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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: modal.ML   Sprache: Lisp

Original von: PVS©
(trees
 (tree?_TCC1 0
  (tree?_TCC1-1 nil 3262616780
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      (("" (expand "del_vert")
        (("" (rewrite "card_remove") (("" (assert) nil))))))))
    nil)
   ((size const-decl "nat" graphs nil)
    (card_remove formula-decl nil finite_sets nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (T formal-type-decl nil trees nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (del_vert const-decl "graph[T]" graph_ops nil))
   nil))
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    nil)
   ((empty? const-decl "bool" graphs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (size const-decl "nat" graphs nil)
    (deg_to_card formula-decl nil graph_deg nil)
    (tree? def-decl "bool" trees nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (T formal-type-decl nil trees nil)
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                (("1" (expand "size" -1)
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                      (("1" (inst -1 "edges(G!1)")
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                          nil))
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                    (("2" (replace -1 -2)
                      (("2" (expand "deg" -3)
                        (("2" (expand "incident_edges" -3)
                          (("2"
                            (lemma
                             "finite_sets[doubleton[T]].card_one")
                            (("2"
                              (inst -1
                               "{e: doubleton[T] | edges(G!1)(e) AND e(v!1)}")
                              (("1"
                                (flatten)
                                (("1"
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                                  (("1"
                                    (skosimp*)
                                    (("1"
                                      (expand "del_vert" -4)
                                      (("1"
                                        (lemma
                                         "finite_sets[doubleton[T]].card_disj_union")
                                        (("1"
                                          (inst
                                           -1
                                           "{e: doubleton[T] | edges(G!1)(e) AND e(v!1)}"
                                           "{e: doubleton[T] | edges(G!1)(e) AND NOT e(v!1)}")
                                          (("1"
                                            (prop)
                                            (("1"
                                              (lemma
                                               "finite_sets[doubleton[T]].card_singleton")
                                              (("1"
                                                (inst -1 "x!1")
                                                (("1"
                                                  (replace -4 -1 rl)
                                                  (("1"
                                                    (replace -1 -2)
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                                                      (("1"
                                                        (replace
                                                         -6
                                                         -2
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                                                           -2)
                                                          (("1"
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                                                              (assert
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                                                              (("1"
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                                                                 -2
                                                                 -)
                                                                (("1"
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                                              edges(G!1)(x) AND x(v!1) OR edges(G!1)(x) AND NOT x(v!1)}=edges(G!1)")
                                                                  (("1"
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                                                                     -1
                                                                     -2)
                                                                    (("1"
                                                                      (assert)
                                                                      nil
                                                                      nil))
                                                                    nil)
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                                                                     -1
                                                                     2)
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                                                                         1)
                                                                        (("2"
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                                                                           2)
                                                                          (("2"
                                                                            (iff
                                                                             1)
                                                                            (("2"
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                                             ("2"
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                                                   "finite_sets[doubleton[T]]")
                                                  (("2"
                                                    (hide -1)
                                                    (("2"
                                                      (grind)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil)
                                           ("2"
                                            (lemma
                                             "finite_subset[doubleton[T]]")
                                            (("2"
                                              (inst
                                               -
                                               "edges(G!1)"
                                               "{e: doubleton[T] | edges(G!1)(e) AND NOT e(v!1)}")
                                              (("2"
                                                (assert)
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                                                          nil
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                                              nil))
                                            nil)
                                           ("3"
                                            (hide-all-but 1)
                                            (("3"
                                              (lemma
                                               "finite_subset[doubleton[T]]")
                                              (("3"
                                                (inst
                                                 -
                                                 "edges(G!1)"
                                                 "{e: doubleton[T] | edges(G!1)(e) AND e(v!1)}")
                                                (("3"
                                                  (assert)
                                                  (("3"
                                                    (hide 2)
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                                                      (grind)
                                                      nil
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                                                    nil))
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                                              nil))
                                            nil))
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                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (hide-all-but 1)
                                (("2"
                                  (lemma "finite_subset[doubleton[T]]")
                                  (("2"
                                    (inst
                                     -
                                     "edges(G!1)"
                                     "{e: doubleton[T] | edges(G!1)(e) AND e(v!1)}")
                                    (("2"
                                      (assert)
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                                        (hide 2)
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                                        nil))
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                            nil))
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                        nil))
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                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((empty_card formula-decl nil finite_sets nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (singleton? const-decl "bool" graphs nil)
    (singleton_edges formula-decl nil graphs nil)
    (size_del_vert formula-decl nil graph_ops nil)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (incident_edges const-decl "finite_set[doubleton[T]]" graph_deg
     nil)
    (G!1 skolem-const-decl "graph[T]" trees nil)
    (v!1 skolem-const-decl "(vert(G!1))" trees nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (intersection const-decl "set" sets nil)
    (empty? const-decl "bool" sets nil)
    (disjoint? const-decl "bool" sets nil)
    (card_singleton formula-decl nil finite_sets nil)
    (union const-decl "set" sets nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set" finite_sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (finite_subset formula-decl nil finite_sets nil)
    (card_disj_union formula-decl nil finite_sets nil)
    (card_one formula-decl nil finite_sets nil)
    (deg const-decl "nat" graph_deg nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (graph_induction_vert formula-decl nil graph_inductions nil)
    (T formal-type-decl nil trees nil)
    (card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
    (Card const-decl "nat" finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (size const-decl "nat" graphs nil)
    (nat nonempty-type-eq-decl nil naturalnumbers 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)
    (number nonempty-type-decl nil numbers nil)
    (tree? def-decl "bool" trees nil)
    (pred type-eq-decl nil defined_types nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
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          nil)
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               ("2" (lemma "tree_nonempty")
                (("2" (inst? -1)
                  (("2" (bddsimp)
                    (("2" (expand "empty?" 1)
                      (("2" (lemma "finite_sets[T].empty_card")
                        (("2" (inst -1 "vert(G!1)")
                          (("2" (bddsimp)
                            (("2" (hide -1 -2 1 4 5 6)
                              (("2" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil trees nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil) (> const-decl "bool" reals nil)
    (is_finite const-decl "bool" finite_sets nil)
    (Card const-decl "nat" finite_sets nil)
    (card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (empty? const-decl "bool" graphs nil)
    (empty_card formula-decl nil finite_sets nil)
    (tree_nonempty formula-decl nil trees nil)
    (int_plus_int_is_int application-judgement "int" integers 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)
    (>= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (size const-decl "nat" graphs nil)
    (G!1 skolem-const-decl "graph[T]" trees nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
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            (("1" (case "card[T](vert(G!1)) = 1")
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               ("2" (split)
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                       ("2" (lemma "size_del_vert")
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                          (("2" (reveal -2)
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                                (assert -2)
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                                  (expand "size" -2)
                                  (("2"
                                    (lemma "finite_sets[T].card_one")
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                                       -1
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                                          (hide -1 -3 -5)
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                                            (skosimp*)
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                                              (name
                                               "HH"
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                                                (replace -1 -2)
                                                (("2"
                                                  (typepred "HH")
                                                  (("2"
                                                    (expand
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                                                     -2)
                                                    (("2"
                                                      (case
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                                                      (("1"
                                                        (hide -3)
                                                        (("1"
                                                          (expand
                                                           "deg"
                                                           -4)
                                                          (("1"
                                                            (lemma
                                                             "finite_sets[doubleton[T]].card_one")
                                                            (("1"
                                                              (inst
                                                               -1
                                                               "incident_edges(v!2, G!1)")
                                                              (("1"
                                                                (bddsimp)
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--> --------------------

--> maximum size reached

--> --------------------

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