    (fullset const-decl "set" sets nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (finite_measure? const-decl "bool" generalized_measure_def nil)
    (finite_measure nonempty-type-eq-decl nil generalized_measure_def
     nil)
    (extended_nnreal nonempty-type-eq-decl nil extended_nnreal
     "extended_nnreal/")
    (measure? const-decl "bool" generalized_measure_def nil)
    (measure_type nonempty-type-eq-decl nil generalized_measure_def
     nil)
    (to_measure const-decl "measure_type" generalized_measure_def nil)
    (y_section_measurable formula-decl nil product_sigma_def nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (setof type-eq-decl nil defined_types nil)
    (setofsets type-eq-decl nil sets nil)
    (sigma_algebra? const-decl "bool" subset_algebra_def nil)
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def nil)
    (S1 formal-const-decl "sigma_algebra[T1]" product_finite_measure
     nil)
    (S2 formal-const-decl "sigma_algebra[T2]" product_finite_measure
     nil)
    (set type-eq-decl nil sets nil)
    (sigma_times const-decl "sigma_algebra[[T1, T2]]" product_sigma_def
     nil)
    (T1 formal-type-decl nil product_finite_measure nil)
    (T2 formal-type-decl nil product_finite_measure nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
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  (x_section_measurable-1 nil 3430980741
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        (("1" (hide-all-but 1)
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            (("1"
              (name "U"
                    "{M:set[[T1,T2]] | sigma_times(S1,S2)(M) & measurable_function?[T1,S1](F(M))}")
              (("1"
                (case "forall (R:measurable_rectangle(S1,S2)): U(R)")
                (("1"
                  (case "FORALL (a, b: (U)): disjoint?(a,b) => U(union(a, b))")
                  (("1" (case "FORALL (a: (U)): U(complement(a))")
                    (("1" (case "monotone?(U)")
                      (("1" (lemma "monotone_class" ("C" "U"))
                        (("1" (typepred "rectangle_algebra")
                          (("1" (typepred "M!1")
                            (("1" (inst -3 "rectangle_algebra")
                              (("1"
                                (split -3)
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                                  (expand "subset?")
                                  (("1"
                                    (inst - "M!1")
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                                          nil)
                                         ("2"
                                          (hide 2)
                                          (("2"
                                            (expand "sigma_times" -1)
                                            (("2"
                                              (lemma
                                               "generated_sigma_algebra_subset2"
                                               ("X"
                                                "extend
                                  [setof[[T1, T2]],
                                   measurable_rectangle[T1, T2](S1, S2),
                                   bool, FALSE]
                                  (fullset
                                       [measurable_rectangle
                                        [T1, T2](S1, S2)])"
                                                "Y"
                                                "generated_sigma_algebra(rectangle_algebra)"))
                                              (("2"
                                                (name-replace
                                                 "SA"
                                                 "generated_sigma_algebra(extend
                                  [setof[[T1, T2]],
                                   measurable_rectangle[T1, T2](S1, S2),
                                   bool, FALSE]
                                  (fullset
                                       [measurable_rectangle
                                        [T1, T2](S1, S2)]))")
                                                (("2"
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                                                                    "rectangle_algebra"))
                                                                  (("2"
                                                                    (expand
                                                                     "subset?")
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                                                                      (inst
                                                                       -
                                                                       "x!1")
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                                                                           (-1
                                                                            1))
                                                                          (("2"
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                                                                            (("2"
                                                                              (expand
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                                                                                         +
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                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
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                                            (("2"
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                                                           "forall (n:nat): U(IUnion(n,E!1))")
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                                                              (("2"
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                                                                 :hide?
                                                                 t)
                                                                (("2"
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                                                                  (("2"
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                                                                    (("2"
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                                                                              (("1"
                                                                                (case-replace
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                                                                                (("1"
                                                                                  (inst
                                                                                   +
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                                                                                     +
                                                                                     "i!1")
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                                                                                       "(x!2,x!3)")
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--> --------------------

--> maximum size reached

--> --------------------

¤ Dauer der Verarbeitung: 0.53 Sekunden  (vorverarbeitet)  ¤





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