(continuity_subspacenil 3301763709"" (expand "continuous_at?" )"" (expand "restrict" )"" (skosimp*)"" (expand "neighbourhood?" )"" (expand "interior_point?" )"" (skosimp*)"" (typepred "U!2" )"" (inst -2 "U!2" )"" (split -2)"1" (skosimp*)"1" (typepred "U!3" )"1" (inst + "U!3" )"1" (typepred "x!1" )"1" (assert )"1" expand "restrict" )"1" expand "subset?" )"1" expand "inverse_image" )"1" assert )"1" "1" "f!1(x!2)" )"1" assert )"1" "x!2" )"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "open?" )"2" (expand "induced_topology" )"2" expand "restrict" )"2" expand "image" )"2" assert )"2" (inst + "U!3" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (inst + "U!2" )"2" (assert )"2" (expand "subset?" )"2" (skosimp) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"R" restrict nil )"bool" topology nil )"[T1 -> boolean]" continuity_subspace nil )nil continuity_subspace nil )"setofsets[T2]" subspace nil )"open[T1, S]" continuity_subspace nil )"(partial_order?[set[T]])" nil )"bool" sets nil )"bool" sets nil )"set[D]" function_image nil )"set[R]" function_image nil )"topology[T1]" continuity_subspace nil )nil continuity_subspace nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil continuity_subspace nil )set type-eq-decl nil sets nil )nil defined_types nil )nil sets nil )"bool" topology_prelim nil )nil topology_prelim nil )"topology[T2]" continuity_subspace nil )"bool" topology nil )nil topology nil )"bool" topology nil )"bool" continuity_def nil ))nil 3302357092"" (lemma "subspace_continuous_at" )"" (expand "continuous?" )"" (skosimp*)"" (typepred "x!1" )"" (inst - "f!1" "x!1" )"" (inst - "x!1" ) (("" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil )"bool" continuity_def nil )nil continuity_subspace nil )"[T1 -> boolean]" continuity_subspace nil )nil continuity_subspace nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )nil continuity_subspace nil )nil continuity_subspace nil ))nil 3358748528"" (skosimp)"" (typepred "F!1" )"" (lemma "subspace_continuous" ("f" "F!1" ))"" (assert ) nil nil )) nil ))nil ))nil )nil continuity_def nil )"bool" continuity_def nil )"topology[T2]" continuity_subspace nil )"topology[T1]" continuity_subspace nil )nil topology_prelim nil )"bool" topology_prelim nil )nil sets nil )nil defined_types nil )nil continuity_subspace nil )nil continuity_subspace nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )nil continuity_subspace nil ))nil )))quality 93%
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