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Datei: numbers_infinite.prf Sprache: Lisp

Original von: PVS^©

(numbers_infinite
(nat_infinite 0
  (nat_infinite-1 nil 3314538968
   ("" (expand "is_finite_type")
    (("" (skolem!)
      ((""
        (lemma
         "composition_injective[below[N!1 + 1], nat, below[N!1]]")
        (("" (inst - "LAMBDA (n: below[N!1 + 1]): n" "g!1")
          (("1" (lemma "injection_n_to_m")
            (("1" (inst - "N!1" "N!1 + 1")
              (("1" (assert) (("1" (inst?) nil nil)) nil)) nil))
            nil)
           ("2" (expand "injective?") (("2" (skosimp) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((N!1 skolem-const-decl "nat" numbers_infinite nil)
    (injective? const-decl "bool" functions nil)
    (g!1 skolem-const-decl "[nat -> below[N!1]]" numbers_infinite nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (O const-decl "T3" function_props nil)
    (injection_n_to_m formula-decl nil nat_fun_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (composition_injective judgement-tcc nil function_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)
    (< 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 nat_types nil)
    (is_finite_type const-decl "bool" finite_sets nil))
   shostak))
(int_infinite 0
  (int_infinite-1 nil 3314539260
   ("" (lemma "nat_infinite")
    (("" (rewrite "finite_full")
      (("" (rewrite "finite_full")
        (("" (assert)
          ((""
            (lemma "finite_subset[int]"
             ("A" "fullset[int]" "s" "fullset[nat]"))
            (("" (rewrite "finite_extension[int, nat]")
              (("" (expand* "extend" "subset?" "member" "fullset") nil
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_full formula-decl nil finite_sets 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)
    (finite_extension formula-decl nil extend_set_props nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (finite_subset formula-decl nil finite_sets nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (fullset const-decl "set" sets nil)
    (FALSE const-decl "bool" booleans nil)
    (extend const-decl "R" extend nil)
    (nat_infinite formula-decl nil numbers_infinite nil))
   shostak))
(rat_infinite 0
  (rat_infinite-1 nil 3314539402
   ("" (lemma "nat_infinite")
    (("" (rewrite "finite_full")
      (("" (rewrite "finite_full")
        (("" (assert)
          ((""
            (lemma "finite_subset[rat]"
             ("A" "fullset[rat]" "s" "fullset[nat]"))
            (("" (rewrite "finite_extension[rat, nat]")
              (("" (expand* "extend" "subset?" "member" "fullset") nil
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_full formula-decl nil finite_sets 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)
    (finite_extension formula-decl nil extend_set_props nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (finite_subset formula-decl nil finite_sets nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (fullset const-decl "set" sets nil)
    (FALSE const-decl "bool" booleans nil)
    (extend const-decl "R" extend nil)
    (rat nonempty-type-eq-decl nil rationals nil)
    (nat_infinite formula-decl nil numbers_infinite nil))
   shostak))
(real_infinite 0
  (real_infinite-1 nil 3314539488
   ("" (lemma "nat_infinite")
    (("" (rewrite "finite_full")
      (("" (rewrite "finite_full")
        (("" (assert)
          ((""
            (lemma "finite_subset[real]"
             ("A" "fullset[real]" "s" "fullset[nat]"))
            (("" (rewrite "finite_extension[real, nat]")
              (("" (expand* "extend" "subset?" "member" "fullset") nil
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_full formula-decl nil finite_sets 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)
    (finite_extension formula-decl nil extend_set_props nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (finite_subset formula-decl nil finite_sets nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (fullset const-decl "set" sets nil)
    (FALSE const-decl "bool" booleans nil)
    (extend const-decl "R" extend nil)
    (nat_infinite formula-decl nil numbers_infinite nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.14 Sekunden (vorverarbeitet) ¤

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