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Datei: poly_rew.prf Sprache: Lisp

Original von: PVS^©

(poly_rew
(poly_sum 0
  (poly_sum-1 nil 3565981489
   ("" (skeep)
    (("" (lemma "sum_polynomial_eq_degree")
      (("" (inst?)
        (("" (decompose-equality -1)
          (("" (inst -1 "x")
            (("" (expand "+" -1 1) (("" (propax) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((sum_polynomial_eq_degree formula-decl nil polynomials nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (+ const-decl "[T -> real]" real_fun_ops nil)
    (polynomial const-decl "[real -> real]" polynomials nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (sequence type-eq-decl nil sequences nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (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))
   shostak))
(poly_neg 0
  (poly_neg-1 nil 3565981917
   ("" (skeep)
    (("" (lemma "neg_polynomial")
      (("" (inst? -1)
        (("" (decompose-equality -1)
          (("" (inst?)
            (("" (assert)
              (("" (expand "-" -1 1) (("" (propax) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((neg_polynomial formula-decl nil polynomials nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (polynomial const-decl "[real -> real]" polynomials nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (sequence type-eq-decl nil sequences nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (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))
   shostak))
(poly_diff 0
  (poly_diff-1 nil 3565981671
   ("" (skeep)
    ((""
      (case-replace
       "polynomial(p, n)(x) - polynomial(q, n)(x) = polynomial(p, n)(x) + -polynomial(q, n)(x)")
      (("1" (hide -1)
        (("1" (rewrite "poly_neg")
          (("1" (rewrite "poly_sum")
            (("1" (expand "polynomial")
              (("1" (rewrite "sigma_eq")
                (("1" (hide 2)
                  (("1" (skeep) (("1" (grind) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (hide 2) (("2" (assert) nil nil)) nil))
      nil))
    nil)
   ((real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" 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)
    (sequence type-eq-decl nil sequences nil)
    (polynomial const-decl "[real -> real]" polynomials nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (poly_neg formula-decl nil poly_rew nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (expt def-decl "real" exponentiation 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)
    (T_low type-eq-decl nil sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (+ const-decl "[T -> real]" real_fun_ops nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sigma_eq formula-decl nil sigma nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (poly_sum formula-decl nil poly_rew nil)
    (- const-decl "[T -> real]" real_fun_ops nil))
   shostak))
(poly_scal 0
  (poly_scal-1 nil 3565985037
   ("" (skeep)
    (("" (lemma "scal_polynomial")
      (("" (expand "const_fun")
        (("" (inst -1 "p" "n" "k")
          (("" (decompose-equality -1)
            (("" (inst -1 "x")
              (("" (expand "*") (("" (propax) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((scal_polynomial formula-decl nil polynomials 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)
    (sequence type-eq-decl nil sequences nil)
    (* const-decl "[T -> real]" real_fun_ops nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (polynomial const-decl "[real -> real]" polynomials nil)
    (* const-decl "[T -> real]" real_fun_ops nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (const_fun const-decl "[T -> real]" real_fun_ops nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ¤

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