(continuity_defnil 3358738874 3358739024"" (lemma "functions_exist" )"" (flatten)"" (split)"1" (skosimp)"1" (expand "empty?" )"1" (inst - "y!1" )"1" (expand "fullset" )"1" (expand "member" ) (("1" (propax) nil nil )) nil ))nil ))nil ))nil ))nil )"2" (expand "fullset" )"2" (expand "nonempty?" )"2" (expand "empty?" )"2" (expand "member" )"2" (lemma "fun_exists[T1,T2]" )"2" (assert )"2" (replace 1 -1)"2" (skosimp) (("2" (inst -2 "f!1" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil function_image nil )nil continuity_def nil )"bool" sets nil )nil continuity_def nil )"bool" sets nil )"set" sets nil )"bool" sets nil )nil continuity_def nil ))nil ))nil 3358738874 3358738875"" (subtype-tcc) nil nil ) unchecked"bool" sets nil )"bool" sets nil )"bool" sets nil )"set" sets nil ))nil nil ))nil 3358739096"" (expand "continuous?" )"" (skosimp)"" (expand "continuous_function_witness" )"" (case-replace "empty?(fullset[T2])" )"1" (name "F" "choose(fullset[[T1 -> T2]])" )"1" (replace -1)"1" (expand "empty?" )"1" (inst - "F(x!1)" )"1" (expand "member" )"1" (expand "fullset" ) (("1" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert )"2" (expand "continuous_at?" )"2" (skosimp)"2" (name "Y" "choose(fullset[T2])" )"2" (replace -1)"2" (case-replace "U!1(Y)" )"1" "inverse_image(LAMBDA x: Y, U!1) = fullset[T1]" )"1" (expand "neighbourhood?" )"1" (expand "interior_point?" )"1" (inst + "fullset[T1]" )"1" rewrite "subset_reflexive" )"1" expand "fullset" )"1" expand "member" )"1" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (apply-extensionality 1 :hide? t)"2" (expand "fullset" )"2" (expand "inverse_image" )"2" expand "member" )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil )"2" "inverse_image(LAMBDA x: Y, U!1) = emptyset[T1]" )"1" (expand "neighbourhood?" )"1" (expand "interior_point?" )"1" (skosimp)"1" expand "member" )"1" expand "subset?" )"1" "Y" )"1" expand "member" )"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (apply-extensionality 1 :hide? t)"2" (expand "emptyset" )"2" (expand "inverse_image" )"2" expand "member" )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil continuity_def nil )nil booleans nil )nil booleans nil )set type-eq-decl nil sets nil ) (empty? const-decl "bool" sets nil )"set" sets nil )"bool" sets nil )nil continuity_def nil )"[T, T -> boolean]" equalities nil )"bool" sets nil )"(p)" sets nil )"bool" continuity_def nil )"bool" topology nil )nil topology nil )"bool" topology nil )"topology[T1]" continuity_def nil )nil topology_def nil )"bool" topology_def nil )nil sets nil )nil defined_types nil )nil sets_lemmas nil )"bool" topology nil )"set[D]" function_image nil )"bool" sets nil )"set" sets nil )"[T1 -> T2]" continuity_defnil )"bool" continuity_def nil ))nil )))quality 100%
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