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Datei: powerseries.prf Sprache: Lisp

Original von: PVS^©

(powerseries
(powerseries_TCC1 0
  (powerseries_TCC1-1 nil 3507981245
   ("" (skosimp*) (("" (grind) nil nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(powerseries_TCC2 0
  (powerseries_TCC2-1 nil 3507981245 ("" (subtype-tcc) nil nil) nil
   nil))
(powerseries_TCC3 0
  (powerseries_TCC3-1 nil 3507981245 ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)) nil))
(cauchy_powerseries_TCC1 0
  (cauchy_powerseries_TCC1-1 nil 3507981245 ("" (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_gt_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))
(cauchy_powerseries_TCC2 0
  (cauchy_powerseries_TCC2-1 nil 3507981245
   ("" (skosimp*)
    (("" (typepred "cxs!1")
      (("" (expand "cauchys_real?")
        (("" (typepred "cx!1")
          (("" (expand "cauchy_real?")
            (("" (skosimp*)
              ((""
                (inst +
                 "(LAMBDA i: IF i = 0 THEN xs!1(i) ELSE xs!1(i)*x!1^i ENDIF)")
                (("" (assert)
                  (("" (expand "cauchys_prop")
                    (("" (skosimp*)
                      (("" (inst - "n!1")
                        (("" (lemma "trichotomy" ("x" "n!1"))
                          (("" (split -1)
                            (("1" (assert)
                              (("1"
                                (lemma
                                 "mul_lemma"
                                 ("x"
                                  "xs!1(n!1)"
                                  "y"
                                  "x!1 ^ n!1"
                                  "cx"
                                  "cxs!1(n!1)"
                                  "cy"
                                  "cauchy_power(cx!1, n!1)"))
                                (("1"
                                  (lemma
                                   "power_lemma"
                                   ("x" "x!1" "pn" "n!1" "cx" "cx!1"))
                                  (("1" (assert) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (assert) nil nil)
                             ("3" (assert) nil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cauchys_real nonempty-type-eq-decl nil sum nil)
    (cauchys_real? const-decl "bool" sum nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (trichotomy formula-decl nil real_axioms nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (power_lemma formula-decl nil power nil)
    (cauchy_power const-decl "cauchy_real" power nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (mul_lemma formula-decl nil mul nil)
    (cauchys_prop const-decl "bool" sum nil)
    (^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
(powerseries_lemma_TCC1 0
  (powerseries_lemma_TCC1-1 nil 3507981245
   ("" (skosimp*)
    (("" (expand "cauchys_real?")
      (("" (inst + "xs!1")
        (("" (expand "cauchys_prop") (("" (propax) nil nil)) nil))
        nil))
      nil))
    nil)
   ((cauchys_real? const-decl "bool" sum nil)
    (cauchys_prop const-decl "bool" sum 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))
   nil))
(powerseries_lemma 0
  (powerseries_lemma-1 nil 3507981245
   ("" (skosimp*)
    (("" (expand "powerseries")
      (("" (expand "cauchy_powerseries")
        ((""
          (lemma "sum_lemma"
           ("xs"
            "(LAMBDA i: IF i = 0 THEN xs!1(i) ELSE xs!1(i) * x!1 ^ i ENDIF)"
            "m" "m!1" "cxs"
            "(LAMBDA i: IF i = 0 THEN cxs!1(i) ELSE cauchy_mul(cxs!1(i), cauchy_power(cx!1, i)) ENDIF)"))
          (("1" (assert)
            (("1" (hide 2)
              (("1" (skosimp*)
                (("1" (lemma "trichotomy" ("x" "n!1"))
                  (("1" (inst - "n!1")
                    (("1" (split -1)
                      (("1" (simplify)
                        (("1" (assert)
                          (("1"
                            (lemma "mul_lemma"
                             ("x" "xs!1(n!1)" "y" "x!1 ^ n!1" "cx"
                              "cxs!1(n!1)" "cy"
                              "cauchy_power(cx!1, n!1)"))
                            (("1" (assert)
                              (("1"
                                (lemma
                                 "power_lemma"
                                 ("x" "x!1" "cx" "cx!1" "pn" "n!1"))
                                (("1" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (assert) nil nil) ("3" (assert) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (skosimp*) (("2" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((powerseries const-decl "real" powerseries nil)
    (^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (cauchy_power const-decl "cauchy_real" power nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (cauchy_mul const-decl "cauchy_real" mul nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy nil)
    (cauchy_real? const-decl "bool" cauchy 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)
    (sum_lemma formula-decl nil sum 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)
    (trichotomy formula-decl nil real_axioms nil)
    (power_lemma formula-decl nil power nil)
    (mul_lemma formula-decl nil mul nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (cauchy_powerseries const-decl "cauchy_real" powerseries nil))
   nil)))

¤ Dauer der Verarbeitung: 0.20 Sekunden (vorverarbeitet) ¤

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