(connected_space
(clopen_def 0
(clopen_def-1 nil 3364197290
("" (skosimp)
(("" (expand "clopen?" )
(("" (typepred "S" )
(("" (expand "connected_space?" )
(("" (flatten)
(("" (expand "connected?" )
(("" (split 1)
(("1" (flatten)
(("1" (expand "open?" )
(("1" (expand "closed?" )
(("1" (expand "member" )
(("1" (inst - "A!1" ) (("1" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (flatten)
(("2" (hide -3)
(("2" (split)
(("1" (replace -1)
(("1" (assert )
(("1" (rewrite "open_emptyset" )
(("1" (rewrite "closed_emptyset" ) nil nil ))
nil ))
nil ))
nil )
("2" (replace -1)
(("2" (rewrite "closed_fullset" )
(("2" (rewrite "open_fullset" ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((clopen? const-decl "bool" topology nil )
(connected? const-decl "bool" topology_prelim nil )
(closed_emptyset formula-decl nil topology nil )
(open_emptyset formula-decl nil topology nil )
(closed_fullset formula-decl nil topology nil )
(open_fullset formula-decl nil topology nil )
(closed? const-decl "bool" topology nil )
(set type-eq-decl nil sets nil )
(A!1 skolem-const-decl "set[T]" connected_space nil )
(finite_emptyset name-judgement "finite_set" finite_sets nil )
(emptyset_is_clopen name-judgement "clopen" connected_space nil )
(emptyset_is_compact name-judgement "compact" connected_space nil )
(fullset_is_clopen name-judgement "clopen" connected_space nil )
(member const-decl "bool" sets nil )
(open? const-decl "bool" topology nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(T formal-type-decl nil connected_space nil )
(setof type-eq-decl nil defined_types nil )
(setofsets type-eq-decl nil sets nil )
(connected_space? const-decl "bool" topology_prelim nil )
(connected_space nonempty-type-eq-decl nil topology_prelim nil )
(S formal-const-decl "connected_space" connected_space nil ))
shostak)))
quality 100%
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