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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: seq.ML   Sprache: Isabelle

Original von: PVS©

(confluence_commute
 (RC_RTC_is_RTC 0
  (RC_RTC_is_RTC-1 nil 3390042971
   ("" (lemma "RTC_characterization")
    (("" (skeep)
      (("" (inst -1 "RTC(R)")
        (("" (lemma "RTC_idempotent")
          (("" (inst -1 "R")
            (("" (prop)
              (("1" (expand reflexive_transitive?)
                (("1" (flatten)
                  (("1" (lemma "RC_characterization")
                    (("1" (inst -1 "RTC(R)") (("1" (assertnil nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (assertnil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((RTC_idempotent formula-decl nil relations_closure nil)
    (RC_characterization formula-decl nil relations_closure nil)
    (PRED type-eq-decl nil defined_types 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (RTC_characterization formula-decl nil relations_closure nil)
    (T formal-type-decl nil confluence_commute nil))
   shostak))
 (RTC_o_RTC_is_RTC 0
  (RTC_o_RTC_is_RTC-1 nil 3401787428
   ("" (skeep)
    (("" (expand "RTC")
      (("" (expand "IUnion")
        (("" (skosimp*)
          (("" (inst 1 "i!1 + i!2")
            (("" (lemma iterate_add)
              (("" (inst -1 "R" "i!1" "i!2")
                (("" (assert) (("" (grind) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((RTC const-decl "reflexive_transitive" relations_closure nil)
    (iterate_add formula-decl nil relation_iterate "orders/")
    (T formal-type-decl nil confluence_commute nil)
    (O const-decl "bool" relation_props nil)
    (pred type-eq-decl nil defined_types nil)
    (PRED type-eq-decl nil defined_types nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (IUnion const-decl "set[T]" indexed_sets nil))
   shostak))
 (RC_o_RTC_is_RTC 0
  (RC_o_RTC_is_RTC-1 nil 3417283391
   ("" (skeep)
    (("" (expand "RTC")
      (("" (expand "RC")
        (("" (expand "IUnion")
          (("" (expand "union")
            (("" (prop)
              (("1" (expand member)
                (("1" (skosimp*)
                  (("1" (inst 1 "i!1 + 1")
                    (("1" (lemma iterate_add)
                      (("1" (inst -1 "R" "1" "i!1")
                        (("1" (assert)
                          (("1" (replace -1)
                            (("1" (hide -1)
                              (("1"
                                (expand o)
                                (("1"
                                  (assert)
                                  (("1"
                                    (inst 1 y)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (hide -2)
                                        (("1" (grind) nil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (skosimp*)
                (("2" (inst 1 "0+i!1")
                  (("2" (lemma iterate_add)
                    (("2" (inst -1 "R" "0" "i!1")
                      (("2" (replace -1)
                        (("2" (hide -1)
                          (("2" (expand member)
                            (("2" (replace -1) (("2" (propax) nil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((RTC const-decl "reflexive_transitive" relations_closure nil)
    (IUnion const-decl "set[T]" indexed_sets nil)
    (iterate_add formula-decl nil relation_iterate "orders/")
    (T formal-type-decl nil confluence_commute nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (iterate def-decl "pred[[T, T]]" relation_iterate "orders/")
    (O const-decl "bool" relation_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (pred type-eq-decl nil defined_types nil)
    (PRED type-eq-decl nil defined_types nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (member const-decl "bool" sets nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (union const-decl "set" sets nil)
    (RC const-decl "reflexive" relations_closure nil))
   shostak))
 (RTC_converse_RTC_R 0
  (RTC_converse_RTC_R-1 nil 3417861331
   ("" (skolem 1 ("R" "_" "_"))
    ((""
      (case "FORALL (i: nat, x,y : T) : (iterate(R,i)(x,y) <=> iterate(converse(R), i)(y, x))")
      (("1" (skeep)
        (("1" (inst -1 "_" x y)
          (("1" (expand RTC)
            (("1" (expand IUnion)
              (("1" (prop)
                (("1" (skosimp)
                  (("1" (inst 1 i!1)
                    (("1" (inst -2 i!1) (("1" (assertnil nil)) nil))
                    nil))
                  nil)
                 ("2" (skosimp)
                  (("2" (inst -2 i!1)
                    (("2" (inst 1 i!1) (("2" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (hide 2)
        (("2" (induct i)
          (("1" (skeep)
            (("1" (expand iterate) (("1" (grind) nil nil)) nil)) nil)
           ("2" (skeep)
            (("2" (skeep)
              (("2" (lemma iterate_add)
                (("2" (inst -1 R j 1)
                  (("2" (replace -1 1)
                    (("2" (expand o)
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                          (("1" (inst -4 "x" "y!1")
                            (("1" (hide -3)
                              (("1"
                                (prop)
                                (("1"
                                  (lemma iterate_add)
                                  (("1"
                                    (inst -1 "converse(R)" "1" "j")
                                    (("1"
                                      (decompose-equality -1)
                                      (("1"
                                        (inst -1 "(y,x)")
                                        (("1"
                                          (expand o -1)
                                          (("1"
                                            (replace -1 1)
                                            (("1"
                                              (hide -1)
                                              (("1"
                                                (inst 1 y!1)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (hide -1 -2 -3)
                                                    (("1"
                                                      (expand iterate)
                                                      (("1"
                                                        (expand o -1)
                                                        (("1"
                                                          (skosimp)
                                                          (("1"
                                                            (expand
                                                             iterate
                                                             -1)
                                                            (("1"
                                                              (replace
                                                               -1
                                                               -2
                                                               rl)
                                                              (("1"
                                                                (hide
                                                                 -1)
                                                                (("1"
                                                                  (expand
                                                                   o)
                                                                  (("1"
                                                                    (inst
                                                                     1
                                                                     y)
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (expand
                                                                         iterate)
                                                                        (("1"
                                                                          (expand
                                                                           converse)
                                                                          (("1"
                                                                            (propax)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide -2)
                          (("2" (lemma iterate_add)
                            (("2" (inst -1 "converse(R)" 1 j)
                              (("2"
                                (decompose-equality)
                                (("2"
                                  (inst -1 "(y,x)")
                                  (("2"
                                    (expand o -1)
                                    (("2"
                                      (replace -1 -2)
                                      (("2"
                                        (hide -1)
                                        (("2"
                                          (skosimp -1)
                                          (("2"
                                            (inst -3 x y!1)
                                            (("2"
                                              (assert)
                                              (("2"
                                                (inst 1 y!1)
                                                (("2"
                                                  (assert)
                                                  (("2"
                                                    (hide -2 -3)
                                                    (("2"
                                                      (expand iterate)
                                                      (("2"
                                                        (expand o -1)
                                                        (("2"
                                                          (skosimp)
                                                          (("2"
                                                            (expand
                                                             iterate
                                                             -1)
                                                            (("2"
                                                              (replace
                                                               -1
                                                               -2
                                                               rl)
                                                              (("2"
                                                                (hide
                                                                 -1)
                                                                (("2"
                                                                  (expand
                                                                   iterate)
                                                                  (("2"
                                                                    (expand
                                                                     o)
                                                                    (("2"
                                                                      (inst
                                                                       1
                                                                       y!1)
                                                                      (("2"
                                                                        (expand
                                                                         converse)
                                                                        (("2"
                                                                          (propax)
                                                                          nil
                                                                          nil))
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                                                                      nil))
                                                                    nil))
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                                                                nil))
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                                                      nil))
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                                              nil))
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                                nil))
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                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((converse const-decl "pred[[T2, T1]]" relation_defs nil)
    (PRED type-eq-decl nil defined_types nil)
    (iterate def-decl "pred[[T, T]]" relation_iterate "orders/")
    (pred type-eq-decl nil defined_types nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (T formal-type-decl nil confluence_commute 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)
    (IUnion const-decl "set[T]" indexed_sets nil)
    (RTC const-decl "reflexive_transitive" relations_closure nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (O const-decl "bool" relation_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (iterate_add formula-decl nil relation_iterate "orders/"))
   shostak))
 (semi_comm_implies_comm 0
  (semi_comm_implies_comm-1 nil 3386429566
   ("" (skeep)
    (("" (expand commute?)
      (("" (skeep)
        (("" (expand "RTC" -2)
          (("" (expand "IUnion" -2)
            (("" (skolem * "i")
              ((""
                (case "FORALL (j: nat, a, b, c: T) : (iterate(R1,j)(a,b) AND RTC(R2)(a,c)) => EXISTS (d: T): RTC(R2)(b, d) & RTC(R1)(c, d)")
                (("1" (inst -1 "i" "x" "y" "z")
                  (("1" (assertnil nil)) nil)
                 ("2" (induct j)
                  (("1" (hide 2 -2 -3)
                    (("1" (assert)
                      (("1" (skeep)
                        (("1" (expand iterate)
                          (("1" (replace -1 -2)
                            (("1" (inst 1 "c")
                              (("1"
                                (assert)
                                (("1"
                                  (expand "RTC" 1)
                                  (("1"
                                    (expand "IUnion")
                                    (("1"
                                      (inst 1 "0")
                                      (("1"
                                        (assert)
                                        (("1"
                                          (expand iterate)
                                          (("1" (propax) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (hide -2 -3 2)
                    (("2" (skeep)
                      (("2" (skeep)
                        (("2" (rewrite "iterate_add_one")
                          (("2" (expand o)
                            (("2" (skolem * "a1")
                              (("2"
                                (expand semi_commute?)
                                (("2"
                                  (inst -4 "a" "a1" "c")
                                  (("2"
                                    (flatten)
                                    (("2"
                                      (assert)
                                      (("2"
                                        (skolem * "c1")
                                        (("2"
                                          (flatten)
                                          (("2"
                                            (inst -1 "a1" "b" "c1")
                                            (("2"
                                              (assert)
                                              (("2"
                                                (skolem * "d1")
                                                (("2"
                                                  (flatten)
                                                  (("2"
                                                    (assert)
                                                    (("2"
                                                      (hide
                                                       -3
                                                       -4
                                                       -5
                                                       -6)
                                                      (("2"
                                                        (inst 1 "d1")
                                                        (("2"
                                                          (assert)
                                                          (("2"
                                                            (hide -1)
                                                            (("2"
                                                              (expand
                                                               "RTC")
                                                              (("2"
                                                                (expand
                                                                 "IUnion")
                                                                (("2"
                                                                  (skolem
                                                                   *
                                                                   "n")
                                                                  (("2"
                                                                    (skolem
                                                                     *
                                                                     "m")
                                                                    (("2"
                                                                      (inst
                                                                       1
                                                                       "m + n")
                                                                      (("2"
                                                                        (lemma
                                                                         iterate_add)
                                                                        (("2"
                                                                          (inst
                                                                           -1
                                                                           "R1"
                                                                           "m"
                                                                           "n")
                                                                          (("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (grind)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
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                                                    nil))
                                                  nil))
                                                nil))
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                                            nil))
                                          nil))
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                                      nil))
                                    nil))
                                  nil))
                                nil))
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                            nil))
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                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((commute? const-decl "bool" ars_terminology nil)
    (RTC const-decl "reflexive_transitive" relations_closure nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (iterate_add_one formula-decl nil relation_iterate "orders/")
    (int_minus_int_is_int application-judgement "int" integers nil)
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--> --------------------

--> maximum size reached

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

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