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Datei: noetherian.prf Sprache: Lisp

Original von: PVS^©

(noetherian
(R_is_Noet_iff_TC_is 0
  (R_is_Noet_iff_TC_is-1 nil 3374059634
   ("" (skeep)
    (("" (split)
      (("1" (flatten)
        (("1" (expand "noetherian?")
          (("1" (lemma "transitive_closure_preserves_well_foundedness")
            (("1" (inst -1 "converse(R)")
              (("1" (hide -2)
                (("1"
                  (case-replace "transitive_closure[T] = TC" :hide? t)
                  (("1" (rewrite "TC_converse")
                    (("1" (lemma "well_founded_order_is_well_founded")
                      (("1" (inst -1 "converse(TC(R))") nil nil)) nil))
                    nil)
                   ("2" (hide-all-but 1)
                    (("2" (expand* "transitive_closure" "TC") nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (flatten)
        (("2" (expand "noetherian?")
          (("2" (expand "well_founded?")
            (("2" (skeep)
              (("2" (inst?)
                (("2" (assert)
                  (("2" (prop)
                    (("2" (hide -2)
                      (("2" (skolem * "y")
                        (("2" (inst 1 "y")
                          (("2" (skeep)
                            (("2" (inst -1 "x")
                              (("2"
                                (expand "converse")
                                (("2"
                                  (expand* "TC" "IUnion")
                                  (("2"
                                    (inst 1 "1")
                                    (("2"
                                      (rewrite "iterate_1")
                                      nil
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((transitive_converse application-judgement "(transitive?[T])"
     relation_converse_props nil)
    (noetherian? const-decl "bool" noetherian nil)
    (R skolem-const-decl "PRED[[T, T]]" noetherian nil)
    (PRED type-eq-decl nil defined_types nil)
    (converse const-decl "pred[[T2, T1]]" relation_defs nil)
    (well_founded? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (TC const-decl "transitive" relations_closure nil)
    (transitive type-eq-decl nil relations_closure nil)
    (transitive_closure const-decl "(transitive?)" closure_ops
     "orders/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (transitive? const-decl "bool" relations nil)
    (well_founded_order_is_well_founded judgement-tcc nil
     well_foundedness "orders/")
    (well_founded_order? const-decl "bool" well_foundedness "orders/")
    (TC_converse formula-decl nil relations_closure nil)
    (transitive_closure_preserves_well_foundedness judgement-tcc nil
     well_foundedness "orders/")
    (T formal-type-decl nil noetherian nil)
    (IUnion const-decl "set[T]" indexed_sets nil)
    (iterate_1 formula-decl nil relation_iterate "orders/")
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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))
   shostak))
(noetherian_induction 0
  (noetherian_induction-1 nil 3374059706
   ("" (skolem * ("S1" "P"))
    (("" (flatten)
      (("" (typepred "S1")
        (("" (lemma "R_is_Noet_iff_TC_is")
          (("" (inst?)
            (("" (assert)
              (("" (hide -2)
                ((""
                  (rewrite "wf_induction[T, converse(TC(S1))]" :subst
                   ("p" "P"))
                  (("1" (hide (-1 2))
                    (("1" (skeep)
                      (("1" (inst -2 "x")
                        (("1" (expand "converse")
                          (("1" (assert) nil nil)) nil))
                        nil))
                      nil))
                    nil)
                   ("2" (hide (-2 2))
                    (("2" (expand "noetherian?")
                      (("2" (propax) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((R_is_Noet_iff_TC_is formula-decl nil noetherian nil)
    (well_founded? const-decl "bool" orders nil)
    (transitive_converse application-judgement "(transitive?[T])"
     relation_converse_props nil)
    (wf_induction formula-decl nil wf_induction nil)
    (pred type-eq-decl nil defined_types nil)
    (converse const-decl "pred[[T2, T1]]" relation_defs nil)
    (transitive? const-decl "bool" relations nil)
    (transitive type-eq-decl nil relations_closure nil)
    (TC const-decl "transitive" relations_closure 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 noetherian nil)
    (PRED type-eq-decl nil defined_types nil)
    (noetherian? const-decl "bool" noetherian nil)
    (noetherian type-eq-decl nil noetherian nil))
   shostak)))

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