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© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: indrec.mli   Sprache: Lisp

Original von: PVS©

(matrices
 (det_id 0
  (det_id-1 nil 3254652082 ("" (grind) nil nil)
   ((id const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (det const-decl "real" matrices nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   nil))
 (det_T 0
  (det_T-1 nil 3254652082 ("" (grind) nil nil)
   ((det const-decl "real" matrices nil)
    (T const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (id_left1 0
  (id_left1-1 nil 3254652082
   ("" (skolem 1 "m")
    (("" (decompose-equality 1) (("" (grind) nil nil)) nil)) nil)
   ((Mat3 type-eq-decl nil matrices nil)
    (* const-decl "Mat3" matrices nil)
    (id const-decl "Mat3" matrices nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (mat3 const-decl "Mat3" matrices nil)
    (row const-decl "Vect3" matrices nil)
    (col const-decl "Vect3" matrices nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "real" vectors nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (id_right1 0
  (id_right1-1 nil 3254652082
   ("" (skolem 1 "m")
    (("" (decompose-equality 1) (("" (grind) nil nil)) nil)) nil)
   ((Mat3 type-eq-decl nil matrices nil)
    (* const-decl "Mat3" matrices nil)
    (id const-decl "Mat3" matrices nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (row const-decl "Vect3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (col const-decl "Vect3" matrices nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "real" vectors nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (id_left2 0
  (id_left2-1 nil 3254652082
   ("" (skolem 1 "v")
    (("" (decompose-equality 1) (("" (grind) nil nil)) nil)) nil)
   ((below type-eq-decl nil naturalnumbers nil)
    (Mat3 type-eq-decl nil matrices nil)
    (Vect3 type-eq-decl nil vect3D nil)
    (* const-decl "Vect3" matrices nil)
    (id const-decl "Mat3" matrices nil)
    (Index type-eq-decl nil vectors nil)
    (< const-decl "bool" reals 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)
    (* const-decl "real" vectors nil)
    (sigma def-decl "real" sigma "reals/")
    (vect3 const-decl "Vect3" vect3D nil)
    (row const-decl "Vect3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (id_right2 0
  (id_right2-1 nil 3254652082
   ("" (skolem 1 "v")
    (("" (decompose-equality 1) (("" (grind) nil nil)) nil)) nil)
   ((Vect3 type-eq-decl nil vect3D nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Mat3 type-eq-decl nil matrices nil)
    (* const-decl "Vect3" matrices nil)
    (id const-decl "Mat3" matrices nil)
    (Index type-eq-decl nil vectors nil)
    (< const-decl "bool" reals 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)
    (* const-decl "real" vectors nil)
    (sigma def-decl "real" sigma "reals/")
    (vect3 const-decl "Vect3" vect3D nil)
    (col const-decl "Vect3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (associativity_1 0
  (associativity_1-1 nil 3254652082 ("" (grind) nil nil)
   ((row const-decl "Vect3" matrices nil)
    (col const-decl "Vect3" matrices nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "real" vectors nil)
    (* const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (associativity_2 0
  (associativity_2-1 nil 3254652082 ("" (grind) nil nil)
   ((row const-decl "Vect3" matrices nil)
    (col const-decl "Vect3" matrices nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "real" vectors nil)
    (* const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (* const-decl "Vect3" matrices nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (associativity_3 0
  (associativity_3-1 nil 3254652082 ("" (grind) nil nil)
   ((col const-decl "Vect3" matrices nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "real" vectors nil)
    (* const-decl "Vect3" matrices nil)
    (row const-decl "Vect3" matrices nil)
    (* const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (distribution_minus 0
  (distribution_minus-1 nil 3254652082
   ("" (grind)
    (("" (decompose-equality 1)
      (("" (lift-if) (("" (ground) nil nil)) nil)) nil))
    nil)
   ((Vect3 type-eq-decl nil vect3D nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (Mat3 type-eq-decl nil matrices nil)
    (Vector type-eq-decl nil vectors nil)
    (Index type-eq-decl nil vectors nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (* const-decl "Vect3" matrices nil)
    (* const-decl "real" vectors nil)
    (sigma def-decl "real" sigma "reals/")
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (- const-decl "real" vectors nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (row const-decl "Vect3" matrices nil))
   nil))
 (distribution_add 0
  (distribution_add-1 nil 3254652082
   ("" (grind)
    (("" (decompose-equality 1)
      (("" (lift-if) (("" (ground) nil nil)) nil)) nil))
    nil)
   ((Vect3 type-eq-decl nil vect3D nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (Mat3 type-eq-decl nil matrices nil)
    (Vector type-eq-decl nil vectors nil)
    (Index type-eq-decl nil vectors nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (* const-decl "Vect3" matrices nil)
    (* const-decl "real" vectors nil)
    (sigma def-decl "real" sigma "reals/")
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (+ const-decl "real" vectors nil)
    (vect3 const-decl "Vect3" vect3D nil)
    (row const-decl "Vect3" matrices nil))
   nil))
 (mat2_TCC1 0
  (mat2_TCC1-1 nil 3254652082 ("" (subtype-tcc) nil nil)
   ((mat3 const-decl "Mat3" matrices nil)) nil))
 (det_mat2 0
  (det_mat2-1 nil 3254652082 ("" (grind) nil nil)
   ((mat2 const-decl "Mat2" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (det const-decl "real" matrices nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (inv_TCC1 0
  (inv_TCC1-1 nil 3254652082 ("" (subtype-tcc) nil nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Mat3 type-eq-decl nil matrices nil)
    (singular? const-decl "bool" matrices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (NonSingular type-eq-decl nil matrices nil)
    (det const-decl "real" matrices nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (inv_id_TCC1 0
  (inv_id_TCC1-1 nil 3254652082 ("" (subtype-tcc) nil nil)
   ((id const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (det const-decl "real" matrices nil)
    (singular? const-decl "bool" matrices nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   nil))
 (inv_id 0
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    (* const-decl "Mat3" matrices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (NonSingular type-eq-decl nil matrices nil)
    (inv const-decl "Mat3" matrices nil)
    (mat3 const-decl "Mat3" matrices nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
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    (int nonempty-type-eq-decl nil integers nil)
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    (row const-decl "Vect3" matrices nil)
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    (* const-decl "Mat3" matrices nil)
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    (sigma def-decl "real" sigma "reals/")
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                                          (expand "D")
                                          (("1"
                                            (expand "det")
                                            (("1" (propax) nil nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (typepred "ns")
                                          (("2"
                                            (expand "singular?")
                                            (("2"
                                              (expand "D")
                                              (("2" (propax) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (split 2)
                                        (("1" (grind) nil nil)
                                         ("2"
                                          (flatten)
                                          (("2"
                                            (split 2)
                                            (("1" (grind) nil nil)
                                             ("2"
                                              (flatten)
                                              (("2"
                                                (split 2)
                                                (("1" (grind) nil nil)
                                                 ("2"
                                                  (flatten)
                                                  (("2"
                                                    (split 2)
                                                    (("1"
                                                      (grind)
                                                      (("1"
                                                        (field 1)
                                                        (("1"
                                                          (expand "D")
                                                          (("1"
                                                            (expand
                                                             "det")
                                                            (("1"
                                                              (propax)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("2"
                                                          (typepred
                                                           "ns")
                                                          (("2"
                                                            (expand
                                                             "singular?")
                                                            (("2"
                                                              (expand
                                                               "D")
                                                              (("2"
                                                                (propax)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil nil))
 (sol_eqs_correctness 0
  (sol_eqs_correctness-1 nil 3254652082
   ("" (skolem 1 ("A" "B"))
    (("" (expand "sol_eqs")
      (("" (lemma "associativity_2")
        (("" (inst?)
          (("" (rewrite "inv_right")
            (("" (rewrite "id_left2") (("" (assertnil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sol_eqs const-decl "Vect3" matrices nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Mat3 type-eq-decl nil matrices nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (singular? const-decl "bool" matrices nil)
    (NonSingular type-eq-decl nil matrices nil)
    (inv const-decl "Mat3" matrices nil)
    (Index type-eq-decl nil vectors nil)
    (Vect3 type-eq-decl nil vect3D nil)
    (id_left2 formula-decl nil matrices nil)
    (inv_right formula-decl nil matrices nil)
    (associativity_2 formula-decl nil matrices nil))
   nil)))


¤ Dauer der Verarbeitung: 0.81 Sekunden  (vorverarbeitet)  ¤





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