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Datei: csequence_length.prf Sprache: Lisp

Original von: PVS^©

(csequence_length
(length_TCC1 0
  (length_TCC1-1 nil 3513452351
   ("" (grind :rewrites ("is_finite_def")) nil nil)
   ((nonempty? const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (is_finite_def formula-decl nil csequence_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nat nonempty-type-eq-decl nil naturalnumbers 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)
    (>= 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)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_length nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
(length_TCC2 0
  (length_TCC2-1 nil 3513452351
   ("" (expand "has_length") (("" (reduce) nil nil)) 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_length nil)
    (csequence type-decl nil csequence_codt nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (has_length def-decl "bool" csequence_props nil))
   nil))
(length_TCC3 0
  (length_TCC3-1 nil 3513452351 ("" (subtype-tcc) nil 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_length nil)
    (csequence type-decl nil csequence_codt nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil))
   nil))
(length_TCC4 0
  (length_TCC4-1 nil 3513452351
   ("" (skosimp :preds? t)
    (("" (expand "is_finite" -) (("" (assert) nil nil)) nil)) 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_length nil)
    (csequence type-decl nil csequence_codt nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil))
   nil))
(length_TCC5 0
  (length_TCC5-1 nil 3513452351
   ("" (skosimp :preds? t)
    (("" (lemma "length_TCC1")
      (("" (inst-cp - "fseq!1")
        (("" (use "is_finite_def")
          (("" (assert)
            (("" (skolem!)
              (("" (lemma "has_length_injective")
                ((""
                  (inst-cp - "fseq!1" "n!1"
                   "choose[nat]({n | has_length[T](fseq!1, n)})")
                  (("" (assert)
                    (("" (expand "has_length" -3)
                      (("" (flatten)
                        (("" (assert)
                          (("" (expand "is_finite" -)
                            (("" (inst - "rest(fseq!1)")
                              ((""
                                (inst
                                 -
                                 "rest(fseq!1)"
                                 "n!1 - 1"
                                 "choose[nat]({n | has_length[T](rest(fseq!1), n)})")
                                (("" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((length_TCC1 subtype-tcc nil csequence_length nil)
    (is_finite_def formula-decl nil csequence_props 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)
    (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (choose const-decl "(p)" sets nil)
    (has_length def-decl "bool" csequence_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
          nil)
    (fseq!1 skolem-const-decl "finite_csequence[T]" csequence_length
     nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (has_length_injective formula-decl nil csequence_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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_length nil)
    (csequence type-decl nil csequence_codt nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil))
   nil))
(length_TCC6 0
  (length_TCC6-1 nil 3513452351
   ("" (expand "has_length") (("" (reduce) nil nil)) 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_length nil)
    (csequence type-decl nil csequence_codt nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (has_length def-decl "bool" csequence_props nil))
   nil))
(length_def 0
  (length_def-1 nil 3513452558
   ("" (skolem!)
    (("" (ground)
      (("" (typepred "length(fseq!1)")
        (("" (use "has_length_injective") (("" (assert) nil nil)) nil))
        nil))
      nil))
    nil)
   ((has_length_injective formula-decl nil csequence_props 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_length 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)
    (has_length def-decl "bool" csequence_props nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil))
   shostak))
(length_empty?_rew 0
  (length_empty?_rew-1 nil 3513452585
   ("" (grind :rewrites ("is_finite_def")) nil nil)
   ((is_finite_def formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_length nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (has_length def-decl "bool" csequence_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)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil))
   shostak))
(length_nonempty?_rew 0
  (length_nonempty?_rew-1 nil 3513452597
   ("" (grind :rewrites ("is_finite_def")) nil nil)
   ((is_finite_def formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_length nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (has_length def-decl "bool" csequence_props nil))
   shostak))
(length_rest_TCC1 0
  (length_rest_TCC1-1 nil 3513452351
   ("" (skolem-typepred)
    (("" (expand "is_finite" -) (("" (propax) nil nil)) nil)) nil)
   ((nonempty_finite_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_length nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
(length_rest 0
  (length_rest-1 nil 3513452625
   ("" (skolem!)
    (("" (expand "length" 1 2) (("" (propax) nil nil)) nil)) nil)
   ((length def-decl "{n | has_length(fseq, n)}" csequence_length nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.2 Sekunden (vorverarbeitet) ¤

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