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("" (skosimp*)
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(("" (prop)
(("1" (lemma "conn_implies_piece[T]")
(("1" (inst?)
(("1" (lemma "piece_implies_path[T]")
(("1" (inst?) (("1" (assert) nil)))))))))
("2" (lemma "path_implies_conn[T]")
(("2" (inst?) (("2" (assert) nil))))))))))
nil)
((path_implies_conn formula-decl nil graph_path_conn nil)
(T formal-type-decl nil graph_connected nil)
(conn_implies_piece formula-decl nil graph_conn_piece nil)
(piece_implies_path formula-decl nil graph_piece_path nil)
(graph type-eq-decl nil graphs nil)
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(set type-eq-decl nil sets nil)
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(boolean nonempty-type-decl nil booleans nil))
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(path_eq_piece 0
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("2" (lemma "piece_implies_path[T]")
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nil)
((piece_implies_path formula-decl nil graph_piece_path nil)
(T formal-type-decl nil graph_connected nil)
(path_implies_conn formula-decl nil graph_path_conn nil)
(boolean nonempty-type-decl nil booleans nil)
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(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)
(conn_implies_piece formula-decl nil graph_conn_piece nil))
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(piece_eq_conn 0
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(("1" (lemma "piece_implies_path[T]")
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(("1" (inst?) (("1" (assert) nil)))))))))
("2" (lemma "conn_implies_piece[T]")
(("2" (inst?) (("2" (assert) nil))))))))))
nil)
((conn_implies_piece formula-decl nil graph_conn_piece nil)
(T formal-type-decl nil graph_connected nil)
(piece_implies_path formula-decl nil graph_piece_path nil)
(path_implies_conn formula-decl nil graph_path_conn nil)
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(finite_set type-eq-decl nil finite_sets nil)
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(conn_eq_complected 0
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(("" (expand "complected?")
(("" (iff) (("" (propax) nil))))))))))
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((T formal-type-decl nil graph_connected nil)
(conn_eq_compl formula-decl nil graph_complected nil)
(complected? const-decl "bool" graph_conn_defs 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))
nil)))
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