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Datei: abstract_min.prf Sprache: Lisp

Original von: PVS^©

(abstract_min
(prep0 0
  (prep0-1 nil 3507100592
   ("" (lemma "T_ne")
    (("" (expand "nonempty?")
      (("" (expand "empty?")
        (("" (skosimp*)
          (("" (expand "member")
            (("" (expand "is_one")
              (("" (inst -2 "size(t!1)")
                (("" (inst 1 "t!1") (("" (assert) nil))))))))))))))))
    nil)
   ((nonempty? const-decl "bool" sets nil)
    (is_one const-decl "bool" abstract_min nil)
    (size formal-const-decl "[T -> nat]" abstract_min nil)
    (T formal-type-decl nil abstract_min 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)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil)
    (T_ne formula-decl nil abstract_min nil))
   nil))
(min_f_TCC1 0
  (min_f_TCC1-1 nil 3507100592
   ("" (lemma "prep0") (("" (propax) nil)) nil)
   ((prep0 formula-decl nil abstract_min nil)) nil))
(prep1 0
  (prep1-1 nil 3507100592
   ("" (expand "nonempty?")
    (("" (expand "empty?")
      (("" (expand "member")
        (("" (expand "min_f")
          (("" (typepred "min({n: nat | is_one(n)})")
            (("1" (expand "is_one")
              (("1" (skosimp*)
                (("1" (inst -4 "S!1") (("1" (assert) nil)))))))
             ("2" (rewrite "prep0") nil))))))))))
    nil)
   ((empty? const-decl "bool" sets nil)
    (min_f const-decl "nat" abstract_min nil)
    (prep0 formula-decl nil abstract_min nil)
    (T formal-type-decl nil abstract_min 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)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (is_one const-decl "bool" abstract_min nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat nil)
    (member const-decl "bool" sets nil)
    (nonempty? const-decl "bool" sets nil))
   nil))
(min_TCC1 0
  (min_TCC1-1 nil 3507100592
   ("" (lemma "prep1")
    (("" (expand "nonempty?")
      (("" (expand "empty?")
        (("" (skosimp*)
          (("" (expand "member")
            (("" (inst?)
              (("" (expand "minimal?")
                (("" (assert)
                  (("" (expand "min_f")
                    (("" (flatten)
                      (("" (assert)
                        (("" (skosimp*)
                          (("" (typepred "min({n: nat | is_one(n)})")
                            (("1" (inst -2 "size(SS!1)")
                              (("1"
                                (hide -1)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "is_one")
                                    (("1"
                                      (inst?)
                                      (("1" (assert) nil)))))))))))
                             ("2" (lemma "prep0")
                              (("2"
                                (propax)
                                nil))))))))))))))))))))))))))))
    nil)
   ((nonempty? const-decl "bool" sets nil)
    (T formal-type-decl nil abstract_min nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (minimal? const-decl "bool" abstract_min nil)
    (x!1 skolem-const-decl "T" abstract_min nil)
    (prep0 formula-decl nil abstract_min nil)
    (size formal-const-decl "[T -> nat]" abstract_min nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (is_one const-decl "bool" abstract_min nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat nil)
    (min_f const-decl "nat" abstract_min nil)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil)
    (prep1 formula-decl nil abstract_min nil))
   nil))
(min_def 0
  (min_def-1 nil 3507100592
   ("" (typepred "min") (("" (propax) nil nil)) nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil abstract_min nil)
    (minimal? const-decl "bool" abstract_min nil)
    (min const-decl "{S: T | minimal?(S)}" abstract_min nil))
   nil))
(min_in 0
  (min_in-1 nil 3507100592
   ("" (typepred "min")
    (("" (expand "minimal?") (("" (flatten) (("" (propax) nil))))))
    nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil abstract_min nil)
    (minimal? const-decl "bool" abstract_min nil)
    (min const-decl "{S: T | minimal?(S)}" abstract_min nil))
   nil))
(min_is_min 0
  (min_is_min-1 nil 3507100592
   ("" (skosimp*)
    (("" (typepred "min")
      (("" (expand "minimal?")
        (("" (flatten) (("" (inst?) (("" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((min const-decl "{S: T | minimal?(S)}" abstract_min nil)
    (minimal? const-decl "bool" abstract_min nil)
    (T formal-type-decl nil abstract_min nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil)))

¤ Dauer der Verarbeitung: 0.27 Sekunden (vorverarbeitet) ¤

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