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Datei: power_series_deriv.prf   Sprache: Lisp

Original von: PVS©
(power_series_deriv
 (deriv_domain 0
  (deriv_domain-1 nil 3472465975
   ("" (lemma "connected_deriv_domain[T]")
    (("" (lemma "connected_domain")
      (("" (lemma "not_one_element") (("" (assert) nil nil)) nil))
      nil))
    nil)
   ((connected_domain formula-decl nil power_series_deriv nil)
    (not_one_element formula-decl nil power_series_deriv nil)
    (connected_deriv_domain formula-decl nil deriv_domain_def
     "analysis/")
    (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)
    (T_pred const-decl "[real -> boolean]" power_series_deriv nil)
    (T formal-subtype-decl nil power_series_deriv nil))
   shostak))
 (IMP_power_series_deriv_scaf_TCC1 0
  (IMP_power_series_deriv_scaf_TCC1-1 nil 3471695693
   ("" (lemma "connected_domain") (("" (propax) nil nil)) nil)
   ((connected_domain formula-decl nil power_series_deriv nil)) nil))
 (IMP_power_series_deriv_scaf_TCC2 0
  (IMP_power_series_deriv_scaf_TCC2-1 nil 3471698428
   ("" (lemma "not_one_element") (("" (propax) nil nil)) nil)
   ((not_one_element formula-decl nil power_series_deriv nil)) nil))
 (IMP_power_series_deriv_scaf_TCC3 0
  (IMP_power_series_deriv_scaf_TCC3-1 nil 3471698428
   ("" (skosimp*) (("" (lemma "open") (("" (inst?) nil nil)) nil)) nil)
   ((open formula-decl nil power_series_deriv 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)
    (T_pred const-decl "[real -> boolean]" power_series_deriv nil)
    (T formal-subtype-decl nil power_series_deriv nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   nil))
 (IMP_power_series_deriv_scaf_TCC4 0
  (IMP_power_series_deriv_scaf_TCC4-1 nil 3471698428
   ("" (lemma "ball") (("" (assert) nil nil)) nil)
   ((minus_real_is_real application-judgement "real" reals nil)
    (ball formula-decl nil power_series_deriv nil))
   nil))
 (powerseries_deriv_TCC1 0
  (powerseries_deriv_TCC1-1 nil 3297517343 ("" (subtype-tcc) nil nil)
   ((powerseries const-decl "sequence[real]" power_series nil)
    (series const-decl "sequence[real]" series nil)
    (convergence const-decl "bool" convergence_sequences "analysis/")
    (convergent? const-decl "bool" convergence_sequences "analysis/")
    (T formal-subtype-decl nil power_series_deriv nil)
    (T_pred const-decl "[real -> boolean]" power_series_deriv nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (conv_powerseries? const-decl "bool" power_series_conv nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   shostak))
 (powerseries_deriv_TCC2 0
  (powerseries_deriv_TCC2-1 nil 3297517343
   ("" (skosimp*)
    (("" (assert)
      (("" (lemma "deriv_domain[T]") (("" (inst?) nil nil)) nil)) nil))
    nil)
   ((deriv_domain formula-decl nil power_series_deriv nil)) shostak))
 (powerseries_deriv_TCC3 0
  (powerseries_deriv_TCC3-1 nil 3299589853
   ("" (skosimp*)
    (("" (lemma "deriv_powerseries_conv")
      (("" (inst?) (("" (assert) (("" (inst?) nil nil)) nil)) nil))
      nil))
    nil)
   ((T formal-subtype-decl nil power_series_deriv nil)
    (T_pred const-decl "[real -> boolean]" power_series_deriv nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (deriv_powerseries_conv formula-decl nil power_series_derivseq nil)
    (sequence type-eq-decl nil sequences nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil))
   shostak))
 (powerseries_deriv_TCC4 0
  (powerseries_deriv_TCC4-1 nil 3471698428 ("" (subtype-tcc) nil nil)
   ((nat nonempty-type-eq-decl nil naturalnumbers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (l!1 skolem-const-decl "real" power_series_deriv nil)
    (>= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (powerseries const-decl "sequence[real]" power_series nil)
    (series const-decl "sequence[real]" series nil)
    (convergence const-decl "bool" convergence_sequences "analysis/")
    (convergent? const-decl "bool" convergence_sequences "analysis/")
    (T formal-subtype-decl nil power_series_deriv nil)
    (T_pred const-decl "[real -> boolean]" power_series_deriv nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (conv_powerseries? const-decl "bool" power_series_conv nil)
    (limit const-decl "real" convergence_sequences "analysis/")
    (fullset const-decl "set" sets nil)
    (adh const-decl "setof[real]" convergence_functions "analysis/")
    (NQ const-decl "real" derivatives_def "analysis/")
    (convergence const-decl "bool" convergence_functions "analysis/")
    (convergence const-decl "bool" lim_of_functions "analysis/")
    (convergent? const-decl "bool" lim_of_functions "analysis/")
    (derivable? const-decl "bool" derivatives_def "analysis/")
    (derivable? const-decl "bool" derivatives "analysis/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil))
   nil))
 (powerseries_deriv 0
  (powerseries_deriv-11 nil 3445341646
   ("" (skosimp*)
    (("" (lemma "not_one_element")
      (("" (lemma "connected_domain")
        (("" (lemma "deriv_powerseries_conv")
          (("" (inst?)
            (("" (assert)
              (("" (expand "conv_powerseries?")
                (("" (lemma "deriv_fun_def[T]")
                  (("1" (inst?)
                    (("1"
                      (inst -
                       "(LAMBDA x: limit(series(deriv_powerseq(a!1, x))))")
                      (("1" (split -1)
                        (("1" (flatten) (("1" (assert) nil nil)) nil)
                         ("2" (hide 2)
                          (("2" (skosimp*)
                            (("2"
                              (name "FA"
                                    "(LAMBDA x: limit(powerseries(a!1)(x)))")
                              (("1"
                                (replace -1)
                                (("1"
                                  (name
                                   "FG"
                                   "(LAMBDA x: limit(series(deriv_powerseq(a!1, x))))")
                                  (("1"
                                    (case-replace
                                     "limit(series(deriv_powerseq(a!1, x!1))) = FG(x!1)")
                                    (("1"
                                      (lemma
                                       "derivative_squeeze_delta[T]")
                                      (("1"
                                        (inst?)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (hide 2)
                                            (("1"
                                              (case-replace
                                               "(LAMBDA (h: (A[T](x!1))): (NQ(FA, x!1)(h) - FG(x!1))) =
                                                                                                                                                                                                                                                                                                        (LAMBDA (h: (A[T](x!1))): inf_sum(2,Gseq(a!1,x!1,h)))")
                                              (("1"
                                                (case
                                                 "EXISTS xp: abs(xp) > abs(x!1) AND (xp >= 0 IFF x!1 >= 0)")
                                                (("1"
                                                  (skosimp*)
                                                  (("1"
                                                    (hide -2 -3)
                                                    (("1"
                                                      (case
                                                       "xp!1 /= 0")
                                                      (("1"
                                                        (flatten)
                                                        (("1"
                                                          (inst
                                                           +
                                                           "(LAMBDA (h: (A[T](x!1))): abs(h)*inf_sum(2,A2seq(a!1,x!1,xp!1)))")
                                                          (("1"
                                                            (split +)
                                                            (("1"
                                                              (name-replace
                                                               "LL"
                                                               "inf_sum(2, A2seq(a!1, x!1, xp!1))")
                                                              (("1"
                                                                (lemma
                                                                 "cv_scal[(A[T](x!1))]")
                                                                (("1"
                                                                  (inst
                                                                   -
                                                                   "0"
                                                                   "LL"
                                                                   "(LAMBDA (h: (A[T](x!1))): abs(h))"
                                                                   "0")
                                                                  (("1"
                                                                    (expand
                                                                     "*")
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (hide
                                                                         2)
                                                                        (("1"
                                                                          (hide-all-but
                                                                           1)
                                                                          (("1"
                                                                            (lemma
                                                                             "cv_abs[(A[T](x!1))]")
                                                                            (("1"
                                                                              (inst?)
                                                                              (("1"
                                                                                (expand
                                                                                 "restrict")
                                                                                (("1"
                                                                                  (expand
                                                                                   "abs")
                                                                                  (("1"
                                                                                    (propax)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil)
                                                                               ("2"
                                                                                (expand
                                                                                 "adh")
                                                                                (("2"
                                                                                  (lemma
                                                                                   "deriv_domain")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "deriv_domain?")
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst?)
                                                                                        (("2"
                                                                                          (inst
                                                                                           -
                                                                                           x!1)
                                                                                          (("2"
                                                                                            (skosimp*)
                                                                                            (("2"
                                                                                              (inst
                                                                                               +
                                                                                               y!1)
                                                                                              (("1"
                                                                                                (hide
                                                                                                 2)
                                                                                                (("1"
                                                                                                  (grind)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide
                                                                                                 2)
                                                                                                (("2"
                                                                                                  (typepred
                                                                                                   "y!1")
                                                                                                  (("2"
                                                                                                    (grind)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 2)
                                                                (("2"
                                                                  (expand
                                                                   "conv_series?")
                                                                  (("2"
                                                                    (lemma
                                                                     "A2_conv[T]")
                                                                    (("2"
                                                                      (inst
                                                                       -
                                                                       "a!1"
                                                                       "x!1"
                                                                       "xp!1")
                                                                      (("2"
                                                                        (assert)
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("3"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (inst
                                                               +
                                                               "abs(xp!1 - x!1)")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (hide
                                                                   -4
                                                                   -5
                                                                   -6
                                                                   -7
                                                                   -10)
                                                                  (("1"
                                                                    (case
                                                                     "(LAMBDA (h: (A[T](x!1))): (NQ(FA, x!1)(h) - FG(x!1)))(h!1) =
                                                                                                                                                                                                                                                                                                                            (LAMBDA (h: (A[T](x!1))): inf_sum(2, Gseq(a!1, x!1, h)))(h!1)")
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (replace
                                                                         -1)
                                                                        (("1"
                                                                          (hide
                                                                           -1)
                                                                          (("1"
                                                                            (lemma
                                                                             "inf_sum_scal")
                                                                            (("1"
                                                                              (inst?)
                                                                              (("1"
                                                                                (lemma
                                                                                 "A2_conv[T]")
                                                                                (("1"
                                                                                  (inst?)
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (replace
                                                                                       -2)
                                                                                      (("1"
                                                                                        (hide
                                                                                         -2)
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "inf_sum_le")
                                                                                          (("1"
                                                                                            (inst
                                                                                             -
                                                                                             "abs(Gseq(a!1, x!1, h!1))"
                                                                                             "abs(h!1)*A2seq(a!1, x!1, xp!1)"
                                                                                             "2")
                                                                                            (("1"
                                                                                              (split
                                                                                               -1)
                                                                                              (("1"
                                                                                                (lemma
                                                                                                 "inf_sum_Gseq_abs[T]")
                                                                                                (("1"
                                                                                                  (inst?)
                                                                                                  (("1"
                                                                                                    (inst
                                                                                                     -
                                                                                                     "x!1")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (inst?)
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide
                                                                                                 2)
                                                                                                (("2"
                                                                                                  (skosimp*)
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "Gseq")
                                                                                                    (("2"
                                                                                                      (case-replace
                                                                                                       "abs(abs(LAMBDA (k):
                                                                                                                                                                                                                                                                                                                                  IF k < 2 THEN k * a!1(k)
                                                                                                                                                                                                                                                                                                                                  ELSE k * a!1(k) * GET_tk(x!1, h!1, k) ^ (k - 1) -
                                                                                                                                                                                                                                                                                                                                        k * a!1(k) * x!1 ^ (k - 1)
                                                                                                                                                                                                                                                                                                                                  ENDIF)
                                                                                                                                                                                                                                                                                                                               (n!1)) =
                                                                                                                                                                                                                                                                                                                                  IF n!1 < 2 THEN abs(n!1 * a!1(n!1))
                                                                                                                                                                                                                                                                                                                                  ELSE abs(n!1) * abs(a!1(n!1)) * abs(GET_tk(x!1, h!1, n!1) ^ (n!1 - 1) -  x!1 ^ (n!1 - 1))
                                                                                                                                                                                                                                                                                                                                  ENDIF")
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "A2seq")
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          (("1"
                                                                                                            (hide
                                                                                                             -1
                                                                                                             -2
                                                                                                             -5)
                                                                                                            (("1"
                                                                                                              (expand
                                                                                                               "*")
                                                                                                              (("1"
                                                                                                                (name-replace
                                                                                                                 "TK"
                                                                                                                 "GET_tk(x!1, h!1, n!1)")
                                                                                                                (("1"
                                                                                                                  (rewrite
                                                                                                                   "abs_mult")
                                                                                                                  (("1"
                                                                                                                    (case-replace
                                                                                                                     "abs(TK ^ (n!1 - 1) - x!1 ^ (n!1 - 1)) <=
                                                                                                                                                                                                                                                                                                                                               abs(max(abs(x!1), abs(xp!1)) ^ (n!1 - 2)) * abs(n!1 - 1) * abs(h!1)")
                                                                                                                    (("1"
                                                                                                                      (mult-by
                                                                                                                       -1
                                                                                                                       "abs(a!1(n!1))*abs(n!1)")
                                                                                                                      (("1"
                                                                                                                        (assert)
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (hide
                                                                                                                       2)
                                                                                                                      (("2"
                                                                                                                        (name
                                                                                                                         "MAX"
                                                                                                                         "max(abs(x!1), abs(xp!1))")
                                                                                                                        (("2"
                                                                                                                          (replace
                                                                                                                           -1)
                                                                                                                          (("2"
                                                                                                                            (lemma
                                                                                                                             "mean_value_abs[T]")
                                                                                                                            (("2"
                                                                                                                              (inst
                                                                                                                               -
                                                                                                                               "TK"
                                                                                                                               "x!1"
                                                                                                                               "(LAMBDA (x:T): x^(n!1-1))")
                                                                                                                              (("2"
                                                                                                                                (lemma
                                                                                                                                 "deriv_x_to_n[T]")
                                                                                                                                (("2"
                                                                                                                                  (inst
                                                                                                                                   -
                                                                                                                                   "(n!1-1)"
                                                                                                                                   "1")
                                                                                                                                  (("2"
                                                                                                                                    (assert)
                                                                                                                                    (("2"
                                                                                                                                      (flatten)
                                                                                                                                      (("2"
                                                                                                                                        (case-replace
                                                                                                                                         "(LAMBDA (x: T): 1 * x ^ (n!1 - 1)) = (LAMBDA (x: T): x ^ (n!1 - 1))")
                                                                                                                                        (("1"
                                                                                                                                          (hide
                                                                                                                                           -1)
                                                                                                                                          (("1"
                                                                                                                                            (assert)
                                                                                                                                            (("1"
                                                                                                                                              (case-replace
                                                                                                                                               "TK = x!1")
                                                                                                                                              (("1"
                                                                                                                                                (assert)
                                                                                                                                                (("1"
                                                                                                                                                  (rewrite
                                                                                                                                                   "abs_0")
                                                                                                                                                  (("1"
                                                                                                                                                    (assert)
                                                                                                                                                    nil
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil)
                                                                                                                                               ("2"
                                                                                                                                                (assert)
                                                                                                                                                (("2"
                                                                                                                                                  (skosimp*)
                                                                                                                                                  (("2"
                                                                                                                                                    (case-replace
                                                                                                                                                     "deriv((LAMBDA (x: T): x ^ (n!1 - 1)), c!1) =
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       (n!1-1)*c!1^(n!1-2)")
                                                                                                                                                    (("1"
                                                                                                                                                      (hide
                                                                                                                                                       -1
                                                                                                                                                       -2
                                                                                                                                                       -3)
                                                                                                                                                      (("1"
                                                                                                                                                        (lemma
                                                                                                                                                         "abs_neg")
                                                                                                                                                        (("1"
                                                                                                                                                          (inst
                                                                                                                                                           -
                                                                                                                                                           "x!1 ^ (n!1 - 1) - TK ^ (n!1 - 1)")
                                                                                                                                                          (("1"
                                                                                                                                                            (replace
                                                                                                                                                             -1
                                                                                                                                                             -
                                                                                                                                                             rl)
                                                                                                                                                            (("1"
                                                                                                                                                              (replace
                                                                                                                                                               -4
                                                                                                                                                               +
                                                                                                                                                               rl)
                                                                                                                                                              (("1"
                                                                                                                                                                (rewrite
                                                                                                                                                                 "abs_mult")
                                                                                                                                                                (("1"
                                                                                                                                                                  (name-replace
                                                                                                                                                                   "NM1"
                                                                                                                                                                   "abs((n!1 - 1))")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (hide
                                                                                                                                                                     -1
                                                                                                                                                                     -4
                                                                                                                                                                     -8
                                                                                                                                                                     -9)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (case-replace
                                                                                                                                                                       "abs(c!1 ^ (n!1 - 2)) <= abs(MAX ^ (n!1 - 2))")
                                                                                                                                                                      (("1"
                                                                                                                                                                        (case-replace
                                                                                                                                                                         "abs(x!1 - TK) <= abs(h!1)")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (mult-ineq
                                                                                                                                                                           -1
                                                                                                                                                                           -2)
                                                                                                                                                                          (("1"
                                                                                                                                                                            (mult-by
                                                                                                                                                                             -1
                                                                                                                                                                             "NM1")
                                                                                                                                                                            (("1"
                                                                                                                                                                              (assert)
                                                                                                                                                                              nil
                                                                                                                                                                              nil))
                                                                                                                                                                            nil)
                                                                                                                                                                           ("2"
                                                                                                                                                                            (prop)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (hide-all-but
                                                                                                                                                                               (-1
                                                                                                                                                                                1))
                                                                                                                                                                              (("1"
                                                                                                                                                                                (grind)
                                                                                                                                                                                nil
                                                                                                                                                                                nil))
                                                                                                                                                                              nil)
                                                                                                                                                                             ("2"
                                                                                                                                                                              (hide-all-but
                                                                                                                                                                               (-2
                                                                                                                                                                                1))
                                                                                                                                                                              (("2"
                                                                                                                                                                                (grind)
                                                                                                                                                                                nil
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil)
                                                                                                                                                                         ("2"
                                                                                                                                                                          (hide
                                                                                                                                                                           -1
                                                                                                                                                                           -2
                                                                                                                                                                           -3
                                                                                                                                                                           3)
                                                                                                                                                                          (("2"
                                                                                                                                                                            (reveal
                                                                                                                                                                             -16)
                                                                                                                                                                            (("2"
                                                                                                                                                                              (typepred
                                                                                                                                                                               "GET_tk(x!1, h!1, n!1)")
                                                                                                                                                                              (("2"
                                                                                                                                                                                (grind)
                                                                                                                                                                                nil
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil)
                                                                                                                                                                       ("2"
                                                                                                                                                                        (hide
                                                                                                                                                                         3)
                                                                                                                                                                        (("2"
                                                                                                                                                                          (typepred
                                                                                                                                                                           "TK")
                                                                                                                                                                          (("2"
                                                                                                                                                                            (reveal
                                                                                                                                                                             -27
                                                                                                                                                                             -28)
                                                                                                                                                                            (("2"
--> --------------------

--> maximum size reached

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

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