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Datei: csequence_insert_remove.pvs Sprache: Lisp

Original von: PVS^©

(csequence_strict_prefix
(strict_prefix?_TCC1 0
  (strict_prefix?_TCC1-1 nil 3513690303 ("" (subtype-tcc) nil nil) nil
   nil))
(strict_prefix?_prefix? 0
  (strict_prefix?_prefix?-1 nil 3513690320
   ("" (skolem!)
    (("" (prop)
      (("1" (lemma "strict_prefix?_induction")
        (("1" (inst - "LAMBDA cseq1, cseq2: prefix?(cseq1, cseq2)")
          (("1" (split)
            (("1" (inst - "cseq1!1" "cseq2!1") (("1" (assert) nil nil))
              nil)
             ("2" (delete -1 2)
              (("2" (skosimp)
                (("2" (ground)
                  (("1" (expand "prefix?") (("1" (propax) nil nil))
                    nil)
                   ("2" (expand "prefix?" +) (("2" (propax) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (lemma "strict_prefix?_induction")
        (("2" (inst - "LAMBDA cseq1, cseq2: cseq1 /= cseq2")
          (("2" (split)
            (("1" (inst - "cseq1!1" "cseq2!1") (("1" (assert) nil nil))
              nil)
             ("2" (delete -1 -2)
              (("2" (skosimp)
                (("2" (ground) (("2" (assert) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil)
       ("3" (use "prefix?_infinite")
        (("1" (assert) nil nil)
         ("2" (lemma "is_finite_induction")
          (("2"
            (inst -
             "LAMBDA cseq1: FORALL cseq2: prefix?(cseq1, cseq2) IMPLIES cseq1 = cseq2 OR strict_prefix?(cseq1, cseq2)")
            (("2" (split)
              (("1" (inst - "cseq1!1")
                (("1" (assert)
                  (("1" (inst - "cseq2!1") (("1" (assert) nil nil))
                    nil))
                  nil))
                nil)
               ("2" (delete -1 -2 2 3)
                (("2" (skosimp*)
                  (("2" (expand "prefix?" -2)
                    (("2" (expand "strict_prefix?" +)
                      (("2" (ground)
                        (("2" (inst - "rest(cseq2!2)")
                          (("2" (assert)
                            (("2"
                              (forward-chain
                               "csequence_add_extensionality")
                              nil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (prefix? coinductive-decl "bool" csequence_prefix nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (strict_prefix?_induction formula-decl nil csequence_strict_prefix
     nil)
    (/= const-decl "boolean" notequal nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
          nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (csequence_add_extensionality formula-decl nil csequence_codt nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (strict_prefix? inductive-decl "bool" csequence_strict_prefix nil)
    (cseq1!1 skolem-const-decl "csequence[T]" csequence_strict_prefix
     nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (prefix?_infinite formula-decl nil csequence_prefix nil))
   shostak))
(strict_prefix?_finite 0
  (strict_prefix?_finite-1 nil 3513690587
   ("" (skosimp)
    (("" (rewrite "strict_prefix?_prefix?")
      (("" (flatten) (("" (rewrite "prefix?_infinite") nil nil)) nil))
      nil))
    nil)
   ((strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (prefix?_infinite formula-decl nil csequence_prefix nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (infinite_csequence type-eq-decl nil csequence_props nil))
   shostak))
(strict_prefix?_first_TCC1 0
  (strict_prefix?_first_TCC1-1 nil 3513690303
   ("" (expand "strict_prefix?") (("" (skosimp) nil nil)) nil)
   ((strict_prefix? inductive-decl "bool" csequence_strict_prefix nil))
   nil))
(strict_prefix?_first 0
  (strict_prefix?_first-1 nil 3513690647
   ("" (expand "strict_prefix?") (("" (skosimp) nil nil)) nil)
   ((strict_prefix? inductive-decl "bool" csequence_strict_prefix nil))
   shostak))
(strict_prefix?_rest 0
  (strict_prefix?_rest-1 nil 3513690661
   ("" (expand "strict_prefix?" 1 1) (("" (skosimp) nil nil)) nil)
   ((strict_prefix? inductive-decl "bool" csequence_strict_prefix nil))
   shostak))
(strict_prefix?_length_TCC1 0
  (strict_prefix?_length_TCC1-1 nil 3513690303
   ("" (skosimp) (("" (forward-chain "strict_prefix?_finite") nil nil))
    nil)
   ((strict_prefix?_finite formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil))
   nil))
(strict_prefix?_length 0
  (strict_prefix?_length-1 nil 3513690705
   ("" (skosimp)
    (("" (rewrite "strict_prefix?_prefix?")
      (("" (flatten)
        (("" (forward-chain "prefix?_length")
          (("" (use "prefix?_length_eq") (("" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (prefix?_length formula-decl nil csequence_prefix nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (prefix?_length_eq formula-decl nil csequence_prefix nil))
   shostak))
(strict_prefix?_index 0
  (strict_prefix?_index-1 nil 3513690739
   ("" (skosimp)
    (("" (rewrite "strict_prefix?_prefix?")
      (("" (flatten) (("" (forward-chain "prefix?_index") nil nil))
        nil))
      nil))
    nil)
   ((strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (prefix?_index formula-decl nil csequence_prefix nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   shostak))
(strict_prefix?_nth_TCC1 0
  (strict_prefix?_nth_TCC1-1 nil 3513690303
   ("" (skosimp :preds? t)
    (("" (forward-chain "strict_prefix?_index") nil nil)) nil)
   ((strict_prefix?_index formula-decl nil csequence_strict_prefix 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 csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt 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)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (index? def-decl "bool" csequence_nth nil)
    (indexes type-eq-decl nil csequence_nth nil))
   nil))
(strict_prefix?_nth 0
  (strict_prefix?_nth-1 nil 3513690796
   ("" (skosimp)
    (("" (rewrite "strict_prefix?_prefix?")
      (("" (flatten)
        (("" (use "prefix?_nth") (("" (assert) nil nil)) nil)) nil))
      nil))
    nil)
   ((strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (prefix?_nth formula-decl nil csequence_prefix nil)
    (indexes type-eq-decl nil csequence_nth nil)
    (index? def-decl "bool" csequence_nth 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))
   shostak))
(strict_prefix?_concatenate 0
  (strict_prefix?_concatenate-1 nil 3513690818
   ("" (induct "fseq" :name "is_finite_induction")
    (("1" (assert) nil nil) ("2" (assert) nil nil)
     ("3" (skosimp*)
      (("3" (expand "strict_prefix?" +)
        (("3" (ground)
          (("1" (rewrite "o_first") nil nil)
           ("2" (inst - "nseq!1") (("2" (rewrite "o_rest") nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((o_nonempty_right application-judgement "nonempty_csequence[T]"
     csequence_strict_prefix nil)
    (o_first formula-decl nil csequence_concatenate nil)
    (o_rest formula-decl nil csequence_concatenate nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (O const-decl "csequence" csequence_concatenate nil)
    (strict_prefix? inductive-decl "bool" csequence_strict_prefix nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil))
   shostak))
(strict_prefix?_def 0
  (strict_prefix?_def-1 nil 3513690864
   ("" (skolem!)
    (("" (rewrite "strict_prefix?_prefix?")
      (("" (use "prefix?_def")
        (("" (smash)
          (("1" (skosimp)
            (("1" (inst + "cseq!1")
              (("1" (rewrite "o_empty_right") nil nil)) nil))
            nil)
           ("2" (skosimp) (("2" (rewrite "o_infinite") nil nil)) nil)
           ("3" (skosimp*)
            (("3" (lemma "o_finiteness")
              (("3" (inst - "cseq1!1" "nseq!1")
                (("3" (assert)
                  (("3" (lemma "o_length")
                    (("3" (inst - "cseq1!1" "nseq!1")
                      (("3" (use "length_empty?_rew")
                        (("3" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("4" (skolem!) (("4" (inst + "nseq!1") nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (boolean nonempty-type-decl nil booleans nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (cseq!1 skolem-const-decl "csequence[T]" csequence_strict_prefix
     nil)
    (o_empty_right formula-decl nil csequence_concatenate nil)
    (empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
     nil)
    (empty_csequence nonempty-type-eq-decl nil csequence_props nil)
    (o_infinite formula-decl nil csequence_concatenate nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (o_finiteness formula-decl nil csequence_concatenate nil)
    (o_nonempty_right application-judgement "nonempty_csequence[T]"
     csequence_strict_prefix nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (length_empty?_rew formula-decl nil csequence_length nil)
    (o_length formula-decl nil csequence_concatenate nil)
    (prefix?_def formula-decl nil csequence_prefix nil))
   shostak))
(strict_prefix?_is_strict_order 0
  (strict_prefix?_is_strict_order-1 nil 3513690303
   ("" (expand* "strict_order?" "irreflexive?" "transitive?")
    (("" (split)
      (("1" (skolem!)
        (("1" (forward-chain "strict_prefix?_finite")
          (("1" (forward-chain "strict_prefix?_length")
            (("1" (assert) nil nil)) nil))
          nil))
        nil)
       ("2" (skosimp)
        (("2" (lemma "strict_prefix?_finite")
          (("2" (inst-cp - "y!1" "z!1")
            (("2" (inst - "x!1" "y!1")
              (("2" (assert)
                (("2" (rewrite "strict_prefix?_prefix?")
                  (("2" (rewrite "strict_prefix?_prefix?")
                    (("2" (rewrite "strict_prefix?_prefix?")
                      (("2" (prop)
                        (("1" (use "prefix?_is_partial_order")
                          (("1"
                            (expand* "partial_order?" "preorder?"
                             "transitive?")
                            (("1" (flatten)
                              (("1"
                                (inst - "x!1" "y!1" "z!1")
                                (("1" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (assert)
                          (("2" (lemma "prefix?_length")
                            (("2" (inst-cp - "y!1" "z!1")
                              (("2"
                                (inst - "x!1" "y!1")
                                (("2"
                                  (assert)
                                  (("2"
                                    (lemma "prefix?_length_eq")
                                    (("2"
                                      (inst - "x!1" "y!1")
                                      (("2" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_prefix?_finite formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (strict_prefix?_length formula-decl nil csequence_strict_prefix
     nil)
    (strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (prefix?_length_eq formula-decl nil csequence_prefix nil)
    (prefix?_length formula-decl nil csequence_prefix nil)
    (prefix?_is_partial_order judgement-tcc nil csequence_prefix nil)
    (partial_order? const-decl "bool" orders nil)
    (preorder? const-decl "bool" orders nil)
    (strict_order? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (irreflexive? const-decl "bool" relations nil))
   nil))
(strict_prefix?_well_ordered 0
  (strict_prefix?_well_ordered-1 nil 3513691147
   ("" (skolem!)
    ((""
      (expand* "well_ordered?" "strict_total_order?" "restrict"
       "trichotomous?" "well_founded?")
      (("" (split)
        (("1" (skosimp* t)
          (("1" (rewrite "strict_prefix?_prefix?")
            (("1" (rewrite "strict_prefix?_prefix?")
              (("1" (rewrite "strict_prefix?_prefix?")
                (("1" (rewrite "strict_prefix?_prefix?")
                  (("1" (ground)
                    (("1" (lemma "prefix?_total_order")
                      (("1" (inst - "cseq!1")
                        (("1"
                          (expand* "restrict" "total_order?"
                           "dichotomous?")
                          (("1" (flatten)
                            (("1" (inst - "x!1" "y!1")
                              (("1" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (skosimp* t)
          (("2" (forward-chain "strict_prefix?_finite")
            (("2"
              (name "min_length"
                    "min({n | EXISTS (seq: (p!1)): is_finite(seq) AND length(seq) = n})")
              (("1" (rewrite "min_def")
                (("1" (expand "minimum?")
                  (("1" (skosimp* t)
                    (("1" (inst + "seq!1")
                      (("1" (skolem-typepred)
                        (("1" (inst - "length(x!1)")
                          (("1" (split)
                            (("1" (lemma "strict_prefix?_length")
                              (("1"
                                (inst - "x!1" "seq!1")
                                (("1" (assert) nil nil))
                                nil))
                              nil)
                             ("2" (inst + "x!1")
                              (("2"
                                (forward-chain "strict_prefix?_finite")
                                nil
                                nil))
                              nil))
                            nil)
                           ("2" (forward-chain "strict_prefix?_finite")
                            nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (expand* "nonempty?" "empty?" "member")
                (("2" (inst - "length(y!1)")
                  (("2" (inst + "y!1") nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_total_order? const-decl "bool" orders nil)
    (trichotomous? const-decl "bool" orders nil)
    (well_founded? const-decl "bool" orders nil)
    (restrict const-decl "R" restrict nil)
    (strict_order_restrict application-judgement "(strict_order?[S])"
     restrict_order_props nil)
    (transitive_restrict application-judgement "(transitive?[S])"
     restrict_order_props nil)
    (antisymmetric_restrict application-judgement "(antisymmetric?[S])"
     restrict_order_props nil)
    (irreflexive_restrict application-judgement "(irreflexive?[S])"
     restrict_order_props nil)
    (well_ordered? const-decl "bool" orders nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (has_length def-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (pred type-eq-decl nil defined_types nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat nil)
    (<= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (nat nonempty-type-eq-decl nil naturalnumbers 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)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number nonempty-type-decl nil numbers nil)
    (minimum? const-decl "bool" min_nat nil)
    (cseq!1 skolem-const-decl "csequence[T]" csequence_strict_prefix
     nil)
    (p!1 skolem-const-decl
     "pred[(LAMBDA (cseq1): strict_prefix?(cseq1, cseq!1))]"
     csequence_strict_prefix nil)
    (x!1 skolem-const-decl "(p!1)" csequence_strict_prefix nil)
    (strict_prefix?_length formula-decl nil csequence_strict_prefix
     nil)
    (strict_prefix?_is_strict_order name-judgement
     "(strict_order?[csequence])" csequence_strict_prefix nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (min_def formula-decl nil min_nat nil)
    (y!1 skolem-const-decl
     "(LAMBDA (cseq1): strict_prefix?(cseq1, cseq!1))"
     csequence_strict_prefix nil)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil)
    (strict_prefix?_finite formula-decl nil csequence_strict_prefix
     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 csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (strict_prefix? inductive-decl "bool" csequence_strict_prefix nil)
    (prefix?_total_order formula-decl nil csequence_prefix nil)
    (total_order? const-decl "bool" orders nil)
    (dichotomous? const-decl "bool" orders nil)
    (prefix? coinductive-decl "bool" csequence_prefix nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil))
   shostak))
(strict_prefix?_prefix 0
  (strict_prefix?_prefix-1 nil 3513691384
   ("" (skolem!)
    (("" (rewrite "strict_prefix?_prefix?")
      (("" (use "prefix?_prefix")
        (("" (ground)
          (("1" (skosimp)
            (("1" (assert)
              (("1" (use "prefix_length") (("1" (assert) nil nil))
                nil))
              nil))
            nil)
           ("2" (skolem!)
            (("2" (inst + "n!1")
              (("2" (ground)
                (("2" (use "prefix_full")
                  (("2" (rewrite "index?_finite")
                    (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil)
           ("3" (skosimp*)
            (("3" (assert)
              (("3" (use "prefix_length") (("3" (assert) nil nil))
                nil))
              nil))
            nil)
           ("4" (skosimp) (("4" (inst + "n!1") nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_prefix?_prefix? formula-decl nil csequence_strict_prefix
     nil)
    (T formal-type-decl nil csequence_strict_prefix nil)
    (csequence type-decl nil csequence_codt nil)
    (prefix?_is_partial_order name-judgement
     "(partial_order?[csequence])" csequence_strict_prefix nil)
    (nat_min application-judgement "{k: nat | k <= i AND k <= j}"
     real_defs nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (prefix_length formula-decl nil csequence_prefix nil)
    (prefix_full formula-decl nil csequence_prefix nil)
    (index?_finite formula-decl nil csequence_nth nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (prefix?_prefix formula-decl nil csequence_prefix nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.33 Sekunden (vorverarbeitet) ¤

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