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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: polar.prf   Sprache: Lisp

Original von: PVS©

(sturm
 (constructed_sturm_sequence?_TCC1 0
  (constructed_sturm_sequence?_TCC1-1 nil 3589569590
   ("" (skeep)
    (("" (skeep)
      (("" (inst - "j1-2" "j1-1")
        (("1" (assertnil nil) ("2" (assertnil nil)
         ("3" (assertnil nil))
        nil))
      nil))
    nil)
   ((real_le_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)
    (below type-eq-decl nil naturalnumbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans 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)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (j1 skolem-const-decl "nat" sturm nil)
    (< const-decl "bool" reals nil)
    (m skolem-const-decl "nat" sturm nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (constructed_sturm_sequence?_TCC2 0
  (constructed_sturm_sequence?_TCC2-1 nil 3589569590
   ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_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)
    (/= const-decl "boolean" notequal nil))
   nil))
 (constructed_sturm_sequence?_TCC3 0
  (constructed_sturm_sequence?_TCC3-1 nil 3589569590
   ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_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)
    (/= const-decl "boolean" notequal nil))
   nil))
 (constructed_sturm_seq_repeated_root 0
  (constructed_sturm_seq_repeated_root-1 nil 3589570933
   ("" (skeep)
    ((""
      (case "FORALL (i:nat): i-1>=0 AND i+1<=m AND polynomial(p(i),n(i))(x)=0 IMPLIES (polynomial(p(i-1),n(i-1))(x)=0 IFF polynomial(p(i+1),n(i+1))(x)=0)")
      (("1" (skeep)
        (("1"
          (case "FORALL (j:nat): i-j>=0 IMPLIES FORALL (k:nat): k<=j IMPLIES polynomial(p(i-k), n(i-k))(x) = 0")
          (("1"
            (case "FORALL (j:nat): i+j<=m IMPLIES FORALL (k:nat): k<=j IMPLIES polynomial(p(i+k), n(i+k))(x) = 0")
            (("1" (skeep)
              (("1" (case "j>=i")
                (("1" (inst - "j-i")
                  (("1" (assert)
                    (("1" (inst - "j-i") (("1" (assertnil nil)) nil))
                    nil)
                   ("2" (assertnil nil))
                  nil)
                 ("2" (inst -2 "i-j")
                  (("1" (assert)
                    (("1" (inst -2 "i-j") (("1" (assertnil nil))
                      nil))
                    nil)
                   ("2" (assertnil nil))
                  nil))
                nil))
              nil)
             ("2" (hide (-1 2))
              (("2" (induct "j")
                (("1" (assert)
                  (("1" (skeep) (("1" (assertnil nil)) nil)) nil)
                 ("2" (assert)
                  (("2" (skosimp*)
                    (("2" (assert)
                      (("2" (case "k!1=0 OR k!1=1")
                        (("1" (ground) nil nil)
                         ("2" (flatten)
                          (("2" (inst-cp - "k!1-1")
                            (("2" (inst - "k!1-2")
                              (("1"
                                (assert)
                                (("1"
                                  (assert)
                                  (("1"
                                    (inst - "i-1+k!1")
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil)
                               ("2" (assertnil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (hide 2)
            (("2" (induct "j")
              (("1" (assert)
                (("1" (skosimp*) (("1" (assertnil nil)) nil)) nil)
               ("2" (skosimp*)
                (("2" (assert)
                  (("2" (case "k!1=0")
                    (("1" (assertnil nil)
                     ("2" (assert)
                      (("2" (inst-cp - "k!1-1")
                        (("2" (case "k!1=1")
                          (("1" (hide -2)
                            (("1" (assert)
                              (("1"
                                (inst - "i")
                                (("1" (assertnil nil))
                                nil))
                              nil))
                            nil)
                           ("2" (inst - "k!1-2")
                            (("1" (assert)
                              (("1"
                                (inst - "i-k!1+1")
                                (("1" (assertnil nil))
                                nil))
                              nil)
                             ("2" (assertnil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("3" (skosimp*) (("3" (assertnil nil)) nil)
               ("4" (assert)
                (("4" (skosimp*) (("4" (assertnil nil)) nil)) nil)
               ("5" (skosimp*) (("5" (assertnil nil)) nil)
               ("6" (skosimp*) (("6" (assertnil nil)) nil)
               ("7" (skosimp*) (("7" (assertnil nil)) nil))
              nil))
            nil)
           ("3" (skosimp*) (("3" (assertnil nil)) nil))
          nil))
        nil)
       ("2" (hide 2)
        (("2" (skeep)
          (("2" (assert)
            (("2" (expand "constructed_sturm_sequence?")
              (("2" (flatten)
                (("2" (inst -10 "1+i")
                  (("2" (assert)
                    (("2" (skeep)
                      (("2"
                        (name "pd"
                              "poly_divide(p(i - 1), n(i - 1))(p(i), n(i))(0)")
                        (("2" (lemma "poly_divide_def")
                          (("2" (inst?)
                            (("2" (assert)
                              (("2"
                                (replace -2)
                                (("2"
                                  (assert)
                                  (("2"
                                    (inst - "i")
                                    (("2"
                                      (assert)
                                      (("2"
                                        (inst - "i-1" "i")
                                        (("2"
                                          (assert)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (inst - "x")
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (replace -1)
                                                  (("2"
                                                    (replace -5)
                                                    (("2"
                                                      (assert)
                                                      (("2"
                                                        (case
                                                         "polynomial(pd`rem, pd`rdeg)(x) = 0 IFF polynomial(-c*pd`rem, pd`rdeg)(x) = 0")
                                                        (("1"
                                                          (replace
                                                           -1
                                                           +)
                                                          (("1"
                                                            (replace
                                                             -13
                                                             +
                                                             :dir
                                                             rl)
                                                            (("1"
                                                              (ground)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("2"
                                                          (hide-all-but
                                                           1)
                                                          (("2"
                                                            (rewrite
                                                             "scal_polynomial2")
                                                            (("2"
                                                              (ground)
                                                              (("2"
                                                                (mult-by
                                                                 1
                                                                 "c")
                                                                (("2"
                                                                  (assert)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((IFF const-decl "[bool, bool -> bool]" booleans nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (sequence type-eq-decl nil sequences nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans 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)
    (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)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (k!1 skolem-const-decl "nat" sturm nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (pred type-eq-decl nil defined_types nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (m skolem-const-decl "nat" sturm nil)
    (j skolem-const-decl "upto(m)" sturm nil)
    (i skolem-const-decl "nat" sturm nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (k!1 skolem-const-decl "nat" sturm nil)
    (constructed_sturm_sequence? const-decl "bool" sturm nil)
    (poly_divide_def formula-decl nil polynomial_division nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (- const-decl "[numfield -> numfield]" number_fields 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)
    (scal_polynomial2 formula-decl nil polynomials "reals/")
    (both_sides_times1 formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (poly_divide def-decl "DivType" polynomial_division nil)
    (/= const-decl "boolean" notequal nil)
    (DivType type-eq-decl nil polynomial_division nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (constructed_sturm_seq_repeated_root_mth 0
  (constructed_sturm_seq_repeated_root_mth-1 nil 3591517436
   ("" (induct "i")
    (("1" (skeep)
      (("1" (skeep) (("1" (inst + "mm") (("1" (assertnil nil)) nil))
        nil))
      nil)
     ("2" (skolem 1 "i")
      (("2" (flatten)
        (("2" (skeep)
          (("2" (inst?)
            (("2" (inst?)
              (("2" (assert)
                (("2" (skeep)
                  (("2" (case "u/=i+1")
                    (("1" (inst - "u") (("1" (assertnil nil)) nil)
                     ("2" (flatten)
                      (("2" (replace -1)
                        (("2" (assert)
                          (("2" (case "i = 0")
                            (("1" (replace -1)
                              (("1"
                                (assert)
                                (("1"
                                  (inst + "mm-1")
                                  (("1"
                                    (assert)
                                    (("1"
                                      (lemma
                                       "max_linear_div_power_derivative")
                                      (("1"
                                        (inst?)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (expand
                                               "constructed_sturm_sequence?")
                                              (("1"
                                                (flatten)
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (label "css" -3)
                              (("2"
                                (copy "css")
                                (("2"
                                  (expand
                                   "constructed_sturm_sequence?"
                                   -1)
                                  (("2"
                                    (flatten)
                                    (("2"
                                      (hide (-1 -2 -3 -4 -5 -6))
                                      (("2"
                                        (inst - "1+i")
                                        (("2"
                                          (assert)
                                          (("2"
                                            (skeep)
                                            (("2"
                                              (name
                                               "pd"
                                               "poly_divide(p(i - 1), n(i - 1))(p(i), n(i))(0)")
                                              (("2"
                                                (replace -1)
                                                (("2"
                                                  (lemma
                                                   "polynomial_degree_existence")
                                                  (("2"
                                                    (inst
                                                     -
                                                     "pd`rem"
                                                     "pd`rdeg")
                                                    (("2"
                                                      (split -)
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (skolem
                                                           -1
                                                           "RD")
                                                          (("1"
                                                            (flatten)
                                                            (("1"
                                                              (case
                                                               "EXISTS (kp: posnat):
                                  kp >= mm - 1 AND max_linear_div_power?(pd`rem,RD, y)(kp)")
                                                              (("1"
                                                                (skeep
                                                                 -)
                                                                (("1"
                                                                  (lemma
                                                                   "max_linear_div_power_scal")
                                                                  (("1"
                                                                    (inst
                                                                     -
                                                                     "pd`rem"
                                                                     "RD"
                                                                     "y"
                                                                     "-c"
                                                                     "kp")
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (case
                                                                         "polynomial(-c * pd`rem, pd`rdeg) = polynomial(-c*pd`rem,RD)")
                                                                        (("1"
                                                                          (replace
                                                                           -1)
                                                                          (("1"
                                                                            (lemma
                                                                             "poly_divide_lengths")
                                                                            (("1"
                                                                              (inst?)
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                                                                                        (("1"
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                                                                                          (("1"
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                                                                                            (("1"
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                                                                                               "constructed_sturm_sequence?"
                                                                                               -1)
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                                                                                                (flatten)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "i"
                                                                                                   "i+1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (assert)
                                                                                            (("2"
                                                                                              (rewrite
                                                                                               "max_linear_div_power_rew2"
                                                                                               -4)
                                                                                              (("2"
                                                                                                (inst
                                                                                                 +
                                                                                                 "kp")
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  (("2"
                                                                                                    (rewrite
                                                                                                     "max_linear_div_power_rew2"
                                                                                                     +)
                                                                                                    (("2"
                                                                                                      (assert)
                                                                                                      (("2"
                                                                                                        (replace
                                                                                                         -10)
                                                                                                        (("2"
                                                                                                          (propax)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("2"
                                                                                      (copy
                                                                                       "css")
                                                                                      (("2"
                                                                                        (expand
                                                                                         "constructed_sturm_sequence?"
                                                                                         -1)
                                                                                        (("2"
                                                                                          (flatten)
                                                                                          (("2"
                                                                                            (inst
                                                                                             -
                                                                                             "i")
                                                                                            (("2"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("3"
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                                                                                      (("3"
                                                                                        (expand
                                                                                         "constructed_sturm_sequence?"
                                                                                         -1)
                                                                                        (("3"
                                                                                          (flatten)
                                                                                          (("3"
                                                                                            (inst
                                                                                             -
                                                                                             "i-1"
                                                                                             "i")
                                                                                            (("3"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("4"
                                                                                      (copy
                                                                                       "css")
                                                                                      (("4"
                                                                                        (expand
                                                                                         "constructed_sturm_sequence?"
                                                                                         -1)
                                                                                        (("4"
                                                                                          (flatten)
                                                                                          (("4"
                                                                                            (inst
                                                                                             -
                                                                                             "i-1"
                                                                                             "i")
                                                                                            (("4"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (expand
                                                                           "polynomial"
                                                                           +
                                                                           1)
                                                                          (("2"
                                                                            (decompose-equality
                                                                             1)
                                                                            (("2"
                                                                              (lemma
                                                                               "sigma_split")
                                                                              (("2"
                                                                                (inst?)
                                                                                (("2"
                                                                                  (inst
                                                                                   -
                                                                                   "RD")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (replaces
                                                                                       -1)
                                                                                      (("2"
                                                                                        (invoke
                                                                                         (case
                                                                                          "%1 = 0")
                                                                                         (!
                                                                                          1
                                                                                          1
                                                                                          2))
                                                                                        (("1"
                                                                                          (replaces
                                                                                           -1)
                                                                                          (("1"
                                                                                            (assert)
                                                                                            (("1"
                                                                                              (expand
                                                                                               "polynomial"
                                                                                               1)
                                                                                              (("1"
                                                                                                (propax)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
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                                                                                          nil)
                                                                                         ("2"
                                                                                          (hide
                                                                                           2)
                                                                                          (("2"
                                                                                            (rewrite
                                                                                             "sigma_restrict_eq_0")
                                                                                            (("2"
                                                                                              (skosimp*)
                                                                                              (("2"
                                                                                                (expand
                                                                                                 "*")
                                                                                                (("2"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "i!1")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 4)
                                                                (("2"
                                                                  (lemma
                                                                   "poly_divide_def")
                                                                  (("2"
                                                                    (inst?)
                                                                    (("2"
                                                                      (assert)
                                                                      (("2"
                                                                        (split
                                                                         -)
                                                                        (("1"
                                                                          (replace
                                                                           -4)
                                                                          (("1"
                                                                            (label
                                                                             "IG"
                                                                             -7)
                                                                            (("1"
                                                                              (copy
                                                                               "IG")
                                                                              (("1"
                                                                                (inst-cp
                                                                                 -
                                                                                 "i")
                                                                                (("1"
                                                                                  (inst
                                                                                   -
                                                                                   "i-1")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (skolem
                                                                                       -1
                                                                                       "Ai")
                                                                                      (("1"
                                                                                        (skolem
                                                                                         -
                                                                                         "Bi")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          (("1"
                                                                                            (flatten)
                                                                                            (("1"
                                                                                              (rewrite
                                                                                               "max_linear_div_power_rew2"
                                                                                               -)
                                                                                              (("1"
                                                                                                (rewrite
                                                                                                 "max_linear_div_power_rew2"
                                                                                                 -)
                                                                                                (("1"
                                                                                                  (skosimp*)
                                                                                                  (("1"
                                                                                                    (case
                                                                                                     "EXISTS (bb:[nat->real],kk:nat): FORALL (x): polynomial(pd`rem, RD)(x) = (x-y)^(mm-1)*polynomial(bb,kk)(x)")
                                                                                                    (("1"
                                                                                                      (skeep)
                                                                                                      (("1"
                                                                                                        (case
                                                                                                         "polynomial(bb,kk)(y)/=0")
                                                                                                        (("1"
                                                                                                          (inst
                                                                                                           +
                                                                                                           "mm-1")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            (("1"
                                                                                                              (rewrite
                                                                                                               "max_linear_div_power_rew2"
                                                                                                               +)
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "bb"
                                                                                                                 "kk")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (flatten)
                                                                                                          (("2"
                                                                                                            (assert)
                                                                                                            (("2"
                                                                                                              (lemma
                                                                                                               "polynomial_degree_existence")
                                                                                                              (("2"
                                                                                                                (inst
                                                                                                                 -
                                                                                                                 "bb"
                                                                                                                 "kk")
                                                                                                                (("2"
                                                                                                                  (split
                                                                                                                   -)
                                                                                                                  (("1"
                                                                                                                    (skosimp*)
                                                                                                                    (("1"
                                                                                                                      (name
                                                                                                                       "DV"
                                                                                                                       "i!1")
                                                                                                                      (("1"
                                                                                                                        (replaces
                                                                                                                         -1)
                                                                                                                        (("1"
                                                                                                                          (assert)
                                                                                                                          (("1"
                                                                                                                            (replaces
                                                                                                                             -2)
                                                                                                                            (("1"
                                                                                                                              (assert)
                                                                                                                              (("1"
                                                                                                                                (lemma
                                                                                                                                 "poly_max_zero_power")
                                                                                                                                (("1"
                                                                                                                                  (inst
                                                                                                                                   -
                                                                                                                                   "bb"
                                                                                                                                   "DV"
                                                                                                                                   "y")
                                                                                                                                  (("1"
                                                                                                                                    (assert)
                                                                                                                                    (("1"
                                                                                                                                      (skolem
                                                                                                                                       -1
                                                                                                                                       "M")
                                                                                                                                      (("1"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "M + mm-1")
                                                                                                                                        (("1"
                                                                                                                                          (assert)
                                                                                                                                          (("1"
                                                                                                                                            (lemma
                                                                                                                                             "max_linear_div_power_additive")
                                                                                                                                            (("1"
                                                                                                                                              (inst
                                                                                                                                               -
                                                                                                                                               "pd`rem"
                                                                                                                                               "RD"
                                                                                                                                               "y"
                                                                                                                                               "mm-1"
                                                                                                                                               "M"
                                                                                                                                               "bb"
                                                                                                                                               "DV")
                                                                                                                                              (("1"
                                                                                                                                                (assert)
                                                                                                                                                nil
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.88 Sekunden  (vorverarbeitet)  ¤





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