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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: power.pvs   Sprache: Lisp

Original von: PVS©

(modulo_equivalence
 (van_oostrom94 0
  (van_oostrom94-1 nil 3383390315
   ("" (skeep)
    (("" (expand"diamond_property?" "confluent_m?")
      (("" (skeep)
        (("" (copy -1)
          (("" (inst -1 "x" "y" "z")
            (("" (typepred "Eq")
              (("" (expand "equivalence?")
                (("" (flatten)
                  (("" (prop)
                    (("1" (skolem * "u1")
                      (("1" (flatten)
                        (("1" (expand "o" (-1 -2))
                          (("1" (skolem * "u2")
                            (("1" (skolem * "u")
                              (("1"
                                (flatten)
                                (("1"
                                  (copy -7)
                                  (("1"
                                    (expand "transitive?" -1)
                                    (("1"
                                      (copy -7)
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                                        (expand "symmetric?" -1)
                                        (("1"
                                          (inst -1 "u" "u1")
                                          (("1"
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                                            (("1"
                                              (assert)
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                                                (hide (-1 -4 -6))
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                                                  (inst -7 "y" "u" "w")
                                                  (("1"
                                                    (prop)
                                                    (("1"
                                                      (skolem * "v2")
                                                      (("1"
                                                        (flatten)
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                                                          (expand "o")
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                                                                                  (("1"
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                                                                                                 "v")
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                                                        (("2"
                                                          (assert)
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                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("3"
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                                                      (("3"
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                                                        (("3"
                                                          (expand
                                                           "reflexive?")
                                                          (("3"
                                                            (inst
                                                             -4
                                                             "w")
                                                            (("3"
                                                              (assert)
                                                              nil
                                                              nil))
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                      nil)
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                        (("2" (inst 1 "x")
                          (("2" (typepred "RTC(R)")
                            (("2" (expand "reflexive_transitive?")
                              (("2"
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                                (("2"
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                                  (("2"
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                          (("3" (expand "reflexive?")
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                            nil))
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          nil))
        nil))
      nil))
    nil)
   ((confluent_m? const-decl "bool" modulo_equivalence nil)
    (diamond_property? const-decl "bool" ars_terminology nil)
    (equivalence type-eq-decl nil relations_closure nil)
    (equivalence? const-decl "bool" relations nil)
    (PRED type-eq-decl nil defined_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (O const-decl "bool" relation_props nil)
    (reflexive? const-decl "bool" relations nil)
    (joinable_m? const-decl "bool" modulo_equivalence nil)
    (RTC const-decl "reflexive_transitive" relations_closure nil)
    (reflexive_transitive type-eq-decl nil relations_closure nil)
    (reflexive_transitive? const-decl "bool" relations_closure nil)
    (pred type-eq-decl nil defined_types nil)
    (symmetric? const-decl "bool" relations nil)
    (transitive? const-decl "bool" relations nil)
    (T formal-type-decl nil modulo_equivalence nil))
   shostak))
 (newman_lemma_general 0
  (newman_lemma_general-1 nil 3383388017
   ("" (skeep)
    (("" (split)
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        (("1" (lemma "van_oostrom94")
          (("1" (inst?)
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              (("1" (hide 2)
                (("1" (lemma "noetherian_induction")
                  (("1" (inst?)
                    (("1" (expand "diamond_property?")
                      (("1" (skeep)
                        (("1"
                          (inst -1
                           "(LAMBDA (a: T): (FORALL (b, c: T):(RTC(R) o Eq)(a, b) AND (RTC(R) o Eq)(a, c) IMPLIES joinable_m?(R, Eq)(c, b)))")
                          (("1" (split)
                            (("1" (inst -1 "x" "y" "z")
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                                (assert)
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                                  (expand "joinable_m?")
                                  (("1"
                                    (skolem -1 ("u" "v"))
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (inst 1 "u")
                                        (("1"
                                          (split)
                                          (("1"
                                            (expand "o" 1)
                                            (("1"
                                              (inst 1 "v")
                                              (("1"
                                                (typepred "Eq")
                                                (("1"
                                                  (expand*
                                                   "equivalence?"
                                                   "symmetric?")
                                                  (("1"
                                                    (flatten)
                                                    (("1"
                                                      (inst -2 "u" "v")
                                                      (("1"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
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                                            nil)
                                           ("2"
                                            (expand "o" 1)
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                                              (("2"
                                                (typepred "Eq")
                                                (("2"
                                                  (expand*
                                                   "equivalence?"
                                                   "reflexive?")
                                                  (("2"
                                                    (flatten)
                                                    (("2"
                                                      (inst -1 "u")
                                                      (("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
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                                nil))
                              nil)
                             ("2" (hide 2)
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                                  (flatten)
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                                      (hide (-4 -5))
                                      (("2"
                                        (expand "o" (-2 -3))
                                        (("2"
                                          (skolem * "b2")
                                          (("2"
                                            (skolem * "c2")
                                            (("2"
                                              (flatten)
                                              (("2"
                                                (expand "RTC" (-2 -4))
                                                (("2"
                                                  (expand
                                                   "IUnion"
                                                   (-2 -4))
                                                  (("2"
                                                    (skolem * "i")
                                                    (("2"
                                                      (skolem * "j")
                                                      (("2"
                                                        (case-replace
                                                         "i = 0"
                                                         :hide?
                                                         t)
                                                        (("1"
                                                          (case-replace
                                                           "j = 0"
                                                           :hide?
                                                           t)
                                                          (("1"
                                                            (expand
                                                             "iterate")
                                                            (("1"
                                                              (replace
                                                               -2
                                                               -3
                                                               rl)
                                                              (("1"
                                                                (replace
                                                                 -4
                                                                 -5
                                                                 rl)
                                                                (("1"
                                                                  (hide-all-but
                                                                   (-3
                                                                    -5
                                                                    1))
                                                                  (("1"
                                                                    (expand
                                                                     "joinable_m?")
                                                                    (("1"
                                                                      (inst
                                                                       1
                                                                       "c"
                                                                       "b")
                                                                      (("1"
                                                                        (typepred
                                                                         "RTC(R)")
                                                                        (("1"
                                                                          (typepred
                                                                           "Eq")
                                                                          (("1"
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                                                                             "reflexive_transitive?")
                                                                            (("1"
                                                                              (flatten)
                                                                              (("1"
                                                                                (hide
                                                                                 -3)
                                                                                (("1"
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                                                                                   "transitive?"
                                                                                   "reflexive?"
                                                                                   "symmetric?")
                                                                                  (("1"
                                                                                    (flatten)
                                                                                    (("1"
                                                                                      (inst
                                                                                       -2
                                                                                       "a"
                                                                                       "c")
                                                                                      (("1"
                                                                                        (inst
                                                                                         -3
                                                                                         "c"
                                                                                         "a"
                                                                                         "b")
                                                                                        (("1"
                                                                                          (copy
                                                                                           -4)
                                                                                          (("1"
                                                                                            (inst
                                                                                             -1
                                                                                             "c")
                                                                                            (("1"
                                                                                              (inst
                                                                                               -5
                                                                                               "b")
                                                                                              (("1"
                                                                                                (assert)
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                                                                                                nil))
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                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (expand
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                                                             -2)
                                                            (("2"
                                                              (replace
                                                               -2
                                                               -3
                                                               rl)
                                                              (("2"
                                                                (hide
                                                                 -2)
                                                                (("2"
                                                                  (lemma
                                                                   iterate_add_one)
                                                                  (("2"
                                                                    (inst?
                                                                     -1
                                                                     ("R"
                                                                      "R"
                                                                      "n"
                                                                      "j - 1"))
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (decompose-equality)
                                                                        (("1"
                                                                          (inst
                                                                           -1
                                                                           "(a, c2)")
                                                                          (("1"
                                                                            (replaces
                                                                             -1)
                                                                            (("1"
                                                                              (expand
                                                                               "o"
                                                                               -3)
                                                                              (("1"
                                                                                (skolem
                                                                                 -3
                                                                                 "c1")
                                                                                (("1"
                                                                                  (flatten)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "iterate_RTC")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -1
                                                                                       "R"
                                                                                       "j - 1")
                                                                                      (("1"
                                                                                        (expand*
                                                                                         "subset?"
                                                                                         "member")
                                                                                        (("1"
                                                                                          (inst
                                                                                           -1
                                                                                           "(c1, c2)")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "locally_coherent?")
                                                                                            (("1"
                                                                                              (typepred
                                                                                               "Eq")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "equivalence?")
                                                                                                (("1"
                                                                                                  (flatten)
                                                                                                  (("1"
                                                                                                    (inst
                                                                                                     -12
                                                                                                     "a"
                                                                                                     "c1"
                                                                                                     "b")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (hide
                                                                                                         (-8
                                                                                                          -11))
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "joinable_m?")
                                                                                                          (("1"
                                                                                                            (skolem
                                                                                                             -10
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                                                                                                              "d2"))
                                                                                                            (("1"
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                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 -5
                                                                                                                 "c1")
                                                                                                                (("1"
                                                                                                                  (lemma
                                                                                                                   "R_subset_TC")
                                                                                                                  (("1"
                                                                                                                    (inst?)
                                                                                                                    (("1"
                                                                                                                      (expand*
                                                                                                                       "subset?"
                                                                                                                       "member")
                                                                                                                      (("1"
                                                                                                                        (inst
                                                                                                                         -1
                                                                                                                         "(a, c1)")
                                                                                                                        (("1"
                                                                                                                          (assert)
                                                                                                                          (("1"
                                                                                                                            (inst
                                                                                                                             -6
                                                                                                                             "d2"
                                                                                                                             "c")
                                                                                                                            (("1"
                                                                                                                              (prop)
                                                                                                                              (("1"
                                                                                                                                (skolem
                                                                                                                                 *
                                                                                                                                 ("r1"
                                                                                                                                  "r2"))
                                                                                                                                (("1"
                                                                                                                                  (flatten)
                                                                                                                                  (("1"
                                                                                                                                    (typepred
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                                                                                                                                    (("1"
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                                                                                                                                       "reflexive_transitive?")
                                                                                                                                      (("1"
                                                                                                                                        (flatten)
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                                                                                                                                          (expand
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                                                                                                                                           -2)
                                                                                                                                          (("1"
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                                                                                                                                             -2
                                                                                                                                             "b"
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                                                                                                                                             "r2")
                                                                                                                                            (("1"
                                                                                                                                              (inst
                                                                                                                                               2
                                                                                                                                               "r1"
                                                                                                                                               "r2")
                                                                                                                                              (("1"
                                                                                                                                                (assert)
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                                                                                                                                                nil))
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                                                                                                                               ("2"
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                                                                                                                                 "o"
                                                                                                                                 1)
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                                                                                                                                  (inst
                                                                                                                                   1
                                                                                                                                   "d1")
                                                                                                                                  (("2"
                                                                                                                                    (assert)
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                                                                                                                               ("3"
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                                                                                                                                 "o"
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                                                                                                                                   1
                                                                                                                                   "c2")
                                                                                                                                  (("3"
                                                                                                                                    (assert)
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                                                                     ("2"
                                                                      (assert)
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                                                                      (assert)
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                                                         ("2"
                                                          (lemma
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                                                          (("2"
                                                            (inst?
                                                             -1
                                                             ("R"
                                                              "R"
                                                              "n"
                                                              "i - 1"))
                                                            (("1"
                                                              (decompose-equality)
                                                              (("1"
                                                                (inst
                                                                 -1
                                                                 "(a, b2)")
                                                                (("1"
                                                                  (replaces
                                                                   -1)
                                                                  (("1"
                                                                    (expand
                                                                     "o"
                                                                     -2)
                                                                    (("1"
                                                                      (skolem
                                                                       -2
                                                                       "b3")
                                                                      (("1"
                                                                        (flatten)
                                                                        (("1"
                                                                          (lemma
                                                                           "iterate_RTC")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "R"
                                                                             "i - 1")
                                                                            (("1"
                                                                              (expand*
                                                                               "subset?"
                                                                               "member")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "(b3, b2)")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (hide
                                                                                     -4)
                                                                                    (("1"
                                                                                      (case-replace
                                                                                       "j = 0"
                                                                                       :hide?
                                                                                       t)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "iterate")
                                                                                        (("1"
                                                                                          (replace
                                                                                           -5
                                                                                           -6
                                                                                           rl)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "locally_coherent?")
                                                                                            (("1"
                                                                                              (typepred
                                                                                               "Eq")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "equivalence?")
                                                                                                (("1"
                                                                                                  (flatten)
                                                                                                  (("1"
                                                                                                    (inst
                                                                                                     -12
                                                                                                     "a"
                                                                                                     "b3"
                                                                                                     "c")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (hide
                                                                                                         (-8
                                                                                                          -11))
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "joinable_m?")
                                                                                                          (("1"
                                                                                                            (skolem
                                                                                                             -10
                                                                                                             ("d1"
                                                                                                              "d2"))
                                                                                                            (("1"
                                                                                                              (flatten)
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 -5
                                                                                                                 "b3")
                                                                                                                (("1"
                                                                                                                  (lemma
                                                                                                                   "R_subset_TC")
                                                                                                                  (("1"
                                                                                                                    (inst?)
                                                                                                                    (("1"
                                                                                                                      (expand*
                                                                                                                       "subset?"
                                                                                                                       "member")
                                                                                                                      (("1"
--> --------------------

--> maximum size reached

--> --------------------

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