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Datei: fseqs_aux_vertical.prf Sprache: Lisp

Original von: PVS^©

(fseqs_aux_vertical
(empty_vs_fseq 0
  (empty_vs_fseq-1 nil 3477413667 ("" (judgement-tcc) nil nil)
   ((empty_seq_fseq name-judgement "fseq[real]" fseqs_aux_vertical nil)
    (vs_fseq? const-decl "bool" fseqs_aux_vertical nil)
    (emptyseq macro-decl "fsq" fseqs "structures/")
    (empty_seq const-decl "fsq" fseqs "structures/")
    (default const-decl "T" fseqs "structures/")
    (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))
   nil))
(comp_vs_fseq 0
  (comp_vs_fseq-1 nil 3477413667 ("" (judgement-tcc) nil nil)
   ((bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (barray type-eq-decl nil fseqs "structures/")
    (fseq type-eq-decl nil fseqs "structures/")
    (< 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)
    (>= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (vsb1!1 skolem-const-decl "(vs_fseq?)" fseqs_aux_vertical nil)
    (vsb2!1 skolem-const-decl "(vs_fseq?)" fseqs_aux_vertical nil)
    (i!1 skolem-const-decl "below(vsb1!1`length + vsb2!1`length)"
     fseqs_aux_vertical 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)
    (default const-decl "T" fseqs "structures/")
    (O const-decl "fseq" fseqs "structures/")
    (vs_fseq? const-decl "bool" fseqs_aux_vertical nil))
   nil))
(sort_vs_fseq 0
  (sort_vs_fseq-2 nil 3477413667
   ("" (skeep)
    (("" (expand "vs_fseq?")
      (("" (skeep)
        (("" (lemma "sort_fseq_lem")
          (("" (inst - "vsb")
            (("" (flatten)
              (("" (expand "permutation?")
                (("" (skosimp*)
                  (("" (expand "bijective?")
                    (("" (flatten)
                      (("" (expand "surjective?")
                        (("" (inst - "i")
                          (("" (skosimp*)
                            (("" (inst - "x!1")
                              ((""
                                (assert)
                                ((""
                                  (typepred "vsb")
                                  ((""
                                    (expand "vs_fseq?")
                                    ((""
                                      (replace -3)
                                      ((""
                                        (inst - "x!1")
                                        ((""
                                          (flatten)
                                          (("" (assert) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((vs_fseq? const-decl "bool" fseqs_aux_vertical nil)
    (<= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (sort_fseq_lem formula-decl nil sort_fseq "structures/")
    (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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (fsq type-eq-decl nil fsq "structures/")
    (increasing? const-decl "bool" sort_fseq "structures/")
    (sort const-decl
          "{ss: fseq | permutation?[T, <=](s, ss) AND increasing?(ss)}"
      sort_fseq "structures/")
    (below type-eq-decl nil naturalnumbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (surjective? const-decl "bool" functions nil)
    (bijective? const-decl "bool" functions nil)
    (permutation? const-decl "bool" permutations_fseq "structures/")
    (fseq type-eq-decl nil fseqs "structures/")
    (barray type-eq-decl nil fseqs "structures/")
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   nil)
  (sort_vs_fseq-1 nil 3477413667 ("" (judgement-tcc) nil nil) nil nil)))

¤ Dauer der Verarbeitung: 0.20 Sekunden (vorverarbeitet) ¤

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