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Datei: lim_of_composition.pvs   Sprache: Lisp

Original von: PVS©

(integral_diff_doms
 (int_diff_dom_TCC1 0
  (int_diff_dom_TCC1-1 nil 3319997019
   ("" (skosimp*)
    (("" (lemma "connected_domain")
      (("" (inst - "x!1" "y!1" "z!1") (("" (assertnil nil)) nil))
      nil))
    nil)
   ((connected_domain formula-decl nil integral_diff_doms nil)) nil))
 (int_diff_dom_TCC2 0
  (int_diff_dom_TCC2-1 nil 3319997019
   ("" (lemma "not_one_element") (("" (skosimp*) nil nil)) nil)
   ((not_one_element formula-decl nil integral_diff_doms nil)) nil))
 (int_diff_dom_TCC3 0
  (int_diff_dom_TCC3-1 nil 3319997019
   ("" (lemma "con_dom_U") (("" (skosimp*) nil nil)) nil)
   ((con_dom_U formula-decl nil integral_diff_doms nil)) nil))
 (int_diff_dom_TCC4 0
  (int_diff_dom_TCC4-1 nil 3319997019
   ("" (lemma "not_one_U ") (("" (skosimp*) nil nil)) nil)
   ((not_one_U formula-decl nil integral_diff_doms nil)) nil))
 (int_diff_dom_TCC5 0
  (int_diff_dom_TCC5-1 nil 3319997019
   ("" (lemma "connected_domain")
    (("" (expand "connected?")
      (("" (skosimp*)
        (("" (inst - "a!1" "b!1" "x!1") (("" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((connected? const-decl "bool" deriv_domain_def nil)
    (number nonempty-type-decl nil numbers nil)
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    (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)
    (T_pred const-decl "[real -> boolean]" integral_diff_doms nil)
    (T formal-nonempty-subtype-decl nil integral_diff_doms nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (connected_domain formula-decl nil integral_diff_doms nil))
   nil))
 (int_diff_dom_TCC6 0
  (int_diff_dom_TCC6-1 nil 3319997019
   ("" (lemma "con_dom_U")
    (("" (expand "connected?")
      (("" (skosimp*)
        (("" (inst - "a!1" "b!1" "x!1") (("" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((connected? const-decl "bool" deriv_domain_def nil)
    (number nonempty-type-decl nil numbers nil)
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    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
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    (real nonempty-type-from-decl nil reals nil)
    (U_pred const-decl "[real -> boolean]" integral_diff_doms nil)
    (U formal-nonempty-subtype-decl nil integral_diff_doms nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (con_dom_U formula-decl nil integral_diff_doms nil))
   nil))
 (int_diff_dom 0
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   ("" (skosimp*)
    (("" (expand "integrable?")
      (("" (skosimp*)
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                                                                             1
                                                                             :hide?
                                                                             t)
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                                                                                (("3"
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                                                                                  (("3"
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                                                                                      (("3"
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                                                                                         "a!1"
                                                                                         "b!1"
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                                                                                        (("3"
                                                                                          (assert)
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                                                                       -12
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                                                                            (("2"
                                                                              (inst
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                                                                               "a!1"
                                                                               "b!1"
                                                                               "xis!1(n!1)")
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                                                                     ("3"
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                                                                              (hide
                                                                               2)
                                                                              (("3"
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                                                                                (("3"
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                                                                                  (("3"
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                                                                                     "a!1"
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                                                                                    (("3"
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                                                                     ("4"
                                                                      (hide
                                                                       2
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                                                                          (assert)
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                                                                   ("2"
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                                                                     -11
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                                                                            (("2"
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                                                                               "a!1"
                                                                               "b!1"
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                                                                          (("3"
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                                                                            (("3"
                                                                              (inst
                                                                               -
                                                                               "a!1"
                                                                               "b!1"
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                                                              (lemma
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                                                              (("1"
                                                                (expand
                                                                 "connected?")
                                                                (("1"
                                                                  (inst
                                                                   -
                                                                   "a!1"
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                                                                   "xis!1(x1!1)")
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                                                                    (assert)
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                                                           "xis!1")
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                                                            (assert)
                                                            (("2"
                                                              (expand
                                                               "xis?")
                                                              (("2"
                                                                (assert)
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                                                                  (skosimp*)
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                                         ("2"
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                                      nil)
                                     ("2"
                                      (prop)
                                      (("2"
                                        (skosimp*)
                                        (("2"
                                          (lemma "parts_order[T]")
                                          (("2"
                                            (inst
                                             -
                                             "a!1"
                                             "b!1"
                                             "P!1"
                                             "0"
                                             "x1!1")
                                            (("2"
                                              (assert)
                                              (("2"
                                                (case-replace
                                                 "x1!1 = 0")
                                                (("1" (assertnil nil)
                                                 ("2"
                                                  (assert)
                                                  (("2"
                                                    (lemma "con_dom_U")
                                                    (("2"
                                                      (expand
                                                       "connected?")
                                                      (("2"
                                                        (inst
                                                         -
                                                         "a!1"
                                                         "b!1"
                                                         "P!1`seq(x1!1)")
                                                        (("2"
                                                          (assert)
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                        nil))
                      nil))
                    nil)
                   ("2" (hide 2)
                    (("2" (lemma "integral_def[U]")
                      (("1" (inst?) (("1" (assertnil nil)) nil)
                       ("2" (lemma "not_one_U")
                        (("2" (propax) nil nil)) nil)
                       ("3" (lemma "con_dom_U")
                        (("3" (propax) nil nil)) nil))
                      nil))
                    nil)
                   ("3" (lemma "not_one_U") (("3" (propax) nil nil))
                    nil)
                   ("4" (lemma "con_dom_U") (("4" (propax) nil nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (lemma "not_one_element")
              (("2" (lemma "connected_domain")
                (("2" (lemma "not_one_U") (("2" (propax) nil nil))
                  nil))
                nil))
              nil)
             ("3" (lemma "con_dom_U") (("3" (propax) nil nil)) nil))
            nil)
           ("2" (lemma "connected_domain")
            (("2" (lemma "not_one_element") (("2" (propax) nil nil))
              nil))
            nil)
           ("3" (lemma "connected_domain") (("3" (propax) nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((integrable? const-decl "bool" integral_def nil)
    (T formal-nonempty-subtype-decl nil integral_diff_doms nil)
    (T_pred const-decl "[real -> boolean]" integral_diff_doms nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (integral_def formula-decl nil integral_def nil)
    (connected? const-decl "bool" deriv_domain_def nil)
    (not_one_element? const-decl "bool" deriv_domain_def nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (not_one_element formula-decl nil integral_diff_doms nil)
    (connected_domain formula-decl nil integral_diff_doms nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (parts_order formula-decl nil integral_def nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (width const-decl "posreal" integral_def nil)
    (Riemann_sum? const-decl "bool" integral_def nil)
    (g!1 skolem-const-decl "[U -> real]" integral_diff_doms nil)
    (f!1 skolem-const-decl "[T -> real]" integral_diff_doms nil)
    (R!1 skolem-const-decl "(Riemann_sum?(a!1, b!1, P!1, f!1))"
     integral_diff_doms nil)
    (xis? const-decl "bool" integral_def nil)
    (xis!1 skolem-const-decl "(xis?(a!1, b!1, P!1))" integral_diff_doms
     nil)
    (real_times_real_is_real application-judgement "real" reals nil)
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    (<= const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
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--> --------------------

--> maximum size reached

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

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