Quellcode-Bibliothek middle_third_pigeonhole.prf Sprache: Lisp

(middle_third_pigeonhole
(middle_third_pigeonhole 0
  (middle_third_pigeonhole-1 nil 3395067970
   ("" (auto-rewrite-theory "extend_set_props[int, below(N)]")
    (("" (skosimp*)
      (("" (lemma "fta_overlap_pigeonhole")
        (("" (inst - "A!1" "B!1" "C!1" "S1!1" "S2!1")
          (("1" (expand "two_thirds_majority_subset?")
            (("1" (expand "byzantine_intersection_majority?")
              (("1" (ground)
                (("1" (skosimp*)
                  (("1" (expand "extend")
                    (("1" (inst?)
                      (("1" (ground) nil nil) ("2" (ground) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (skosimp*)
            (("2" (expand "extend") (("2" (assert) nil nil)) nil)) nil)
           ("3" (skosimp*)
            (("3" (expand "extend") (("3" (assert) nil nil)) nil)) nil)
           ("4" (skosimp*)
            (("4" (expand "extend") (("4" (assert) nil nil)) nil)) nil)
           ("5" (skosimp*)
            (("5" (expand "extend") (("5" (assert) nil nil)) nil)) nil)
           ("6" (skosimp*)
            (("6" (expand "extend") (("6" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_extend application-judgement "finite_set[T]"
     extend_set_props nil)
    (A!1 skolem-const-decl "finite_set[below(N)]"
     middle_third_pigeonhole nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil) (extend const-decl "R" extend nil)
    (FALSE const-decl "bool" booleans nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" middle_third_pigeonhole nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans 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)
    (B!1 skolem-const-decl "finite_set[below(N)]"
     middle_third_pigeonhole nil)
    (C!1 skolem-const-decl "finite_set[below(N)]"
     middle_third_pigeonhole nil)
    (S1!1 skolem-const-decl "finite_set[below(N)]"
     middle_third_pigeonhole nil)
    (S2!1 skolem-const-decl "finite_set[below(N)]"
     middle_third_pigeonhole nil)
    (nat_set type-eq-decl nil pigeonhole_int nil)
    (byzantine_intersection_majority? const-decl "bool" pigeonhole nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (x!1 skolem-const-decl "int" middle_third_pigeonhole nil)
    (subset_extend formula-decl nil extend_set_props nil)
    (intersection_extend formula-decl nil extend_set_props nil)
    (card_extend formula-decl nil extend_set_props nil)
    (difference_extend formula-decl nil extend_set_props nil)
    (union_extend formula-decl nil extend_set_props nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (finite_union application-judgement "finite_set" finite_sets nil)
    (finite_difference application-judgement "finite_set" finite_sets
     nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (finite_intersection1 application-judgement "finite_set"
     finite_sets nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (two_thirds_majority_subset? const-decl "bool" pigeonhole nil)
    (fta_overlap_pigeonhole formula-decl nil pigeonhole_int nil))
   shostak)))

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Beweissystem der NASA

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NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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