(prelude_sets_auxnil 3293875050"" (skolem 1 ("A" "B" ))"" (rewrite "difference_intersection" )"" (rewrite "demorgan2" )"" (rewrite "complement_complement" ) nil nil )) nil ))nil ))nil )nil sets_lemmas nil )nil booleans nil )nil booleans nil )set type-eq-decl nil sets nil )nil prelude_sets_aux nil )nil sets_lemmas nil )"set" sets nil )nil sets_lemmas nil ))nil 3293730468 ("" (grind) nil nil )"set" sets nil )"bool" sets nil ))nil 3293730569"" (skosimp*)"" (apply-extensionality 1 :hide? t)"" (lemma "Intersection_member" ("x" "x!1" ))"" (inst-cp - "A!1" )"" (expand "intersection" )"" (expand "member" )"" (inst - "rest(A!1)" )"" (case-replace (prelude_sets_aux"1" (simplify -3)"1" (flatten)"1" (hide -2)"1" (split -2)"1" (inst - "choose(A!1)" )"1" (assert ) nil nil )) nil )"2" (hide 2)"2" (skosimp*)"2" "a!1" )"2" "rest_subset" ("a" "A!1" ))"2" expand "subset?" )"2" expand "member" )"2" "a!1" )"2" assert )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))"2" (assert boolnonempty-type-eq-declnil booleans)"2" (replace -4)" skosimp*java.lang.StringIndexOutOfBoundsException: Range [40, 41) out of bounds for length 40 "chooseA1=!" java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64assert java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42"2" "1) "" "rest) "2" expand "nonempty?" )"( Intersection(A!1(x1" java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60assert )"2 ((" "( 2java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40 "" () nil ))"2" expand "member "2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil prelude_sets_aux nil )"!1" )"set" sets) chooseconst-decl"p" setsnil java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71"bool" setsnil java.lang.StringIndexOutOfBoundsException: Range [42, 43) out of bounds for length 42"set ) "set" nil )set type-eq-decl nil sets nil )nil java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35nil )"(surjective?[setofsets[T],nil) nil )NOT const-decl "[bool (" " (*) "" setsnil "() "setofsets[T]" prelude_sets_aux nil )"[T, T -> boolean]" equalities nil )nil nil )nil 3293823392" skosimp* "" (name "N" "card(A!1)" )"1" case "FORALL (A:setofsets[T],n:nat): subset?(A,A!1) & card(A) <= ((2" "1" (inst - "A! ((" " "1" (assert ) (("1" (rewrite "subset_reflexive" ) nil nil ))nil ))nil )"2" (hide 2)"" (induct "n" java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28"1" (skosimp*)expand <"-) 5"1" (assert ) nil))"2" (rewrite "card_is_0" -1)"1" (replace " "" hide-all-but"1" (rewrite "fullset_is_full?" )" nil)) nil ))nil ))nil )"2" (lemma nil )"2" (assert ) nil nil )nil (T formal-type-decl nil nil )nil ))nil )nil )"" (*)"" nil )"2" (split -3)"!2" (1 assert nil nil ) )"" (lemma finite_subset("s" "!" A A1)"2" (assert )"" A2)"2 nil) "" (lemma card_rest"" "!2)java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63 "(?[[T] setT]]" sets_lemmas)"1" "" "" "!" )"1" set sets)"A!2" "c" 43"1" assert "1" "(A!)) th 48"1" "choose_member" " " A2") "1" nil )"1 (2" ( )"(expand " <" -) "1" "hooseA!2" java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70rewrite fullset_is_full)"Intersection(rest(A!2))" )"1" assert )"A" "A!2" ))"1" assert )nil ))nil ))nil ))"?" )"2" " (" " lemma" card_rest "" "!" )"2" expand "member" )"2" nil nil ))((1nil ))" nil ))nil )"2" expand "nonempty?" )(assert nil ))nil ))nil ))"choose_member "a" "A2) nil )"2" expand "?" )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27nil java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25nil ))java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23nil ))nil )"" (ide"3" (skosimp*)"" (finite_subset "" "!" "" "!" ))"3" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil )"3" (skosimp*)"finite_subset" (s A2 A"A!1" )"3" (assert ) nil nil )) nil ))nil ))nil ))nil )"2" (propax) nil nil ))nil ))nil )"n:nat| n =CardS)" finite_sets nil )"nat finite_sets nil) nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[ - ]" integersnil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" realsnil ))nil nil )"[number -> boolean]" nil finite_sets nil )set type-eq-decl nil sets nil )nil defined_types nil )nil booleans nil )nil prelude_sets_aux nil )"[T, T -> boolean] (" " nil booleans nil )nil numbers nil )"posint" nil java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18nil ))"(strict_total_order?[real])" java.lang.StringIndexOutOfBoundsException: Range [54, 50) out of bounds for length 59nil sets_lemmas nil )"set" sets nil )nil sets_lemmas nil nil ))"bool" setsnil nil prelude_sets_aux nil )expand "onempty?) "(p)" sets nil nil )java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51"int nil)java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45 nil sets_lemmas nil )nil finite_setsnil nil finite_setsnil )nil finite_sets nil )"(strict_total_order?[real])" real_props nil )nil sets_lemmas nil )"set" sets nil )nil nil )java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35"finite_set" finite_sets nil )nil finite_sets nil )nil naturalnumbers )"setofsets[T]" prelude_sets_aux nil )nil sets_lemmas nil )"(?[setofsetsT],setT]" sets_lemmas nil )"(partial_order?[set[T]])" nil "(total_order?[realnil)) nil )"bool bool - bool" nil nil )"bool" nil )"bool" reals nil )"set" sets nil (3" skosimp) "()nilniljava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53 "set" sets nil nil "bool" sets nil ))nil 3293732078"n =Card()" finite_sets)"" (apply-extensionality 1 :hide? t)" expand" "java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27 "" (> "bool reals nil) "" (lemma "Union_member" ("x" "x( const-decl " - ] nil "" (expand "member" )"( " UnionA!1(!)") nil nil )"" (!java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33"1 ( const-decl [ >boolean" number_fields"1" (assert ) nil nil )"2" (flatten 2)"2" (replace -2 3)"2" (inst + "a!1" )"2" (expand "rest" )"2" expand "nonempty?" )"2" assert )"2" expand "remove" )"2" expand "member" )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert )"2" (split -2)"1" (inst + "choose(A!1)" ) nil nil )"2" (assert )"2" (skolem!)"2" (typepred "a!1" )"2" (lemma "rest_subset" ("a" "A!1" ))"" (expand subset" "" )expand "member" )"" "a!1" )"" nil java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53 out of bounds for length 49nil ))nil )nil ( n )nil ))nil ))f bounds for length 67nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil prelude_sets_aux nil )nil booleans nil )"set" sets nil ) (choose const-decl "(p)" sets nil )"bool" sets nil )"set" sets nil ) (Union const-decl "set" sets nil )set type-eq-decl nil sets nil )nil sets nil )nil defined_types nil )nil booleans nil )"(surjective?[setofsets[T], set[T]])" sets_lemmas nil )nil prelude_sets_aux nil )"bool" sets nil )NOT const-decl "[bool -> bool]" booleans nil )"bool" sets nil )nil sets_lemmas nil )"[T, T -> boolean]" equalities nil )"set" sets nil )"(A!1)" prelude_sets_aux nil )"setofsets[T]" prelude_sets_aux nil ))nil 3293825830"" (skosimp*)"" (lemma "Intersection_finite" )"" "Complement(A!1)" "lambda (x:set[T]): P!1(complement(x))" )"" (rewrite "Demorgan2" -1)"" (rewrite "Complement_Complement" )"" (rewrite "complement_fullset" -1)"" (replace -2)"" (split -1)"1" (propax) nil nil )"2" (hide-all-but (-2 1))"2" (expand "is_finite" )"2" (skolem!)"2" "N!1" "lambda (a:(Complement(A!1))): f!1(complement(a))" )"1" (expand "injective?" )"1" (skosimp*)"1" "x1!1" )"1" "x2!1" )"1" expand "Complement" )"1" "1" replace -1)"1" replace -2)"1" rewrite "complement_complement" )"1" rewrite "complement_complement" )"1" "b!1" )"1" "b!2" )"1" "b!2" "b!1" )"1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide -1)"2" (skolem!)"2" "a!1" )"2" expand "Complement" )"2" "2" "b!1" )"2" replace -2)"2" rewrite "complement_complement" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (hide-all-but (1 -3))"3" (skosimp*)"3" (typepred "a!1" )"3" (expand "Complement" )"3" (skolem!)"3" (typepred "b!1" )"3" "b!1" )"3" replace -2)"3" rewrite "complement_complement" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"4" (hide-all-but (1 -4))"4" (skosimp*)"4" "complement(a!1)" "complement(b!1)" )"4" (assert )"4" (rewrite "demorgan2" 1) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil prelude_sets_aux nil )nil sets_lemmas nil )"(bijective?[setofsets[T], setofsets[T]])" sets_lemmas nil )"(surjective?[setofsets[T], set[T]])" sets_lemmas nil )nil sets_lemmas nil )"finite_set" finite_sets nil )"bool" finite_sets nil )"setofsets[T]" prelude_sets_aux nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"bool" reals nil )nil nat_types nil )nil sets_lemmas nil )NOT const-decl "[bool -> bool]" booleans nil )"bool" functions nil )nil sets_lemmas nil )nil sets_lemmas nil )"set" sets nil )set type-eq-decl nil sets nil )"setofsets[T]" sets_lemmas nil )nil sets nil )nil defined_types nil )nil booleans nil )nil booleans nil )nil prelude_sets_aux nil ))nil 3293865693"" (skosimp*)"" (typepred "F!1" )"" (name "N" "card(F!1)" )"" (case-replace "N=0" )"1" (rewrite "card_is_0" -2)"1" (replace -2)"1" (hide -2 -3 -1) (("1" (assert ) nil nil )) nil ))nil ))nil )"2" (expand "is_finite" )"2" (skosimp*)"2" "N!1" "lambda (a:(Complement(F!1))): f!1(complement(a))" )"1" (hide -1 1)"1" (expand "injective?" )"1" (skosimp*)"1" "complement(x1!1)" "complement(x2!1)" )"1" (assert )"1" (rewrite "complement_equal" ) nil nil ))nil )"2" (typepred "x2!1" )"2" (expand "Complement" )"2" (skolem!)"2" replace -1)"2" rewrite "complement_complement" )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"3" (typepred "x1!1" )"3" (expand "Complement" )"3" (skolem!)"3" replace -1)"3" rewrite "complement_complement" )"3" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide-all-but 1)"2" (grind)"2" (rewrite "complement_complement" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil finite_sets nil )"bool" finite_sets nil )set type-eq-decl nil sets nil )nil prelude_sets_aux nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"(bijective?[setofsets[T], setofsets[T]])" sets_lemmas nil )"finite_set[set[T]]" nil )"finite_set" finite_sets nil )nil finite_sets nil )nil sets_lemmas nil )nil sets_lemmas nil )"bool" functions nil )nil nat_types nil )"bool" reals nil )"set" sets nil )"finite_set[set[T]]" prelude_sets_aux nil )"setofsets[T]" sets_lemmas nil )nil sets nil )nil defined_types nil )nil numbers nil )"[T, T -> boolean]" equalities nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" finite_sets nil )"{n: nat | n = Card(S)}" finite_sets nil ))
Messung V0.5 C=100 H=100 G=100
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