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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: cd_vertical.pvs   Sprache: Lisp

Original von: PVS©

(sturmtarski
 (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_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))
   nil))
 (constructed_sturm_sequence?_TCC2 0
  (constructed_sturm_sequence?_TCC2-1 nil 3589569590
   ("" (subtype-tcc) nil 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)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers 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_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (constructed_sturm_sequence?_TCC4 0
  (constructed_sturm_sequence?_TCC4-1 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers 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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (/= const-decl "boolean" notequal nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil))
   nil))
 (constructed_sturm_sequence?_TCC5 0
  (constructed_sturm_sequence?_TCC5-1 nil 3619446702
   ("" (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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (/= const-decl "boolean" notequal nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil))
   nil))
 (constructed_sturm_sequence?_TCC6 0
  (constructed_sturm_sequence?_TCC6-1 nil 3619446702
   ("" (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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers 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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (/= const-decl "boolean" notequal nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers 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 -11 "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")
                                        (("1"
                                          (assert)
                                          (("1"
                                            (inst - "x")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (replace -1)
                                                (("1"
                                                  (replace -5)
                                                  (("1"
                                                    (assert)
                                                    (("1"
                                                      (case
                                                       "polynomial(pd`rem, pd`rdeg)(x) = 0 IFF polynomial(-c*pd`rem, pd`rdeg)(x) = 0")
                                                      (("1"
                                                        (replace -1 +)
                                                        (("1"
                                                          (replace
                                                           -14
                                                           +
                                                           :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)
                                         ("2"
                                          (assert)
                                          (("2"
                                            (case "NOT i = 1")
                                            (("1" (assertnil nil)
                                             ("2"
                                              (replace -1)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (replace -13)
                                                  (("2"
                                                    (case
                                                     "polynomial(pd`rem, pd`rdeg)(x) = 0 IFF polynomial(-c*pd`rem, pd`rdeg)(x) = 0")
                                                    (("1"
                                                      (replace
                                                       -1
                                                       :dir
                                                       rl)
                                                      (("1"
                                                        (inst - "x")
                                                        (("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)
   ((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)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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" sturmtarski 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 "posnat" sturmtarski nil)
    (j skolem-const-decl "upto(m)" sturmtarski nil)
    (i skolem-const-decl "nat" sturmtarski 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" sturmtarski nil)
    (constructed_sturm_sequence? const-decl "bool" sturmtarski nil)
    (poly_divide_def formula-decl nil polynomial_division "Sturm/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (odd_plus_odd_is_even application-judgement "even_int" integers
     nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (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)
    (subrange type-eq-decl nil integers nil)
    (i skolem-const-decl "nat" sturmtarski 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 "Sturm/")
    (/= const-decl "boolean" notequal nil)
    (DivType type-eq-decl nil polynomial_division "Sturm/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (default_root_degree?_TCC1 0
  (default_root_degree?_TCC1-1 nil 3617013590
   ("" (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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers 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)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (^ const-decl "real" exponentiation nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (/= const-decl "boolean" notequal nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (default_root_degree?_TCC2 0
  (default_root_degree?_TCC2-1 nil 3617610964
   ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)
    (^ const-decl "real" exponentiation nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (constructed_sturm_seq_root_degrees_TCC1 0
  (constructed_sturm_seq_root_degrees_TCC1-1 nil 3617013872
   ("" (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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers 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)
    (real_le_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)
    (int_max application-judgement "{k: int | i <= k AND j <= k}"
     real_defs nil)
    (rat_max application-judgement "{s: rat | s >= q AND s >= r}"
     real_defs nil)
    (/= const-decl "boolean" notequal nil)
    (constructed_sturm_sequence? const-decl "bool" sturmtarski nil)
    (^ const-decl "real" exponentiation nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (default_root_degree? const-decl "bool" sturmtarski nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
 (constructed_sturm_seq_root_degrees 0
  (constructed_sturm_seq_root_degrees-2 nil 3617123921
   ("" (skeep)
    (("" (label "css" -1)
      (("" (case "g(k)=0")
        (("1" (expand "constructed_sturm_sequence?")
          (("1" (ground) nil nil)) nil)
         ("2"
          (name "dd"
                "IF polynomial(g,k)(y)=0 THEN root_degree(p(0),n(0))(y) ELSE max(root_degree(p(0), n(0))(y) - 1, 0) ENDIF")
          (("2"
            (case "FORALL (k,i:nat): i<=k AND k+1=dd AND root_degree(p(i+1),n(i+1))(y)>=dd))")
            (("1" (case "root_degree(p(m-1),n(m-1))(y)=dd")
              (("1" (label "igz" -1)
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                  (("1" (assert)
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                            (("1" (flatten)
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                                  (inst?)
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                                    (assert)
                                    (("1"
                                      (hide 3)
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                                                      (assert)
                                                      (("1"
                                                        (replace -4 +)
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                                                          (("1"
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                                                                (("1"
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                                                                             -
                                                                             "0")
                                                                            nil
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                                                                           ("3"
                                                                            (lemma
                                                                             "root_degree_pos")
                                                                            (("3"
                                                                              (inst?)
                                                                              (("3"
                                                                                (assert)
                                                                                (("3"
                                                                                  (inst
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                                                                                   "0")
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                                                                                    (("2"
                                                                                      (expand
                                                                                       "sigma"
                                                                                       1)
                                                                                      (("2"
                                                                                        (assert)
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                                                                                      nil))
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                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (reveal "igz")
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                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
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                             ("2" (flatten)
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                                                  (("1"
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                                                                (("1"
                                                                  (assert)
                                                                  nil
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                                                                 ("2"
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                                                                  (("2"
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                                                                       "0")
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                                                   ("2"
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                                                      (hide 2)
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                                                            (("2"
                                                              (lemma
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                                                              (("2"
                                                                (inst
                                                                 -
                                                                 "p(0)"
                                                                 "n(0)"
                                                                 "y")
                                                                (("2"
                                                                  (assert)
                                                                  (("2"
                                                                    (split
                                                                     -1)
                                                                    (("1"
                                                                      (expand
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                                                                       -2)
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (assert)
                                                                          (("1"
                                                                            (copy
                                                                             -4)
                                                                            (("1"
                                                                              (expand
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                                                                              (("1"
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                                                                                  (assert)
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                                                                                    (replace
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                                                                                    (("1"
                                                                                      (replace
                                                                                       -3)
                                                                                      (("1"
                                                                                        (rewrite
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                                                                                        (("1"
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                                                                                             "poly_deriv"
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                                                                                                   1
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                                                                                                  (("2"
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                                                                                                    nil
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                                                                      (("2"
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                                                                           -5
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                                                                          (("2"
                                                                            (assert)
                                                                            nil
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                                                (hide -1)
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                                                           "i-1")
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                                                           ("2"
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                                                       ("2"
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                                                (reveal "igz")
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               ("2" (hide (3 4))
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                                                                 -
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                                                                     -14
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                                                                       "polynomial"
                                                                       +
                                                                       1)
                                                                      (("1"
                                                                        (expand
                                                                         "sigma"
--> --------------------

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

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Entwicklung einer Software für die statische Quellcodeanalyse


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