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Datei: seq_pigeon.prf Sprache: Lisp

Original von: PVS^©

(seq_pigeon
(seq_pigeon_lem 0
  (seq_pigeon_lem-1 nil 3507100594
   ("" (skosimp*)
    (("" (case "length(w!1) = card(fullset[below(length(w!1))])")
      (("1" (replace -1)
        (("1" (hide -1)
          (("1" (lemma "injection_and_cardinal[below(length(w!1)),T]")
            (("1" (inst?)
              (("1" (assert)
                (("1" (hide 2)
                  (("1"
                    (inst 1 "(LAMBDA (i: below(length(w!1))): w!1(i))")
                    (("1" (expand "restrict")
                      (("1" (expand "injective?")
                        (("1" (skosimp*)
                          (("1" (inst?)
                            (("1" (inst -2 "x2!1")
                              (("1" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (rewrite "card_below_fullset") nil nil)
       ("3" (rewrite "finite_below") nil nil))
      nil))
    nil)
   ((fullset const-decl "set" sets nil)
    (card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
    (Card const-decl "nat" finite_sets nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (S formal-const-decl "finite_set[T]" seq_pigeon 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (T formal-type-decl nil seq_pigeon nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (injective? const-decl "bool" functions nil)
    (restrict const-decl "R" restrict nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (injection_and_cardinal formula-decl nil finite_sets_card_eq
     "finite_sets/")
    (card_below_fullset formula-decl nil finite_sets_below
     "finite_sets/")
    (finite_below formula-decl nil finite_sets_below "finite_sets/"))
   nil))
(seq_pigeon_hole 0
  (seq_pigeon_hole-1 nil 3507100594
   ("" (skosimp*)
    (("" (lemma "seq_pigeon_lem")
      (("" (inst?)
        (("" (assert)
          (("" (skosimp*) (("" (inst?) (("" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((seq_pigeon_lem formula-decl nil seq_pigeon nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (number nonempty-type-decl nil numbers 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)
    (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (S formal-const-decl "finite_set[T]" seq_pigeon 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil seq_pigeon nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   nil)))

¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤

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