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Datei: middle_third_overlap.prf Sprache: Lisp

Original von: PVS^©

(middle_third_overlap
(middle_third_overlap 0
  (middle_third_overlap-4 nil 3414576950
   ("" (skosimp*)
    (("" (rewrite "min_reduce")
      (("" (rewrite "max_reduce")
        (("" (lemma "middle_third_pigeonhole[N]")
          ((""
            (inst - "highset(v1!1, e1!1, byz(card(e1!1)))"
             "lowset(v2!1, e2!1, card(e2!1) - 1 - byz(card(e2!1)))"
             "src_set!1" "e1!1" "e2!1")
            (("" (prop)
              (("1" (expand* "highset" "lowset")
                (("1" (skosimp*)
                  (("1" (inst?) (("1" (prop) nil nil)) nil)) nil))
                nil)
               ("2" (use "card_highset")
                (("2" (expand* "two_thirds_majority_subset?" "byz")
                  (("2" (assert)
                    (("2" (expand* "subset?" "highset" "member")
                      (("2" (skosimp*) nil nil)) nil))
                    nil))
                  nil))
                nil)
               ("3" (use "card_lowset")
                (("3" (expand* "two_thirds_majority_subset?" "byz")
                  (("3" (assert)
                    (("3" (expand* "subset?" "lowset" "member")
                      (("3" (skosimp*) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((min_reduce formula-decl nil reduce_properties nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers 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)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (empty? const-decl "bool" sets nil)
    (non_empty_finite_set type-eq-decl nil finite_sets nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (tau_type type-eq-decl nil tau_declaration nil)
    (byz const-decl "tau_type" tau_declaration nil)
    (vec type-eq-decl nil node 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" middle_third_overlap nil)
    (T formal-nonempty-type-decl nil middle_third_overlap nil)
    (pred type-eq-decl nil defined_types nil)
    (total_order? const-decl "bool" orders nil)
    (<= formal-const-decl "(total_order?[T])" middle_third_overlap nil)
    (vec2seq_type application-judgement "ne_seqs[T]"
     middle_third_overlap nil)
    (middle_third_pigeonhole formula-decl nil middle_third_pigeonhole
     nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (two_thirds_majority_subset? const-decl "bool" pigeonhole nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (card_highset formula-decl nil reduce_properties nil)
    (card_lowset formula-decl nil reduce_properties nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Card const-decl "nat" finite_sets nil)
    (card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
    (highset const-decl "finite_set[below(N)]" reduce_properties nil)
    (lowset const-decl "finite_set[below(N)]" reduce_properties nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields 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)
    (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)
    (max_reduce formula-decl nil reduce_properties nil))
   nil)
  (middle_third_overlap-3 nil 3403897718
   ("" (skosimp*)
    (("" (rewrite "min_reduce")
      (("" (rewrite "max_reduce")
        (("" (lemma "middle_third_pigeonhole[N]")
          ((""
            (inst - "highset(e1!1, f1!1, byz(card(e1!1)))"
             "lowset(e2!1, f2!1, card(e2!1) - 1 - byz(card(e2!1)))"
             "src_set!1" "e1!1" "e2!1")
            (("" (prop)
              (("1" (expand* "highset" "lowset")
                (("1" (skosimp*)
                  (("1" (inst?) (("1" (prop) nil nil)) nil)) nil))
                nil)
               ("2" (use "card_highset")
                (("2" (expand* "two_thirds_majority_subset?" "byz")
                  (("2" (assert)
                    (("2" (expand* "subset?" "highset" "member")
                      (("2" (skosimp*) nil nil)) nil))
                    nil))
                  nil))
                nil)
               ("3" (use "card_lowset")
                (("3" (expand* "two_thirds_majority_subset?" "byz")
                  (("3" (assert)
                    (("3" (expand* "subset?" "lowset" "member")
                      (("3" (skosimp*) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((min_reduce formula-decl nil reduce_properties nil)
    (vec type-eq-decl nil node nil)
    (tau_type type-eq-decl nil tau_declaration nil)
    (byz const-decl "tau_type" tau_declaration nil)
    (total_order? const-decl "bool" orders nil)
    (middle_third_pigeonhole formula-decl nil middle_third_pigeonhole
     nil)
    (two_thirds_majority_subset? const-decl "bool" pigeonhole nil)
    (card_highset formula-decl nil reduce_properties nil)
    (card_lowset formula-decl nil reduce_properties nil)
    (highset const-decl "finite_set[below(N)]" reduce_properties nil)
    (lowset const-decl "finite_set[below(N)]" reduce_properties nil)
    (max_reduce formula-decl nil reduce_properties nil))
   nil)
  (middle_third_overlap-2 nil 3398091778
   ("" (skosimp*)
    (("" (rewrite "min_reduce")
      (("" (rewrite "max_reduce")
        (("" (typepred "index(enabled1!1, f1!1)(byz(enabled1!1))")
          ((""
            (typepred
             "index(enabled2!1, f2!1)(card[below(N)](enabled2!1) - 1 - byz(enabled2!1))")
            (("" (expand "index_value")
              (("" (flatten)
                (("" (hide -1 -2 -4 -5 -6 -7)
                  (("" (expand "byz")
                    (("" (lemma "middle_third_pigeonhole[N]")
                      ((""
                        (invoke (inst - "%1" "%2" _ _ _) (! -3 l 1)
                         (! -2 l 1))
                        (("1" (inst?)
                          (("1" (expand "two_thirds_majority_subset?")
                            (("1" (rewrite "subset_filter")
                              (("1"
                                (rewrite "subset_filter")
                                (("1"
                                  (assert)
                                  (("1"
                                    (hide-all-but (-1 1))
                                    (("1"
                                      (skosimp*)
                                      (("1"
                                        (expand "filter")
                                        (("1"
                                          (expand ">=")
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (inst?)
                                              (("1" (assert) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (assert) nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((total_order? const-decl "bool" orders nil)
    (middle_third_pigeonhole formula-decl nil middle_third_pigeonhole
     nil)
    (two_thirds_majority_subset? const-decl "bool" pigeonhole nil))
   nil)
  (middle_third_overlap-1 nil 3377615981
   ("" (skosimp*)
    (("" (rewrite "min_reduce")
      (("" (rewrite "max_reduce")
        (("" (typepred "index(eligible1!1, f1!1)(tau(eligible1!1))")
          ((""
            (typepred "index(eligible2!1, f2!1)
                                    (card[below(N)](eligible2!1) - 1 - tau(eligible2!1))")
            (("" (expand "index_value")
              (("" (flatten)
                (("" (hide -1 -2 -4 -5 -6 -7)
                  (("" (expand "tau")
                    (("" (lemma "middle_third_pigeonhole[N]")
                      ((""
                        (invoke (inst - "%1" "%2" _ _ _) (! -3 l 1)
                         (! -2 l 1))
                        (("1" (inst?)
                          (("1" (expand "two_thirds_majority_subset?")
                            (("1" (rewrite "subset_filter")
                              (("1"
                                (rewrite "subset_filter")
                                (("1"
                                  (assert)
                                  (("1"
                                    (hide-all-but (-1 1))
                                    (("1"
                                      (skosimp*)
                                      (("1"
                                        (expand "filter")
                                        (("1"
                                          (expand ">=")
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (inst?)
                                              (("1" (assert) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (assert) nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((total_order? const-decl "bool" orders nil)
    (middle_third_pigeonhole formula-decl nil middle_third_pigeonhole
     nil)
    (two_thirds_majority_subset? const-decl "bool" pigeonhole nil))
   nil)))

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