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Datei: ordered_message.prf Sprache: Lisp

Original von: PVS^©

(ordered_message
(valid_iff_ord1 0
  (valid_iff_ord1-1 nil 3394812915
   ("" (skosimp*) (("" (expand "ord") (("" (ground) nil nil)) nil))
    nil)
   ((ord const-decl "upto(1)" message_adt nil)) shostak))
(eq_iff 0
  (eq_iff-1 nil 3394814913
   ("" (skosimp*)
    (("" (split)
      (("1" (flatten)
        (("1" (replace -1)
          (("1" (rewrite "valid_iff_ord1") (("1" (assert) nil nil))
            nil))
          nil))
        nil)
       ("2" (flatten)
        (("2" (prop)
          (("1" (use "message_valid_extensionality")
            (("1" (assert) nil nil)) nil)
           ("2" (expand "ord")
            (("2" (lift-if) (("2" (ground) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((message type-decl nil message_adt nil)
    (T formal-nonempty-type-decl nil ordered_message nil)
    (valid_iff_ord1 formula-decl nil ordered_message nil)
    (boolean nonempty-type-decl nil booleans nil)
    (valid? adt-recognizer-decl "[message -> boolean]" message_adt nil)
    (message_valid_extensionality formula-decl nil message_adt nil)
    (ord const-decl "upto(1)" message_adt nil))
   shostak))
(message_total_order 0
  (message_total_order-1 nil 3394808860
   ("" (typepred "leq")
    (("" (expand "total_order?")
      (("" (expand "partial_order?")
        (("" (expand "preorder?")
          (("" (expand "<=")
            (("" (prop)
              (("1" (expand "reflexive?")
                (("1" (skosimp*)
                  (("1" (inst?)
                    (("1" (assert) nil nil) ("2" (assert) nil nil))
                    nil))
                  nil))
                nil)
               ("2" (expand "transitive?")
                (("2" (skosimp*)
                  (("2"
                    (case "valid?(x!1) & valid?(y!1) & valid?(z!1)")
                    (("1" (flatten)
                      (("1" (assert)
                        (("1"
                          (inst - "value(x!1)" "value(y!1)"
                           "value(z!1)")
                          (("1" (assert) nil nil)) nil))
                        nil))
                      nil)
                     ("2" (rewrite "valid_iff_ord1")
                      (("2" (rewrite "valid_iff_ord1")
                        (("2" (rewrite "valid_iff_ord1")
                          (("2" (ground) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("3" (expand "antisymmetric?")
                (("3" (skosimp*)
                  (("3" (case " valid?(x!1)")
                    (("1" (case " valid?(y!1)")
                      (("1" (assert)
                        (("1" (inst?)
                          (("1" (apply-extensionality) nil nil)) nil))
                        nil)
                       ("2" (rewrite "eq_iff")
                        (("2" (flatten)
                          (("2" (assert)
                            (("2" (expand "ord")
                              (("2" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (rewrite "eq_iff")
                      (("2" (assert)
                        (("2" (expand "ord") (("2" (assert) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("4" (expand "dichotomous?")
                (("4" (skosimp*)
                  (("4" (inst?)
                    (("1" (ground) nil nil) ("2" (assert) nil nil)
                     ("3" (assert) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((preorder? const-decl "bool" orders nil)
    (value adt-accessor-decl "[(valid?) -> T]" message_adt nil)
    (x!1 skolem-const-decl "message[T]" ordered_message nil)
    (valid? adt-recognizer-decl "[message -> boolean]" message_adt nil)
    (message type-decl nil message_adt nil)
    (reflexive? const-decl "bool" relations nil)
    (valid_iff_ord1 formula-decl nil ordered_message nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (transitive? const-decl "bool" relations nil)
    (message_valid_extensionality formula-decl nil message_adt nil)
    (ord const-decl "upto(1)" message_adt nil)
    (eq_iff formula-decl nil ordered_message nil)
    (antisymmetric? const-decl "bool" relations nil)
    (y!1 skolem-const-decl "message[T]" ordered_message nil)
    (x!1 skolem-const-decl "message[T]" ordered_message nil)
    (dichotomous? const-decl "bool" orders nil)
    (<= const-decl "bool" ordered_message nil)
    (partial_order? const-decl "bool" orders 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-nonempty-type-decl nil ordered_message nil)
    (pred type-eq-decl nil defined_types nil)
    (total_order? const-decl "bool" orders nil)
    (leq formal-const-decl "(total_order?[T])" ordered_message nil))
   nil)))

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