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Datei: max_upto.prf Sprache: Lisp

Original von: PVS^©

(max_upto
(max_TCC1 0
  (max_TCC1-1 nil 3507100930
   ("" (case "FORALL (S): nonempty?[upto[N]]({y: upto[N] | S(N - y)})")
    (("1" (inst 1 "(LAMBDA S: N - min({y: upto[N] | S(N-y)}))")
      (("1" (skosimp*)
        (("1" (inst?)
          (("1" (typepred "min[upto[N]]({y: upto[N] | S!1(N - y)})")
            (("1" (ground)
              (("1" (skosimp*)
                (("1" (inst - "N - x!1") (("1" (assert) nil nil)) nil))
                nil))
              nil)
             ("2" (propax) nil nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide 2)
      (("2" (skosimp*)
        (("2" (typepred "S!1")
          (("2" (expand "nonempty?")
            (("2" (expand "empty?")
              (("2" (expand "member")
                (("2" (skosimp*)
                  (("2" (inst - "N-x!1") (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((empty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (int_minus_int_is_int application-judgement "int" integers 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)
    (N formal-const-decl "nat" max_upto nil)
    (upto nonempty-type-eq-decl nil nat_types nil)
    (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields
       nil))
   nil))
(max_def 0
  (max_def-1 nil 3507100930
   ("" (skolem-typepred)
    (("" (typepred "max(S!1)")
      (("" (prop)
        (("1" (expand "maximum?")
          (("1" (assert)
            (("1" (skosimp*)
              (("1" (inst?) (("1" (assert) nil nil)) nil)) nil))
            nil))
          nil)
         ("2" (expand "maximum?")
          (("2" (flatten)
            (("2" (inst -5 "a!1")
              (("2" (assert)
                (("2" (inst -2 "max(S!1)") (("2" (assert) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((max const-decl
         "{a: upto[N] | S(a) AND (FORALL x: S(x) IMPLIES a >= x)}"
         max_upto nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (maximum? const-decl "bool" max_upto nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (upto nonempty-type-eq-decl nil nat_types nil)
    (N formal-const-decl "nat" max_upto nil)
    (<= const-decl "bool" reals 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))
   nil))
(max_lem 0
  (max_lem-1 nil 3507100930
   ("" (skosimp*)
    (("" (expand "maximum?")
      (("" (assert)
        (("" (lemma "max_def")
          (("" (inst?) (("" (inst?) (("" (assert) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((maximum? const-decl "bool" max_upto nil)
    (max_def formula-decl nil max_upto nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (max const-decl
         "{a: upto[N] | S(a) AND (FORALL x: S(x) IMPLIES a >= x)}"
         max_upto nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (upto nonempty-type-eq-decl nil nat_types nil)
    (N formal-const-decl "nat" max_upto 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))
   nil)))

¤ Dauer der Verarbeitung: 0.17 Sekunden (vorverarbeitet) ¤

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