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Datei: metric_space_real_fun.prf   Sprache: Lisp

Original von: PVS©

(metric_space_real_fun
 (IMP_continuity_ms_def_TCC1 0
  (IMP_continuity_ms_def_TCC1-1 nil 3462120666
   ("" (lemma "fullset_metric_space") (("" (propax) nil nil)) nil)
   ((fullset_metric_space formula-decl nil metric_space_real_fun nil))
   nil))
 (IMP_continuity_ms_def_TCC2 0
  (IMP_continuity_ms_def_TCC2-1 nil 3462120666
   ("" (lemma "real_metric_space")
    (("" (inst - "fullset[real]"nil nil)) nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil) (fullset const-decl "set" sets nil)
    (real_metric_space formula-decl nil real_metric_space nil))
   nil))
 (scal_continuous 0
  (scal_continuous-1 nil 3462120679
   ("" (skosimp*)
    (("" (expand "continuous?")
      (("" (skosimp*)
        (("" (inst - "x!1")
          (("" (expand "continuous_at?")
            (("" (skosimp*)
              (("" (case "c!1 = 0")
                (("1" (grind) nil nil)
                 ("2" (inst - "epsilon!1/abs(c!1)")
                  (("1" (skosimp*)
                    (("1" (inst + "delta!1")
                      (("1" (skosimp*)
                        (("1" (inst - "y!1")
                          (("1" (expand "member")
                            (("1" (expand "ball")
                              (("1"
                                (expand "*")
                                (("1"
                                  (expand "real_dist")
                                  (("1"
                                    (prop)
                                    (("1"
                                      (cross-mult -1)
                                      (("1"
                                        (lemma "abs_mult")
                                        (("1"
                                          (inst
                                           -
                                           "f!1(x!1) - f!1(y!1)"
                                           "c!1")
                                          (("1" (assertnil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (prop)
                    (("1" (cross-mult 1) (("1" (assertnil nil)) nil)
                     ("2" (cross-mult 1) (("2" (assertnil nil)) nil))
                    nil)
                   ("3" (assertnil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((continuous? const-decl "bool" continuity_ms_def nil)
    (T formal-nonempty-type-decl nil metric_space_real_fun nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (real_gt_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)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (c!1 skolem-const-decl "real" metric_space_real_fun nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (epsilon!1 skolem-const-decl "posreal" metric_space_real_fun nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (div_mult_pos_lt2 formula-decl nil real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (abs_nat formula-decl nil abs_lems "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (abs_mult formula-decl nil real_props nil)
    (div_mult_pos_gt1 formula-decl nil extra_real_props nil)
    (div_mult_pos_ge1 formula-decl nil real_props nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (member const-decl "bool" sets nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (real_dist const-decl "nnreal" real_metric_space nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (number nonempty-type-decl nil numbers nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (continuous_at? const-decl "bool" continuity_ms_def nil))
   shostak))
 (neg_continuous 0
  (neg_continuous-1 nil 3462121435
   ("" (skosimp*)
    (("" (lemma "scal_continuous")
      (("" (inst - "S!1" "-1" "f!1") (("" (grind) nil nil)) nil)) nil))
    nil)
   ((scal_continuous formula-decl nil metric_space_real_fun nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (member const-decl "bool" sets nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (real_dist const-decl "nnreal" real_metric_space nil)
    (d formal-const-decl "[T, T -> nnreal]" metric_space_real_fun nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (continuous_at? const-decl "bool" continuity_ms_def nil)
    (continuous? const-decl "bool" continuity_ms_def nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-nonempty-type-decl nil metric_space_real_fun nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil))
   shostak))
 (sum_continuous 0
  (sum_continuous-1 nil 3462121520
   ("" (skosimp*)
    (("" (expand "continuous?")
      (("" (skosimp*)
        (("" (inst - "x!1")
          (("" (inst - "x!1")
            (("" (expand "continuous_at?")
              (("" (skosimp*)
                (("" (inst - "epsilon!1/2")
                  (("" (inst - "epsilon!1/2")
                    (("" (skosimp*)
                      (("" (inst + "min(delta!1,delta!2)")
                        (("" (skosimp*)
                          (("" (inst - "y!1")
                            (("" (inst - "y!1")
                              ((""
                                (expand "member")
                                ((""
                                  (expand "ball")
                                  ((""
                                    (expand "real_dist")
                                    ((""
                                      (expand "+")
                                      ((""
                                        (lemma "triangle")
                                        ((""
                                          (inst
                                           -
                                           "f!1(x!1) - f!1(y!1)"
                                           "g!1(x!1) - g!1(y!1)")
                                          (("" (assertnil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((continuous? const-decl "bool" continuity_ms_def nil)
    (T formal-nonempty-type-decl nil metric_space_real_fun nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (continuous_at? const-decl "bool" continuity_ms_def nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (triangle formula-decl nil real_props nil)
    (real_dist const-decl "nnreal" real_metric_space nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (member const-decl "bool" sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posreal_min application-judgement
     "{z: posreal | z <= x AND z <= y}" real_defs nil))
   shostak))
 (diff_continuous 0
  (diff_continuous-2 nil 3462121763
   ("" (skosimp*)
    (("" (expand "continuous?")
      (("" (skosimp*)
        (("" (inst - "x!1")
          (("" (inst - "x!1")
            (("" (expand "continuous_at?")
              (("" (skosimp*)
                (("" (inst - "epsilon!1/2")
                  (("" (inst - "epsilon!1/2")
                    (("" (skosimp*)
                      (("" (inst + "min(delta!1,delta!2)")
                        (("" (skosimp*)
                          (("" (inst - "y!1")
                            (("" (inst - "y!1")
                              ((""
                                (expand "member")
                                ((""
                                  (expand "ball")
                                  ((""
                                    (expand "-")
                                    ((""
                                      (expand "real_dist")
                                      ((""
                                        (lemma "triangle")
                                        ((""
                                          (inst
                                           -
                                           "f!1(x!1) - f!1(y!1)"
                                           "-g!1(x!1) + g!1(y!1)")
                                          (("" (grind) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((continuous? const-decl "bool" continuity_ms_def nil)
    (T formal-nonempty-type-decl nil metric_space_real_fun nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (continuous_at? const-decl "bool" continuity_ms_def nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (ball const-decl "set[T]" metric_spaces nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_dist const-decl "nnreal" real_metric_space nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (triangle formula-decl nil real_props nil)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (member const-decl "bool" sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posreal_min application-judgement
     "{z: posreal | z <= x AND z <= y}" real_defs nil))
   nil)
  (diff_continuous-1 nil 3462121727
   (";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
    (skosimp*)
    ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
      (expand "continuous?")
      ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
        (skosimp*)
        ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
          (inst - "x!1")
          ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
            (inst - "x!1")
            ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
              (expand "continuous_at?")
              ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                (skosimp*)
                ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                  (inst - "epsilon!1/2")
                  ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                    (inst - "epsilon!1/2")
                    ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                      (skosimp*)
                      ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                        (inst + "min(delta!1,delta!2)")
                        ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                          (skosimp*)
                          ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                            (inst - "y!1")
                            ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                              (inst - "y!1")
                              ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                (expand "member")
                                ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                  (expand "ball")
                                  ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                    (expand "real_dist")
                                    ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                      (expand "+")
                                      ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                        (lemma "triangle")
                                        ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                          (inst
                                           -
                                           "f!1(x!1) - f!1(y!1)"
                                           "g!1(x!1) - g!1(y!1)")
                                          ((";;; Proof sum_continuous-1 for formula metric_space_real_fun.sum_continuous"
                                            (assert)
                                            nil))))))))))))))))))))))))))))))))))))))))
    ";;; developed with shostak decision procedures")
   nil nil))
 (prod_continuous 0
  (prod_continuous-2 nil 3462270340
   ("" (skosimp*)
    (("" (expand "continuous?")
      (("" (skosimp*)
        (("" (inst - "x!1")
          (("" (inst - "x!1")
            (("" (expand "continuous_at?")
              (("" (skosimp*)
                (("" (case "g!1(x!1) = 0")
                  (("1" (inst - "1")
                    (("1" (inst - "epsilon!1/(abs(f!1(x!1)) + 1)")
                      (("1" (skosimp*)
                        (("1" (inst + "min(delta!1,delta!2)")
                          (("1" (skosimp*)
                            (("1" (inst - "y!1")
                              (("1"
                                (inst - "y!1")
                                (("1"
                                  (expand "member")
                                  (("1"
                                    (expand "ball")
                                    (("1"
                                      (expand "*")
                                      (("1"
                                        (replace -1)
                                        (("1"
                                          (expand "real_dist")
                                          (("1"
                                            (lemma "abs_mult")
                                            (("1"
                                              (inst
                                               -
                                               "-1"
                                               "f!1(y!1)*g!1(y!1)")
                                              (("1"
                                                (replace -1)
                                                (("1"
                                                  (expand "abs" 1 1)
                                                  (("1"
                                                    (field)
                                                    (("1"
                                                      (hide -1)
                                                      (("1"
                                                        (lemma
                                                         "triangle")
                                                        (("1"
                                                          (inst
                                                           -
                                                           "f!1(x!1) - f!1(y!1)"
                                                           "- f!1(x!1)")
                                                          (("1"
                                                            (case
                                                             "abs(f!1(x!1) - f!1(y!1) + -f!1(x!1)) = abs(f!1(y!1))")
                                                            (("1"
                                                              (replace
                                                               -1)
                                                              (("1"
                                                                (hide
                                                                 -1)
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (cross-mult
                                                                     -4)
                                                                    (("1"
                                                                      (case
                                                                       "abs(-1 * g!1(y!1)) = abs(g!1(y!1))")
                                                                      (("1"
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                                                                         -1)
                                                                        (("1"
                                                                          (hide
                                                                           -1)
                                                                          (("1"
                                                                            (case
                                                                             "abs(-1 * f!1(x!1)) = abs(f!1(x!1))")
                                                                            (("1"
                                                                              (replace
                                                                               -1)
                                                                              (("1"
                                                                                (hide
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                                                                                (("1"
                                                                                  (add-formulas
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                                                                                   -3)
                                                                                  (("1"
                                                                                    (both-sides
                                                                                     "-"
                                                                                     "abs(f!1(x!1) - f!1(y!1))"
                                                                                     -1)
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (mult-by
                                                                                         -1
                                                                                         "abs(g!1(y!1))")
                                                                                        (("1"
                                                                                          (grind)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (hide-all-but
                                                                               (1))
                                                                              (("2"
                                                                                (grind)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (hide-all-but
                                                                         (1))
                                                                        (("2"
                                                                          (grind)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (hide-all-but
                                                               (1))
                                                              (("2"
                                                                (grind)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (label "fcont" -1)
                    (("2" (label "gcont" -2)
                      (("2" (name "ep1" "epsilon!1/(2*abs(g!1(x!1)))")
                        (("1"
                          (name "ep2"
                                "epsilon!1/(2*(abs(f!1(x!1)) + ep1))")
                          (("1" (label "ep1name" -2)
                            (("1" (label "ep2name" -1)
                              (("1"
                                (inst - "ep1")
                                (("1"
                                  (inst - "ep2")
                                  (("1"
                                    (skosimp*)
                                    (("1"
                                      (inst + "min(delta!1,delta!2)")
                                      (("1"
                                        (skosimp*)
                                        (("1"
                                          (inst - "y!1")
                                          (("1"
                                            (inst - "y!1")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (expand "ball")
                                                (("1"
                                                  (copy "fcont")
                                                  (("1"
                                                    (label "fct2" -1)
                                                    (("1"
                                                      (hide "fct2")
                                                      (("1"
                                                        (replace
                                                         "ep1name"
                                                         -
                                                         rl)
                                                        (("1"
                                                          (replace
                                                           "ep2name"
                                                           -
                                                           rl)
                                                          (("1"
                                                            (label
                                                             "mindelta"
                                                             -5)
                                                            (("1"
                                                              (expand
                                                               "real_dist")
                                                              (("1"
                                                                (prop)
                                                                (("1"
                                                                  (cross-mult
                                                                   -2)
                                                                  (("1"
                                                                    (field
                                                                     -2)
                                                                    (("1"
                                                                      (expand
                                                                       "*")
                                                                      (("1"
                                                                        (lemma
                                                                         "triangle")
                                                                        (("1"
                                                                          (inst
                                                                           -
                                                                           "f!1(x!1) * g!1(x!1) - f!1(y!1) * g!1(x!1)"
                                                                           " f!1(y!1) * g!1(x!1) -
                                                                                                                                                                                                                       f!1(y!1) * g!1(y!1)")
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (lemma
                                                                               "abs_mult")
                                                                              (("1"
                                                                                (inst
                                                                                 -
                                                                                 "f!1(x!1)-f!1(y!1)"
                                                                                 "g!1(x!1)")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (replace
                                                                                     -1)
                                                                                    (("1"
                                                                                      (lemma
                                                                                       "abs_mult")
                                                                                      (("1"
                                                                                        (inst
                                                                                         -
                                                                                         "f!1(y!1)"
                                                                                         "g!1(x!1) - g!1(y!1)")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          (("1"
                                                                                            (replace
                                                                                             -1)
                                                                                            (("1"
                                                                                              (hide
                                                                                               -1)
                                                                                              (("1"
                                                                                                (hide
                                                                                                 -1)
                                                                                                (("1"
                                                                                                  (hide
                                                                                                   "ep1name")
                                                                                                  (("1"
                                                                                                    (hide
                                                                                                     "ep2name")
                                                                                                    (("1"
                                                                                                      (label
                                                                                                       "finaltop"
                                                                                                       -1)
                                                                                                      (("1"
                                                                                                        (hide
                                                                                                         "mindelta")
                                                                                                        (("1"
                                                                                                          (reveal
                                                                                                           "ep1name")
                                                                                                          (("1"
                                                                                                            (case
                                                                                                             "abs(f!1(y!1)) <= abs(f!1(x!1)) + ep1")
                                                                                                            (("1"
                                                                                                              (replace
                                                                                                               "ep1name"
                                                                                                               -
                                                                                                               rl)
                                                                                                              (("1"
                                                                                                                (hide
                                                                                                                 "ep1name")
                                                                                                                (("1"
                                                                                                                  (name
                                                                                                                   "A"
                                                                                                                   "f!1(x!1)")
                                                                                                                  (("1"
                                                                                                                    (name
                                                                                                                     "B"
                                                                                                                     "f!1(y!1)")
                                                                                                                    (("1"
                                                                                                                      (name
                                                                                                                       "X"
                                                                                                                       "g!1(x!1)")
                                                                                                                      (("1"
                                                                                                                        (name
                                                                                                                         "Y"
                                                                                                                         "g!1(y!1)")
                                                                                                                        (("1"
                                                                                                                          (label
                                                                                                                           "yname"
                                                                                                                           -1)
                                                                                                                          (("1"
                                                                                                                            (label
                                                                                                                             "xname"
                                                                                                                             -2)
                                                                                                                            (("1"
                                                                                                                              (label
                                                                                                                               "bname"
                                                                                                                               -3)
                                                                                                                              (("1"
                                                                                                                                (label
                                                                                                                                 "aname"
                                                                                                                                 -4)
                                                                                                                                (("1"
                                                                                                                                  (replace
                                                                                                                                   "aname")
                                                                                                                                  (("1"
                                                                                                                                    (replace
                                                                                                                                     "bname")
                                                                                                                                    (("1"
                                                                                                                                      (replace
                                                                                                                                       "xname")
                                                                                                                                      (("1"
                                                                                                                                        (replace
                                                                                                                                         "yname")
                                                                                                                                        (("1"
                                                                                                                                          (hide
                                                                                                                                           "aname")
                                                                                                                                          (("1"
                                                                                                                                            (hide
                                                                                                                                             "bname")
                                                                                                                                            (("1"
                                                                                                                                              (hide
                                                                                                                                               "xname")
                                                                                                                                              (("1"
                                                                                                                                                (hide
                                                                                                                                                 "yname")
                                                                                                                                                (("1"
                                                                                                                                                  (copy
                                                                                                                                                   "gcont")
                                                                                                                                                  (("1"
                                                                                                                                                    (name
                                                                                                                                                     "myvar"
                                                                                                                                                     "abs(A) + epsilon!1 / (2 * abs(X))")
                                                                                                                                                    (("1"
                                                                                                                                                      (label
                                                                                                                                                       "namemyvar"
                                                                                                                                                       -1)
                                                                                                                                                      (("1"
                                                                                                                                                        (replace
                                                                                                                                                         "namemyvar")
                                                                                                                                                        (("1"
                                                                                                                                                          (copy
                                                                                                                                                           "namemyvar")
                                                                                                                                                          (("1"
                                                                                                                                                            (label
                                                                                                                                                             "nmv2"
                                                                                                                                                             -1)
                                                                                                                                                            (("1"
                                                                                                                                                              (case
                                                                                                                                                               "2=2")
                                                                                                                                                              (("1"
                                                                                                                                                                (mult-eq
                                                                                                                                                                 -1
                                                                                                                                                                 -2)
                                                                                                                                                                (("1"
                                                                                                                                                                  (assert)
                                                                                                                                                                  (("1"
                                                                                                                                                                    (replace
                                                                                                                                                                     -1)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (hide
                                                                                                                                                                       -1)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (hide
                                                                                                                                                                         "nmv2")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (mult-ineq
                                                                                                                                                                           -2
                                                                                                                                                                           -3)
                                                                                                                                                                          (("1"
                                                                                                                                                                            (field
                                                                                                                                                                             -1)
                                                                                                                                                                            nil
                                                                                                                                                                            nil)
                                                                                                                                                                           ("2"
                                                                                                                                                                            (prop)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (case
                                                                                                                                                                               "myvar > 0")
                                                                                                                                                                              (("1"
                                                                                                                                                                                (grind)
                                                                                                                                                                                nil
                                                                                                                                                                                nil)
                                                                                                                                                                               ("2"
                                                                                                                                                                                (grind)
                                                                                                                                                                                nil
                                                                                                                                                                                nil))
                                                                                                                                                                              nil)
                                                                                                                                                                             ("2"
                                                                                                                                                                              (grind)
                                                                                                                                                                              nil
                                                                                                                                                                              nil)
                                                                                                                                                                             ("3"
                                                                                                                                                                              (grind)
                                                                                                                                                                              nil
                                                                                                                                                                              nil)
                                                                                                                                                                             ("4"
                                                                                                                                                                              (grind)
                                                                                                                                                                              nil
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil)
                                                                                                                                                               ("2"
                                                                                                                                                                (propax)
                                                                                                                                                                nil
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.85 Sekunden  (vorverarbeitet)  ¤





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