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Datei: di_subgraphs.prf Sprache: Lisp

Original von: PVS^©

(di_subgraphs
(finite_vert_subset 0
  (finite_vert_subset-1 nil 3253624236
   ("" (skosimp*)
    (("" (lemma "finite_subset[T]")
      (("" (inst?)
        (("" (inst -1 "vert(G!1)")
          (("" (assert) (("" (hide 2) (("" (grind) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil di_subgraphs nil)
    (finite_subset formula-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (digraph type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" 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)
    (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))
   nil))
(finite_edge_subset 0
  (finite_edge_subset-1 nil 3307706313
   ("" (skosimp*)
    (("" (lemma "finite_subset[edgetype[T]]")
      (("" (inst?)
        (("" (inst - "edges(G!1)")
          (("" (assert) (("" (hide 2) (("" (grind) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((edgetype type-eq-decl nil digraphs nil)
    (T formal-type-decl nil di_subgraphs nil)
    (finite_subset formula-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (digraph type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets 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))
   nil))
(di_subgraph_TCC1 0
  (di_subgraph_TCC1-1 nil 3253624236
   ("" (skosimp*)
    (("" (lemma "finite_subset[edgetype[T]]")
      (("" (inst?)
        (("" (inst - "edges(G!1)")
          (("" (assert) (("" (hide 2) (("" (grind) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((edgetype type-eq-decl nil digraphs nil)
    (T formal-type-decl nil di_subgraphs nil)
    (finite_subset formula-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (digraph type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets 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))
   nil))
(di_subgraph_TCC2 0
  (di_subgraph_TCC2-1 nil 3307703845
   ("" (skosimp*) (("" (rewrite "finite_vert_subset") nil nil)) nil)
   ((finite_vert_subset formula-decl nil di_subgraphs nil)
    (T formal-type-decl nil di_subgraphs 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))
   nil))
(di_subgraph_TCC3 0
  (di_subgraph_TCC3-2 nil 3307706135
   ("" (skosimp*)
    (("" (prop)
      (("1" (skosimp*)
        (("1" (typepred "G!1")
          (("1" (inst?) (("1" (assert) nil nil)) nil)) nil))
        nil)
       ("2" (expand "di_subgraph?")
        (("2" (prop) (("1" (grind) nil nil) ("2" (grind) nil nil))
          nil))
        nil))
      nil))
    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 di_subgraphs nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (di_subgraph? const-decl "bool" di_subgraphs nil))
   nil)
  (di_subgraph_TCC3-1 nil 3307703845 ("" (subtype-tcc) nil nil)
   ((edgetype type-eq-decl nil digraphs nil)
    (predigraph type-eq-decl nil digraphs nil)
    (digraph type-eq-decl nil digraphs nil))
   nil))
(di_subgraph_vert_sub 0
  (di_subgraph_vert_sub-1 nil 3253624236
   ("" (skosimp*)
    (("" (expand "di_subgraph")
      (("" (apply-extensionality 1 :hide? t)
        (("" (expand "subset?")
          (("" (inst?)
            (("" (expand "member")
              (("" (iff 1) (("" (ground) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((di_subgraph const-decl "di_subgraph(G)" di_subgraphs nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (edgetype type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (predigraph type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (digraph type-eq-decl nil digraphs nil)
    (set type-eq-decl nil sets nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil di_subgraphs nil))
   nil))
(di_subgraph_lem 0
  (di_subgraph_lem-1 nil 3253624236
   ("" (skosimp*) (("" (assert) nil nil)) nil) nil nil))
(di_subgraph_smaller 0
  (di_subgraph_smaller-1 nil 3253624236
   ("" (skosimp*)
    (("" (expand "size")
      (("" (expand "di_subgraph?")
        (("" (rewrite "card_subset[T]") nil nil)) nil))
      nil))
    nil)
   ((size const-decl "nat" digraphs nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (card_subset 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)
    (edgetype type-eq-decl nil digraphs nil)
    (predigraph type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (digraph type-eq-decl nil digraphs nil)
    (T formal-type-decl nil di_subgraphs nil)
    (di_subgraph? const-decl "bool" di_subgraphs nil))
   nil)))

¤ Dauer der Verarbeitung: 0.3 Sekunden (vorverarbeitet) ¤

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