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Datei: continuity_ms.prf   Sprache: Lisp

Original von: PVS©

(continuity_ms
 (IMP_continuity_ms_def_TCC1 0
  (IMP_continuity_ms_def_TCC1-1 nil 3459678538
   ("" (rewrite "fullset_metric_space1"nil nil)
   ((fullset_metric_space1 formula-decl nil continuity_ms nil)) nil))
 (IMP_continuity_ms_def_TCC2 0
  (IMP_continuity_ms_def_TCC2-1 nil 3459678538
   ("" (rewrite "fullset_metric_space2"nil nil)
   ((fullset_metric_space2 formula-decl nil continuity_ms nil)) nil))
 (image_inverse_image 0
  (image_inverse_image-1 nil 3293835710
   ("" (skosimp*)
    (("" (expand "restrict")
      (("" (expand "subset?")
        (("" (expand "image")
          (("" (expand "inverse_image")
            (("" (expand "extend")
              (("" (expand "member")
                (("" (skosimp*)
                  (("" (typepred "x!2")
                    (("" (replace -5 -2)
                      (("" (simplify -2) (("" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((restrict const-decl "R" restrict nil)
    (image const-decl "set[R]" function_image nil)
    (extend const-decl "R" extend nil) (set type-eq-decl nil sets nil)
    (T1 formal-nonempty-type-decl nil continuity_ms nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (member const-decl "bool" sets nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (subset? const-decl "bool" sets nil))
   shostak))
 (inverse_image_image 0
  (inverse_image_image-1 nil 3293835874
   ("" (expand "subset?")
    (("" (expand "extend")
      (("" (expand "inverse_image")
        (("" (expand "member")
          (("" (expand "image")
            (("" (skosimp*)
              (("" (inst -1 "x!1")
                (("" (assert)
                  (("" (inst - "f!1(x!1)")
                    (("" (case-replace "T!1(f!1(x!1))")
                      (("1" (replace -3)
                        (("1" (assert)
                          (("1" (inst + "x!1")
                            (("1" (expand "restrict")
                              (("1" (propax) nil nil)) nil))
                            nil))
                          nil))
                        nil)
                       ("2" (assertnil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((extend const-decl "R" extend nil)
    (member const-decl "bool" sets nil)
    (x!1 skolem-const-decl "T1" continuity_ms nil)
    (X!1 skolem-const-decl "set[T1]" continuity_ms nil)
    (S!1 skolem-const-decl "set[T1]" continuity_ms nil)
    (restrict const-decl "R" restrict nil)
    (T2 formal-nonempty-type-decl nil continuity_ms nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T1 formal-nonempty-type-decl nil continuity_ms nil)
    (image const-decl "set[R]" function_image nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (subset? const-decl "bool" sets nil))
   shostak))
 (continuous_open_sets 0
  (continuous_open_sets-3 nil 3459689578
   ("" (skosimp*)
    (("" (prop)
      (("1" (expand "continuous?")
        (("1" (expand "continuous_at?")
          (("1" (skeep)
            (("1" (expand "open_in?")
              (("1" (prop)
                (("1" (skosimp*)
                  (("1" (case "inverse_image(f!1,Y)(s!1)")
                    (("1" (expand "subset?")
                      (("1" (expand "member")
                        (("1" (expand "intersection")
                          (("1" (expand "member")
                            (("1" (expand "ball")
                              (("1"
                                (expand "inverse_image")
                                (("1"
                                  (expand "member")
                                  (("1"
                                    (inst - "s!1")
                                    (("1"
                                      (expand "open?")
                                      (("1"
                                        (expand "interior")
                                        (("1"
                                          (expand "interior_point?")
                                          (("1"
                                            (expand "subset?")
                                            (("1"
                                              (expand "ball")
                                              (("1"
                                                (decompose-equality)
                                                (("1"
                                                  (expand "member")
                                                  (("1"
                                                    (inst - "f!1(s!1)")
                                                    (("1"
                                                      (iff)
                                                      (("1"
                                                        (prop)
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (copy -5)
                                                            (("1"
                                                              (inst
                                                               -
                                                               "r!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   +
                                                                   "delta!1")
                                                                  (("1"
                                                                    (skosimp*)
                                                                    (("1"
                                                                      (prop)
                                                                      (("1"
                                                                        (inst
                                                                         -
                                                                         "x!1")
                                                                        (("1"
                                                                          (prop)
                                                                          (("1"
                                                                            (inst
                                                                             -
                                                                             "f!1(x!1)")
                                                                            (("1"
                                                                              (prop)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (typepred "s!1")
                                      (("2"
                                        (expand "inverse_image")
                                        (("2"
                                          (expand "intersection")
                                          (("2"
                                            (expand "member")
                                            (("2" (prop) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (typepred "s!1")
                      (("2" (expand "intersection")
                        (("2" (expand "member") (("2" (prop) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand "subset?")
                  (("2" (expand "member")
                    (("2" (expand "intersection")
                      (("2" (expand "member")
                        (("2" (skosimp*) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "continuous?")
        (("2" (skosimp*)
          (("2" (typepred "x!1")
            (("2" (expand "continuous_at?")
              (("2" (expand "member")
                (("2" (expand "ball")
                  (("2" (expand "open_in?")
                    (("2" (expand "subset?")
                      (("2" (expand "intersection")
                        (("2" (expand "inverse_image")
                          (("2" (expand "member")
                            (("2" (expand "ball")
                              (("2"
                                (skosimp*)
                                (("2"
                                  (case
                                   "open?[T2,d2](ball[T2,d2](f!1(x!1),epsilon!1))")
                                  (("1"
                                    (inst
                                     -
                                     "ball[T2,d2](f!1(x!1),epsilon!1)")
                                    (("1"
                                      (prop)
                                      (("1"
                                        (inst - "x!1")
                                        (("1"
                                          (skosimp*)
                                          (("1"
                                            (inst + "r!1")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (inst - "y!1")
                                                (("1"
                                                  (prop)
                                                  (("1"
                                                    (expand "ball")
                                                    (("1"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (typepred "y!1")
                                                    (("2"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "inverse_image")
                                          (("2"
                                            (expand "intersection")
                                            (("2"
                                              (expand "member")
                                              (("2"
                                                (expand "ball")
                                                (("2"
                                                  (lemma
                                                   "fullset_metric_space2")
                                                  (("2"
                                                    (expand
                                                     "metric_space?")
                                                    (("2"
                                                      (expand
                                                       "space_zero?")
                                                      (("2"
                                                        (prop)
                                                        (("2"
                                                          (inst
                                                           -
                                                           "f!1(x!1)"
                                                           "f!1(x!1)")
                                                          (("1"
                                                            (prop)
                                                            (("1"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (expand
                                                             "fullset")
                                                            (("2"
                                                              (propax)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (lemma "ball_open[T2,d2]")
                                    (("2"
                                      (inst - "epsilon!1" "f!1(x!1)")
                                      nil
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((continuous_at? const-decl "bool" continuity_ms_def nil)
    (open_in? const-decl "bool" metric_spaces nil)
    (subset? const-decl "bool" sets nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (open? const-decl "bool" metric_spaces nil)
    (interior_point? const-decl "bool" metric_spaces nil)
    (x!1 skolem-const-decl "T1" continuity_ms nil)
    (d2 formal-const-decl "[T2, T2 -> nnreal]" continuity_ms nil)
    (nnreal type-eq-decl nil real_types nil)
    (< const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans 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)
    (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)
    (number nonempty-type-decl nil numbers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (interior const-decl "set[T]" metric_spaces nil)
    (s!1 skolem-const-decl "(intersection(inverse_image(f!1, Y), S!1))"
     continuity_ms nil)
    (Y skolem-const-decl "set[T2]" continuity_ms nil)
    (f!1 skolem-const-decl "[T1 -> T2]" continuity_ms nil)
    (S!1 skolem-const-decl "set[T1]" continuity_ms nil)
    (member const-decl "bool" sets nil)
    (T1 formal-nonempty-type-decl nil continuity_ms nil)
    (T2 formal-nonempty-type-decl nil continuity_ms nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (intersection const-decl "set" sets nil)
    (continuous? const-decl "bool" continuity_ms_def nil)
    (fullset_metric_space2 formula-decl nil continuity_ms nil)
    (space_zero? const-decl "bool" metric_spaces_def nil)
    (fullset const-decl "set" sets nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (metric_space? const-decl "bool" metric_spaces_def nil)
    (epsilon!1 skolem-const-decl "posreal" continuity_ms nil)
    (x!1 skolem-const-decl "(S!1)" continuity_ms nil)
    (ball_open formula-decl nil metric_spaces nil))
   nil)
  (continuous_open_sets-2 nil 3459689494
   ("" (skosimp*)
    (("" (prop)
      (("1" (expand "continuous?")
        (("1" (expand "continuous_at?")
          (("1" (skeep)
            (("1" (expand "open?" +)
              (("1" (expand "interior")
                (("1" (apply-extensionality)
                  (("1" (hide 2)
                    (("1" (case "inverse_image(f!1,Y)(x!1)")
                      (("1" (assert)
                        (("1" (expand "interior_point?")
                          (("1" (expand "subset?")
                            (("1" (expand "member")
                              (("1"
                                (inst - "x!1")
                                (("1"
                                  (expand "inverse_image")
                                  (("1"
                                    (expand "member")
                                    (("1"
                                      (expand "open?")
                                      (("1"
                                        (expand "interior")
                                        (("1"
                                          (decompose-equality)
                                          (("1"
                                            (inst - "f!1(x!1)")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (expand
                                                 "interior_point?")
                                                (("1"
                                                  (skosimp*)
                                                  (("1"
                                                    (inst - "r!1")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (inst
                                                         +
                                                         "delta!1")
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (expand
                                                             "ball")
                                                            (("1"
                                                              (inst
                                                               -
                                                               "x!2")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (expand
                                                                   "subset?")
                                                                  (("1"
                                                                    (expand
                                                                     "member")
                                                                    (("1"
                                                                      (inst
                                                                       -
                                                                       "f!1(x!2)")
                                                                      (("1"
                                                                        (assert)
                                                                        nil)))))))))
                                                               ("2"
                                                                (expand
                                                                 "fullset[T1]")
                                                                (("2"
                                                                  (propax)
                                                                  nil)))))))))))))))))))))))))))))))))
                                 ("2"
                                  (expand "fullset[T1]")
                                  (("2" (propax) nil)))))))))))))
                       ("2" (assertnil)))))
                   ("2" (lemma fullset_metric_space1)
                    (("2" (propax) nil)))))))))))))))
       ("2" (expand "continuous?")
        (("2" (expand "continuous_at?")
          (("2" (expand "member")
            (("2" (expand "ball")
              (("2" (skosimp*)
                (("2" (lemma "ball_open[T2,d2]")
                  (("2" (inst - "epsilon!1" "f!1(x!1)")
                    (("2"
                      ("" (skosimp*) (prop)
                       (("1" (expand "continuous?")
                         (expand "continuous_at?") (skeep)
                         (expand "open_in?") (prop)
                         (("1" (skosimp*)
                           (case "inverse_image(f!1,Y)(s!1)")
                           (("1" (expand "subset?") (expand "member")
                             (expand "intersection") (expand "member")
                             (expand "ball") (expand "inverse_image")
                             (expand "member") (inst - "s!1")
                             (("1" (expand "open?") (expand "interior")
                               (expand "interior_point?")
                               (expand "subset?") (expand "ball")
                               (decompose-equality) (expand "member")
                               (inst - "f!1(s!1)") (iff) (prop)
                               (skosimp*) (copy -5) (inst - "r!1")
                               (skosimp*) (inst + "delta!1") (skosimp*)
                               (prop) (inst - "x!1") (prop)
                               (inst - "f!1(x!1)") (prop))
                              ("2" (typepred "s!1")
                               (expand "inverse_image")
                               (expand "intersection")
                               (expand "member") (prop))))
                            ("2" (typepred "s!1")
                             (expand "intersection") (expand "member")
                             (prop))))
                          ("2" (expand "subset?") (expand "member")
                           (expand "intersection") (expand "member")
                           (skosimp*))))
                        ("2" (expand "continuous?") (skosimp*)
                         (typepred "x!1") (expand "continuous_at?")
                         (expand "member") (expand "ball")
                         (expand "open_in?") (expand "subset?")
                         (expand "intersection")
                         (expand "inverse_image") (expand "member")
                         (expand "ball") (skosimp*)
                         (case "open?[T2,d2](ball[T2,d2](f!1(x!1),epsilon!1))")
                         (("1"
                           (inst - "ball[T2,d2](f!1(x!1),epsilon!1)")
                           (prop) (inst - "x!1")
                           (("1" (skosimp*) (inst + "r!1") (skosimp*)
                             (inst - "y!1") (prop)
                             (("1" (expand "ball") (propax))
                              ("2" (typepred "y!1") (propax))))
                            ("2" (expand "inverse_image")
                             (expand "intersection") (expand "member")
                             (expand "ball")
                             (lemma "fullset_metric_space2")
                             (expand "metric_space?")
                             (expand "space_zero?") (prop)
                             (inst - "f!1(x!1)" "f!1(x!1)")
                             (("1" (prop) (assert))
                              ("2" (expand "fullset") (propax))))))
                          ("2" (lemma "ball_open[T2,d2]")
                           (inst - "epsilon!1" "f!1(x!1)"))))))
                      nil))))))))))))))))))
    nil)
   nil nil)
  (continuous_open_sets-1 nil 3459597870
   ("" (skosimp*)
    (("" (prop)
      (("1" (expand "continuous?")
        (("1" (expand "continuous_at?")
          (("1" (skeep)
            (("1" (expand "open?" +)
              (("1" (expand "interior")
                (("1" (apply-extensionality)
                  (("1" (hide 2)
                    (("1" (case "inverse_image(f!1,Y)(x!1)")
                      (("1" (assert)
                        (("1" (expand "interior_point?")
                          (("1" (expand "subset?")
                            (("1" (expand "member")
                              (("1"
                                (inst - "x!1")
                                (("1"
                                  (expand "inverse_image")
                                  (("1"
                                    (expand "member")
                                    (("1"
                                      (expand "open?")
                                      (("1"
                                        (expand "interior")
                                        (("1"
                                          (decompose-equality)
                                          (("1"
                                            (inst - "f!1(x!1)")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (expand
                                                 "interior_point?")
                                                (("1"
                                                  (skosimp*)
                                                  (("1"
                                                    (inst - "r!1")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (inst
                                                         +
                                                         "delta!1")
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (expand
                                                             "ball")
                                                            (("1"
                                                              (inst
                                                               -
                                                               "x!2")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (expand
                                                                   "subset?")
                                                                  (("1"
                                                                    (expand
                                                                     "member")
                                                                    (("1"
                                                                      (inst
                                                                       -
                                                                       "f!1(x!2)")
                                                                      (("1"
                                                                        (assert)
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (expand
                                                                 "fullset[T1]")
                                                                (("2"
                                                                  (propax)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (expand "fullset[T1]")
                                  (("2" (propax) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (assertnil nil))
                      nil))
                    nil)
                   ("2" (lemma fullset_metric_space1)
                    (("2" (propax) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "continuous?")
        (("2" (expand "continuous_at?")
          (("2" (expand "member")
            (("2" (expand "ball")
              (("2" (skosimp*)
                (("2" (lemma "ball_open[T2,d2]")
                  (("2" (inst - "epsilon!1" "f!1(x!1)")
                    (("2" (inst - "ball[T2,d2](f!1(x!1),epsilon!1)")
                      (("2" (assert)
                        (("2" (hide -1)
                          (("2" (expand "open?")
                            (("2" (expand "interior")
                              (("2"
                                (expand "interior_point?")
                                (("2"
                                  (expand "subset?")
                                  (("2"
                                    (expand "ball")
                                    (("2"
                                      (expand "member")
                                      (("2"
                                        (decompose-equality)
                                        (("2"
                                          (inst - "x!1")
                                          (("2"
                                            (expand "inverse_image")
                                            (("2"
                                              (expand "member")
                                              (("2"
                                                (lemma
                                                 "fullset_metric_space2")
                                                (("2"
                                                  (expand
                                                   "metric_space?")
                                                  (("2"
                                                    (prop)
                                                    (("2"
                                                      (expand
                                                       "space_zero?")
                                                      (("2"
                                                        (inst
                                                         -
                                                         "f!1(x!1)"
                                                         "f!1(x!1)")
                                                        (("1"
                                                          (prop)
                                                          (("1"
                                                            (assert)
                                                            (("1"
                                                              (skosimp*)
                                                              (("1"
                                                                (inst
                                                                 +
                                                                 "r!1")
                                                                (("1"
                                                                  (skosimp*)
                                                                  (("1"
                                                                    (inst
                                                                     -
                                                                     "y!1")
                                                                    (("1"
                                                                      (assert)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("2"
                                                          (expand
                                                           "fullset")
                                                          (("2"
                                                            (propax)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((space_zero? const-decl "bool" metric_spaces_def nil)
    (ball_open formula-decl nil metric_spaces nil)
    (interior const-decl "set[T]" metric_spaces nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (metric_space? const-decl "bool" metric_spaces_def nil)
    (interior_point? const-decl "bool" metric_spaces nil)
    (open? const-decl "bool" metric_spaces nil))
   shostak))
 (continuous_closed_sets 0
  (continuous_closed_sets-1 nil 3293836724
   ("" (skosimp*)
    (("" (lemma "continuous_open_sets")
      (("" (inst - "S!1" "f!1")
        (("" (replace -1)
          (("" (hide -1)
            (("" (prop)
              (("1" (skosimp*)
                (("1" (expand "closed?")
                  (("1" (expand "closed_in?")
                    (("1" (inst - "complement(Y!1)")
                      (("1" (prop)
                        (("1"
                          (case "inverse_image(f!1, complement(Y!1)) = complement(intersection
                                       (inverse_image(f!1, Y!1), S!1))")
                          (("1" (replace -1) (("1" (propax) nil nil))
                            nil)
                           ("2" (lemma "demorgan2[T1]")
                            (("2"
                              (inst - "inverse_image(f!1,Y!1)" "S!1")
                              (("2"
                                (replace -1)
                                (("2" (grind) nil nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (grind) nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (skosimp*)
                (("2" (expand "closed?")
                  (("2" (expand "closed_in?")
                    (("2" (inst - "complement(Y!1)")
                      (("2" (lemma "complement_complement[T2]")
                        (("2" (inst - "Y!1")
                          (("2" (replace -1)
                            (("2" (prop)
                              (("2"
                                (hide -2 -3 -4 -5 -6 -7 -8 -9)
                                (("2"
                                  (case
                                   "intersection(complement(intersection
                                       (inverse_image
                                        (f!1, complement(Y!1)),
                                        S!1)),
                            S!1) = intersection(inverse_image(f!1, Y!1), S!1)")
                                  (("1"
                                    (replace -1)
                                    (("1" (propax) nil nil))
                                    nil)
                                   ("2"
                                    (hide-all-but 1)
                                    (("2"
                                      (apply-extensionality)
                                      (("2" (grind) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((continuous_open_sets formula-decl nil continuity_ms nil)
    (closed? const-decl "bool" metric_spaces nil)
    (complement const-decl "set" sets nil)
    (intersection const-decl "set" sets nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (member const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (union const-decl "set" sets nil)
    (subset? const-decl "bool" sets nil)
    (open_in? const-decl "bool" metric_spaces nil)
    (open? const-decl "bool" metric_spaces nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (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)
    (number nonempty-type-decl nil numbers 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_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (s!1 skolem-const-decl
     "(intersection(union(complement(inverse_image(f!1, Y!1)), complement(S!1)),
              S!1))" continuity_ms nil)
    (S!1 skolem-const-decl "set[T1]" continuity_ms nil)
    (f!1 skolem-const-decl "[T1 -> T2]" continuity_ms nil)
    (Y!1 skolem-const-decl "set[T2]" continuity_ms nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (demorgan2 formula-decl nil sets_lemmas nil)
    (closed_in? const-decl "bool" metric_spaces nil)
    (complement_complement formula-decl nil sets_lemmas nil)
    (T2 formal-nonempty-type-decl nil continuity_ms nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-nonempty-type-decl nil continuity_ms nil))
   shostak)))


¤ Dauer der Verarbeitung: 0.32 Sekunden  (vorverarbeitet)  ¤





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