Quelle max_subtrees.prf Sprache: Lisp

(max_subtrees
(sing_is_tree 0
  (sing_is_tree-1 nil 3301744077
   ("" (skosimp*)
    (("" (expand "tree?")
      (("" (expand "singleton_digraph")
        (("" (rewrite "card_singleton") nil nil)) nil))
      nil))
    nil)
   ((tree? def-decl "bool" trees nil)
    (card_singleton formula-decl nil finite_sets nil)
    (T formal-type-decl nil max_subtrees nil)
    (singleton_digraph const-decl "digraph" digraphs nil))
   nil))
(tree_in 0
  (tree_in-1 nil 3301744077
   ("" (skosimp*)
    (("" (typepred "G!1")
      (("" (hide -1)
        (("" (expand "nonempty?")
          (("" (expand "empty?")
            (("" (skosimp*)
              (("" (expand "member")
                (("" (inst 1 "singleton_digraph(x!1)")
                  (("1" (grind) nil nil)
                   ("2" (rewrite "sing_is_tree") nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Digraph type-eq-decl nil digraphs nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (edgetype type-eq-decl nil digraphs nil)
    (T formal-type-decl nil max_subtrees nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (tree? def-decl "bool" trees nil)
    (singleton_digraph const-decl "digraph" digraphs nil)
    (x!1 skolem-const-decl "T" max_subtrees nil)
    (Tree type-eq-decl nil trees nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (finite_emptyset name-judgement "finite_set" finite_sets nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set" finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (emptyset const-decl "set" sets nil)
    (di_subgraph? const-decl "bool" di_subgraphs nil)
    (singleton const-decl "(singleton?)" sets nil)
    (sing_is_tree formula-decl nil max_subtrees nil)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil))
   nil))
(max_subtree_TCC1 0
  (max_subtree_TCC1-1 nil 3301744077
   ("" (skosimp*)
    (("" (lemma "tree_in")
      (("" (inst?)
        (("" (skosimp*)
          (("" (inst?)
            (("" (prop)
              (("" (expand "extend") (("" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((tree_in formula-decl nil max_subtrees nil)
    (tree? def-decl "bool" trees nil) (Tree type-eq-decl nil trees nil)
    (Digraph type-eq-decl nil digraphs nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (edgetype type-eq-decl nil digraphs nil)
    (T formal-type-decl nil max_subtrees nil))
   nil))
(max_subtree_TCC2 0
  (max_subtree_TCC2-1 nil 3301744077
   ("" (skosimp*)
    (("" (prop)
      (("1" (lemma "max_di_subgraph_in")
        (("1" (inst?)
          (("1" (expand "extend") (("1" (assert) nil)))
           ("2" (hide 2)
            (("2" (lemma "tree_in")
              (("2" (inst?)
                (("2" (skosimp*)
                  (("2" (inst?)
                    (("2" (assert)
                      (("2" (expand "extend")
                        (("2" (propax) nil)))))))))))))))))))
       ("2" (expand "extend") (("2" (assert) nil))))))
    nil)
   ((tree? def-decl "bool" trees nil)
    (Gpred type-eq-decl nil max_di_subgraphs nil)
    (di_subgraph? const-decl "bool" di_subgraphs nil)
    (pred type-eq-decl nil defined_types nil)
    (Digraph type-eq-decl nil digraphs nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (edgetype type-eq-decl nil digraphs nil)
    (max_di_subgraph_in formula-decl nil max_di_subgraphs nil)
    (T formal-type-decl nil max_subtrees nil))
   nil))
(max_subtree_tree 0
  (max_subtree_tree-1 nil 3301744077
   ("" (skosimp*)
    (("" (expand "max_subtree")
      (("" (lemma "max_di_subgraph_in")
        (("" (inst?)
          (("1" (expand "extend") (("1" (assert) nil)))
           ("2" (hide 2)
            (("2" (lemma "tree_in")
              (("2" (inst?)
                (("2" (skosimp*)
                  (("2" (inst?)
                    (("2" (expand "extend")
                      (("2" (assert) nil))))))))))))))))))))
    nil)
   ((max_subtree const-decl "Subtree(G)" max_subtrees nil)
    (tree? def-decl "bool" trees nil)
    (Gpred type-eq-decl nil max_di_subgraphs nil)
    (di_subgraph? const-decl "bool" di_subgraphs nil)
    (pred type-eq-decl nil defined_types nil)
    (Digraph type-eq-decl nil digraphs nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (edgetype type-eq-decl nil digraphs nil)
    (max_di_subgraph_in formula-decl nil max_di_subgraphs nil)
    (T formal-type-decl nil max_subtrees nil))
   nil))
(max_subtree_di_subgraph 0
  (max_subtree_di_subgraph-1 nil 3301744077
   ("" (skosimp*) (("" (assert) nil)) nil) nil nil))
(max_subtree_max 0
  (max_subtree_max-1 nil 3301744077
   ("" (skosimp*)
    (("" (expand "max_subtree")
      (("" (lemma "max_di_subgraph_is_max")
        (("" (inst?)
          (("1" (expand "extend")
            (("1" (ground)
              (("1" (hide 2)
                (("1" (typepred "SS!1")
                  (("1" (hide -1 -3)
                    (("1" (lemma "tree_nonempty")
                      (("1" (inst?)
                        (("1" (expand "empty?")
                          (("1" (expand "nonempty?")
                            (("1" (propax) nil)))))))))))))))))))
           ("2" (hide 2)
            (("2" (lemma "tree_in")
              (("2" (inst?)
                (("2" (skosimp*)
                  (("2" (inst?)
                    (("2" (assert)
                      (("2" (expand "extend")
                        (("2" (propax) nil))))))))))))))))))))))
    nil)
   ((max_subtree const-decl "Subtree(G)" max_subtrees nil)
    (edgetype type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (predigraph type-eq-decl nil digraphs nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (digraph type-eq-decl nil digraphs nil)
    (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (Digraph type-eq-decl nil digraphs nil)
    (pred type-eq-decl nil defined_types nil)
    (di_subgraph? const-decl "bool" di_subgraphs nil)
    (Gpred type-eq-decl nil max_di_subgraphs nil)
    (tree? def-decl "bool" trees nil)
    (di_subgraph type-eq-decl nil di_subgraphs nil)
    (Tree type-eq-decl nil trees nil)
    (Subtree type-eq-decl nil max_subtrees nil)
    (max_di_subgraph_is_max formula-decl nil max_di_subgraphs nil)
    (T formal-type-decl nil max_subtrees nil))
   nil)))

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