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Datei: sort_seq_lems.prf Sprache: Lisp

Original von: PVS^©

(sort_seq_lems
(sort_seq_min_TCC1 0
  (sort_seq_min_TCC1-1 nil 3254568023
   ("" (skosimp*)
    (("" (rewrite "sort_length") (("" (assert) nil nil)) nil)) nil)
   ((sort_length formula-decl nil sort_seq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (seqs type-eq-decl nil sort_seq nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (number nonempty-type-decl nil numbers 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)
    (> const-decl "bool" reals nil) (ne_seqs type-eq-decl nil seqs nil)
    (T formal-nonempty-type-decl nil sort_seq_lems nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (pred type-eq-decl nil defined_types nil)
    (total_order? const-decl "bool" orders nil)
    (<= formal-const-decl "(total_order?[T])" sort_seq_lems nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(sort_seq_min 0
  (sort_seq_min-1 nil 3254568023
   ("" (skosimp*)
    (("" (typepred "sort(s!1)")
      (("" (typepred "min(s!1)")
        (("" (expand "increasing?")
          (("" (skosimp*)
            (("" (expand "permutation?")
              (("" (assert)
                (("" (rewrite "sort_length")
                  (("" (assert)
                    (("" (skosimp*)
                      (("" (expand "bijective?")
                        (("" (flatten)
                          (("" (expand "surjective?")
                            (("" (inst -4 "0")
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                                  (("1"
                                    (replace -4)
                                    (("1"
                                      (hide -4)
                                      (("1"
                                        (inst -1 "x!1")
                                        (("1"
                                          (reveal -3)
                                          (("1"
                                            (inst -1 "jj!1")
                                            (("1"
                                              (inst -6 "0" "f!1(jj!1)")
                                              (("1"
                                                (replace -1 * rl)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (hide -1)
                                                    (("1"
                                                      (replace -2)
                                                      (("1"
                                                        (replace -4)
                                                        (("1"
                                                          (hide
                                                           -2
                                                           -3
                                                           -4)
                                                          (("1"
                                                            (typepred
                                                             "sort_seq_lems.<=")
                                                            (("1"
                                                              (expand
                                                               "total_order?")
                                                              (("1"
                                                                (expand
                                                                 "partial_order?")
                                                                (("1"
                                                                  (flatten)
                                                                  (("1"
                                                                    (expand
                                                                     "antisymmetric?")
                                                                    (("1"
                                                                      (inst?)
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (typepred
                                                                           "f!1(jj!1)")
                                                                          (("1"
                                                                            (rewrite
                                                                             "sort_length")
                                                                            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"
                                (rewrite "sort_length")
                                (("2" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sort const-decl
          "{ss: seqs | permutation?[T, <=](s, ss) AND increasing?(ss)}"
      sort_seq nil)
    (increasing? const-decl "bool" sort_seq nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (seqs type-eq-decl nil sort_seq nil)
    (ne_seqs type-eq-decl nil seqs nil) (> const-decl "bool" reals 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)
    (permutation? const-decl "bool" permutations_seq nil)
    (<= formal-const-decl "(total_order?[T])" sort_seq_lems nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (T formal-nonempty-type-decl nil sort_seq_lems nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (surjective? const-decl "bool" functions nil)
    (bijective? const-decl "bool" functions nil)
    (sort_length formula-decl nil sort_seq 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)
    (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (dom type-eq-decl nil min_seq nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (min const-decl "{t: T |
         (FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_seq nil))
   nil))
(sort_seq_max_TCC1 0
  (sort_seq_max_TCC1-1 nil 3254568023
   ("" (skosimp*)
    (("" (assert) (("" (rewrite "sort_length") (("" (assert) nil))))))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (sort_length formula-decl nil sort_seq nil)
    (T formal-nonempty-type-decl nil sort_seq_lems nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (pred type-eq-decl nil defined_types nil)
    (total_order? const-decl "bool" orders nil)
    (<= formal-const-decl "(total_order?[T])" sort_seq_lems nil))
   nil))
(sort_seq_max 0
  (sort_seq_max-1 nil 3254568023
   ("" (skosimp*)
    (("" (typepred "sort(s!1)")
      (("" (typepred "max(s!1)")
        (("" (expand "increasing?")
          (("" (skosimp*)
            (("" (expand "permutation?")
              (("" (rewrite "sort_length")
                (("" (assert)
                  (("" (skosimp*)
                    (("" (inst-cp -4 "jj!1")
                      (("" (expand "bijective?")
                        (("" (flatten)
                          (("" (expand "surjective?")
                            (("" (inst -4 "length(sort(s!1))-1")
                              (("1"
                                (skosimp*)
                                (("1"
                                  (inst -5 "x!1")
                                  (("1"
                                    (replace -4)
                                    (("1"
                                      (hide -4)
                                      (("1"
                                        (inst -1 "x!1")
                                        (("1"
                                          (replace -4)
                                          (("1"
                                            (hide -4)
                                            (("1"
                                              (inst
                                               -5
                                               "f!1(jj!1)"
                                               "length(sort(s!1))-1")
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (replace -2)
                                                  (("1"
                                                    (hide -2)
                                                    (("1"
                                                      (replace -3 * rl)
                                                      (("1"
                                                        (hide -2 -3)
                                                        (("1"
                                                          (typepred
                                                           "sort_seq_lems.<=")
                                                          (("1"
                                                            (expand
                                                             "total_order?")
                                                            (("1"
                                                              (expand
                                                               "partial_order?")
                                                              (("1"
                                                                (flatten)
                                                                (("1"
                                                                  (expand
                                                                   "antisymmetric?")
                                                                  (("1"
                                                                    (inst?)
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (rewrite
                                                                         "sort_length")
                                                                        (("1"
                                                                          (typepred
                                                                           "f!1(jj!1)")
                                                                          (("1"
                                                                            (rewrite
                                                                             "sort_length")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (rewrite
                                                                       "sort_length")
                                                                      (("2"
                                                                        (assert)
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (rewrite "sort_length")
                                                (("2"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (rewrite "sort_length")
                                (("2" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sort const-decl
          "{ss: seqs | permutation?[T, <=](s, ss) AND increasing?(ss)}"
      sort_seq nil)
    (increasing? const-decl "bool" sort_seq nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (seqs type-eq-decl nil sort_seq nil)
    (ne_seqs type-eq-decl nil seqs nil) (> const-decl "bool" reals 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)
    (permutation? const-decl "bool" permutations_seq nil)
    (<= formal-const-decl "(total_order?[T])" sort_seq_lems nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (T formal-nonempty-type-decl nil sort_seq_lems nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (partial_order? const-decl "bool" orders nil)
    (antisymmetric? const-decl "bool" relations nil)
    (surjective? const-decl "bool" functions nil)
    (bijective? const-decl "bool" functions nil)
    (sort_length formula-decl nil sort_seq 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)
    (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (dom type-eq-decl nil max_seq nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (max const-decl "{t: T |
         (FORALL (ii: dom(s)): seq(s)(ii) <= t) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" max_seq nil))
   nil)))

¤ Dauer der Verarbeitung: 0.29 Sekunden (vorverarbeitet) ¤

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