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((tree? def-decl "bool" trees nil)
(card_singleton formula-decl nil finite_sets nil)
(T formal-type-decl nil max_subtrees nil)
(singleton_graph const-decl "(singleton?)" graphs nil))
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(tree_in 0
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("2"
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("2"
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("3"
(inst -1 "x!3")
(("3"
(expand "dbl")
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(expand
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(expand
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(expand
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(assert)
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nil))
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nil))
nil))
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("6"
(inst -1 "x!3")
(("6"
(expand "dbl")
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(propax)
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nil))
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nil))
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("2"
(split +)
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("2"
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2)
(("1"
(expand
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(("1"
(expand
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(("1"
(case-replace
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(("1"
(rewrite
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(("1"
(inst
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"x!3"
"y!1")
(("1"
(assert)
nil
nil))
nil))
nil)
("2"
(hide
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(("2"
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(("1"
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nil)
("2"
(inst?)
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("3"
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("3"
(inst?)
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("4"
(skosimp*)
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(inst?)
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(assert)
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nil))
nil))
nil))
nil))
nil)
("2"
(case-replace
"del_vert[T]((# vert := edg[T](x!3, y!1),
edges :=
singleton[doubleton]
(dbl[T](x!3,
y!1))
#),
x!3) = singleton_graph(y!1)")
(("1"
(hide -1)
(("1"
(rewrite
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nil
nil))
nil)
("2"
(hide
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3)
(("2"
(hide
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-2)
(("2"
(apply-extensionality
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(("1"
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("2"
(skosimp*)
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("2"
(expand
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(("2"
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(("2"
(expand
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(("2"
(expand
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(("2"
(expand
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(("2"
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("3"
(skosimp*)
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(assert)
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nil))
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nil))
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("4"
(inst?)
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(assert)
nil
nil))
nil))
nil))
nil))
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("3"
(skosimp*)
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(expand
"singleton")
(("3"
(expand
"edg")
(("3"
(assert)
nil
nil))
nil))
nil))
nil)
("4"
(expand
"edg")
(("4"
(inst?)
(("4"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("2"
(assert)
(("2"
(expand
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(expand
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(("2"
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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("3"
(inst?)
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(assert)
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nil))
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nil))
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("2"
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(("2" (assert) nil nil))
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nil))
nil))
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nil))
nil))
nil))
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nil))
nil))
nil))
nil))
nil))
nil)
((Graph type-eq-decl nil graphs nil)
(nonempty? const-decl "bool" sets nil)
(graph type-eq-decl nil graphs nil)
(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans 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)
(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)
(isolated? const-decl "bool" graphs nil)
(sing_is_tree formula-decl nil max_subtrees nil)
(G!1 skolem-const-decl "Graph[T]" max_subtrees nil)
(singleton const-decl "(singleton?)" sets nil)
(subgraph? const-decl "bool" subgraphs nil)
(emptyset const-decl "set" sets nil)
(subset? const-decl "bool" sets nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set" finite_sets nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(Tree type-eq-decl nil trees nil)
(x!1 skolem-const-decl "T" max_subtrees nil)
(singleton_graph const-decl "(singleton?)" graphs nil)
(singleton? const-decl "bool" graphs nil)
(tree? def-decl "bool" trees nil)
(nil application-judgement "finite_set[T]" max_subtrees nil)
(singleton? const-decl "bool" sets nil)
(x!3 skolem-const-decl "T" max_subtrees nil)
(y!1 skolem-const-decl "T" max_subtrees nil)
(edg const-decl "doubleton[T]" graphs nil)
(finite_doubleton formula-decl nil doubletons nil)
(deg const-decl "nat" graph_deg nil)
(card_singleton formula-decl nil finite_sets nil)
(incident_edges const-decl "finite_set[doubleton[T]]" graph_deg
nil)
(finite_remove application-judgement "finite_set" finite_sets nil)
(remove const-decl "set" sets nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(del_vert const-decl "graph[T]" graph_ops nil)
(member const-decl "bool" sets nil)
(empty? const-decl "bool" sets nil))
nil))
(max_subtree_TCC1 0
(max_subtree_TCC1-1 nil 3251113228
("" (skosimp*)
(("" (lemma "tree_in")
(("" (inst?)
(("" (skosimp*)
(("" (inst?)
(("" (prop)
(("" (expand "extend") (("" (assert) nil))))))))))))))
nil)
((tree_in formula-decl nil max_subtrees nil)
(extend const-decl "R" extend nil)
(tree? def-decl "bool" trees nil) (Tree type-eq-decl nil trees nil)
(Graph type-eq-decl nil graphs nil)
(nonempty? const-decl "bool" sets 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)
(T formal-type-decl nil max_subtrees nil))
nil))
(max_subtree_TCC2 0
(max_subtree_TCC2-1 nil 3251113228
("" (skosimp*)
(("" (prop)
(("1" (lemma "max_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)
((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)
(nonempty? const-decl "bool" sets nil)
(Graph type-eq-decl nil graphs nil)
(pred type-eq-decl nil defined_types nil)
(subgraph? const-decl "bool" subgraphs nil)
(Gpred type-eq-decl nil max_subgraphs nil)
(FALSE const-decl "bool" booleans nil)
(extend const-decl "R" extend nil)
(tree? def-decl "bool" trees nil)
(max_subgraph_in formula-decl nil max_subgraphs nil)
(T formal-type-decl nil max_subtrees nil))
nil))
(max_subtree_tree 0
(max_subtree_tree-1 nil 3251113228
("" (skosimp*)
(("" (expand "max_subtree")
(("" (lemma "max_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)
(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)
(nonempty? const-decl "bool" sets nil)
(Graph type-eq-decl nil graphs nil)
(pred type-eq-decl nil defined_types nil)
(subgraph? const-decl "bool" subgraphs nil)
(Gpred type-eq-decl nil max_subgraphs nil)
(FALSE const-decl "bool" booleans nil)
(extend const-decl "R" extend nil)
(tree? def-decl "bool" trees nil)
(max_subgraph_in formula-decl nil max_subgraphs nil)
(T formal-type-decl nil max_subtrees nil))
nil))
(max_subtree_subgraph 0
(max_subtree_subgraph-1 nil 3251113228
("" (skosimp*) (("" (assert) nil)) nil) nil nil))
(max_subtree_max 0
(max_subtree_max-1 nil 3251113228
("" (skosimp*)
(("" (expand "max_subtree")
(("" (lemma "max_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)
(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)
(nonempty? const-decl "bool" sets nil)
(Graph type-eq-decl nil graphs nil)
(pred type-eq-decl nil defined_types nil)
(subgraph? const-decl "bool" subgraphs nil)
(Gpred type-eq-decl nil max_subgraphs nil)
(FALSE const-decl "bool" booleans nil)
(extend const-decl "R" extend nil)
(tree? def-decl "bool" trees nil)
(Subgraph type-eq-decl nil subgraphs nil)
(Tree type-eq-decl nil trees nil)
(Subtree type-eq-decl nil max_subtrees nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(tree_nonempty formula-decl nil trees nil)
(empty? const-decl "bool" graphs nil)
(max_subgraph_is_max formula-decl nil max_subgraphs nil)
(T formal-type-decl nil max_subtrees nil))
nil)))
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