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Datei: csequence_concatenate_extract.prf Sprache: Lisp

Original von: PVS^©

(csequence_concatenate_extract
(o_extract 0
  (o_extract-1 nil 3513610241
   ("" (auto-rewrite "o_empty_left")
    (("" (auto-rewrite "o_empty_right")
      (("" (induct "fseq" :name "is_finite_induction")
        (("1" (assert) nil nil) ("2" (assert) nil nil)
         ("3" (skosimp*)
          (("3" (ground)
            (("1" (expand "^") (("1" (assert) nil nil)) nil)
             ("2" (expand "^" +)
              (("2" (smash)
                (("1" (inst - "i!1 - 1" "j!1 - 1" "k!1 - 1")
                  (("1" (assert) nil nil)) nil)
                 ("2" (rewrite "o_add")
                  (("2" (decompose-equality) nil nil)) nil)
                 ("3" (rewrite "o_add")
                  (("3" (decompose-equality 5)
                    (("3" (inst - "i!1" "j!1 - 1" "k!1 - 1")
                      (("3" (assert) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
    (rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
          nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (empty_cseq adt-constructor-decl "(empty?)" csequence_codt nil)
    (empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
     nil)
    (o_add formula-decl nil csequence_concatenate nil)
    (o_empty_left formula-decl nil csequence_concatenate nil)
    (add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
     csequence_codt nil)
    (csequence_add_extensionality formula-decl nil csequence_codt nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (add_finite application-judgement "nonempty_finite_csequence[T]"
     csequence_concatenate_extract nil)
    (o_nonempty_left application-judgement "nonempty_csequence"
     csequence_concatenate_extract nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (o_empty_right formula-decl nil csequence_concatenate nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (o_finite application-judgement "finite_csequence"
     csequence_concatenate_extract nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_concatenate_extract nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (^ def-decl "finite_csequence" csequence_extract nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (O const-decl "csequence" csequence_concatenate nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans 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)
    (number nonempty-type-decl nil numbers 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)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   shostak))
(o_extract_eta 0
  (o_extract_eta-1 nil 3513610334
   ("" (skosimp)
    (("" (lemma "o_extract")
      (("" (inst - "fseq!1" 0 "i!1" "j!1")
        (("" (assert)
          (("" (replace -1)
            (("" (rewrite "extract_def" 1)
              (("" (expand "^" +) (("" (propax) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((o_extract formula-decl nil csequence_concatenate_extract nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (o_finite application-judgement "finite_csequence"
     csequence_concatenate_extract nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nonempty_finite_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (extract_def formula-decl nil csequence_extract nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (^ def-decl "finite_csequence" csequence_extract 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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_concatenate_extract nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤

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