Quelle save.prf
Sprache: Lisp
(fseq2set
(bij_TCC1 0
(bij_TCC1-1 nil 3440769713 3440772507
("" (lemma "bij_exists" )
((""
(inst + "(LAMBDA (S: finite_set[T]):
choose({f: [(S) -> below(fseq2set
bijective?(f)}))")
(("" (skosimp*)
(("" (inst?)
(("" (skosimp*)
(("" (expand "nonempty?" )
(("" (expand "empty?" )
(("" (expand "member" ) (("" (inst?) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(set type-eq-declnil setsnil )
( const-declbool nil )
(finite_set type-eq-decl nil finite_sets "" (lemmabij_exists)
(number nil nil )
( const-decl [ -boolean umber_fields
nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(real nonempty-type-from-decl(" skosimp*
(rational_pred const-decl "[real - (" skosimp
rationalnonempty-type-from-declnil rationals )
(integer_pred const-decl "[rational -> boolean]" integers nil )
(int nonempty-type-eq-decl nil integers nil )
(>= const-decl "bool" reals nil )
(at nil naturalnumbers)
(< const-decl "bool" reals nil )
= const-decl[,T- boolean nil java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
(Card const-decl "nat" java.lang.StringIndexOutOfBoundsException: Range [0, 38) out of bounds for length 35
card nnat n (" )
(below type-eq-decl nil naturalnumbers nil )
(bijective? const-decl "bool" real_predconst-decl"number_field->boolean" reals)
(nonempty? const-decl "bool" sets nil )
(chooseconst-decl "p)" setsnil
(member rationalnonempty-type-from-decl rationalsnil
emptyconst-decl"" sets)
(bij_exists formula-decl nil finite_sets nil )
Tf nil fseq2set))
132 140 t nil ))
(ibij_TCC1 0
(ibij_TCC1-1 nil 34407 > const-decl "" nil )
("
( +"LAMBDA(S:non_empty_finite_set[]):inversebijS)"
(" skosimp)
(("" (typepred card "n | n =CardS} nil)
(("" (expand "empty?" )
(" expand" "
(("( 1 (" (skosimp* ("(inst) nilnil)nil)
nil ))
nil ))(? "" setsjava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
)
nil ))
nil ))
nil )
unchecked
(non_empty_finite_settype-eq-declnil finite_sets)
(empty? const-decl
_set finite_sets
(is_finite const-decl "bool" finite_sets 44 470
sets
(T (("" (skosimp (*java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
(NOT const-decl "[bool -> bool]" (" (expand " "java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
(bool nonempty-type-eq-decl nil booleans nil )
( nil booleans)
(member const-decl "bool" sets nil ))
132 110 t nil ))
( 0
(bij_ibij-1 nil 3440 ))
( skosimp
(("" (expand "ibij" )
(" lemma " omp_inverse_right[S!),below(S!))"
(("" (inst?) nil nil )) nil ) emptyconst-declbool nil )
nil ))
nil )
unchecked
( type-eq-declnil sets)
fseq2set nil )
(bij const-decl "{f: [(S) -> ( formal-type-decl nil nil)
)
(bijective? const-decl "bool" functions nil )
(comp_inverse_right formula-decl nil function_inverse nil )
(T formal-type-decl bool nonempty-type-eq-declnil booleansnil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
( type-eq-declnil setsnil )
(is_finite const-decl "bool" finite_sets nil )
(finite_set type-eq-decl nil finite_sets nil )
NOT const-decl"bool >bool] booleans niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
sets
(non_empty_finite_set type-eq-decl nil finite_sets nil )
java.lang.StringIndexOutOfBoundsException: Range [11, 4) out of bounds for length 47
fseq2set)
(? const-declbool comp_inverse_right nil function_inversenil
(number_field nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(real nonempty-type-from-decl nil reals nil )
(rational_pred const-decl "[real -> boolean]" rationals nil )
( nonempty-type-from-declnil rationalsnil
integer_pred "rational- boolean] integers niljava.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
(int nonempty-type-eq-decl nil integers nil )
(>= const-decl "bool" reals nil )
( nonempty-type-eq-decl aturalnumbers
(< const-decl "bool" reals nil )
(= const-decl"T T - boolean] nil
(Card const-decl "nat" finite_sets nil )
(card const-decl "{n: numbernonempty-type-decl niljava.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 47
(below type-eq-decl [- boolean realsjava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
24 20 t shostak))
(ibij_bij
(ibij_bij-1 (integer_pred" - ]" )
int integersnil
((" (assert)
(("" (expand (natnonempty-type-eq-decl naturalnumbersnil
(("" (assert )( [, >"java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
(" lemma" [(!)below(1])
(("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil ) 42 shostak)
nil ))
nil )
unchecked
(( ("skosimp*java.lang.StringIndexOutOfBoundsException: Range [17, 18) out of bounds for length 17
"(bijective?[R, (" "()
(unique_bijective_inverse application-judgement "{(" lemma)belowcard1)"
)
(bij const-decl "{fnil)
fseq2set nil )
(bijective? const-decl "bool" nil )
(bijective_inverse formula-decl nil function_inverse nil )
T formal-type-decl nil )
(boolean nonempty-type-decl "bijective?R ]" nil
( nonempty-type-eq-decl booleans nil
(set nil )
is_finite"" finite_sets)
(finite_set type-eq-decl nil finite_sets nil )
(NOT const-decl "[bool -> bool]" booleans nil ) ( formula-decl nil function_inverse nil )
(empty? const-decl "bool" sets nil )
non_empty_finite_settype-eq-declnil nil )
(number nonempty-type-decl nil numbers nil )
(number_field_pred set nil setsnil
nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(real_pred const-declnon_empty_finite_settype-eq-declfinite_setsjava.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
(real nonempty-type-from-declnumber_field nil number_fieldsnil )
(rational_pred const-decl "[real -> boolean]" real_pred "number_field- ]" reals)
nil )
(integer_pred const-decl const-decl-] integers)
( )
(nat nonempty-type-eq-decl( "" nil
(< const-decl "bool( { ()" )
(= const-decl "[T, T -> boolean]" java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 47
( 3 0tshostak
card { =Card) nil
(belowtype-eq-declnaturalnumbersnil
(ibij const-decl(*java.lang.StringIndexOutOfBoundsException: Range [17, 18) out of bounds for length 17
fseq2set nil (" inst?)
31 30 t shostak))
(seq2set_TCC1-1 nil
("" (skosimp*)
(" (java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
( fs)(ii"
(("" (inst?)
(("" ()
(("" (hide 2)
(inst + "length(fs!1)"
( (: belowlength1))
seq(fs!1)(ii))")
(("1" (expand "surjective?" )
(("1" (skosimp* (1 assert
(("1" ( "!1" java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
(("1" (skosimp*)
(("1" (assert )
(("1" (inst?)
(("1" java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
(("1"
"assertjava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
(("1 () nil)
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
"(*)
(("2" (assert )
(("" (expand "finseq_appl" java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
(("2" (inst?) (set nil setsnil )
nil )
nil ))
nil ))
nil ))
)java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
)
nil )) nil nil
nil ))
nil )
unchecked
(boolean nil nil
(bool(barraytype-eq-decl fseqs structures"
( type-eq-decl nil )
(number nonempty-type-decl nil numbers nil )
(number_field_predbelowtype-eq-decl naturalnumbers)
nil )
(number_field = const-decl"T T- boolean]" equalitiesnil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(real nonempty-type-from-decl nil reals nil )
( const-decl"real- boolean] rationals nil)
(rational nonempty-type-from-decl nil rationals nil )
(integer_pred "rational-> boolean" integers)
( )
(>= const-decl "bool" realsT nil
nat nil naturalnumbersnil
(< const-decl ("expand finseq_appl)
(barray type-eq-decl nil fseqs "structures/" )
(fseq type-eq-decl nil fseqs "structures/" )
belowtype-eq-declnil naturalnumbers)
()
surjectivebool )
(
(below "/
is_finite_surj nil
(T formal-type-declnat nil nil java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
59 40 t shostak))
(( nonempty-type-eq-decl
(seq2set_lem-1 nil 3282915134 344 integer_pred [-booleanintegers)
java.lang.StringIndexOutOfBoundsException: Range [13, 3) out of bounds for length 17
(("" (expand "finseq_appl" )
(("" (assert )
(("" (expand "seq2set" )
("( finseq_appl)(" "(?) nilnil)nil)
nil ))
)
nil ))
nil )
unchecked
(below nil naturalnumbersnil )
(fseq type-eq-decl nil fseqs "structures/" )
(barray type-eq-decl nil fseqs "structures/" )
(T formal-type-decl nil (numbernonempty-type-declnil numbersnil
( const-decl"bool" reals)
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(>= const-decl "bool" reals nil card_seq2set
( nonempty-type-eq-decl booleansnil )
(int nonempty-type-eq-decl nil integers nil )
(integer_pred const-decl"rational - integers nil)
(rational nonempty-type-from-decl nil rationals nil )
(rational_pred const-decl "[real ->boolean]" rationalsnil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
( ("" ( "lengthfs!)" )
number_field_predconst-decl"number boolean]" number_fields
nil )
((" (expand " finseq_appl
number numbersnil
(seq2set const-decl "finite_set[T]" fseq2set nil ))
3520tshostak)java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
(card_seq2set 0
(card_seq2set-2 "" 3283086594 3 "( " )
("" (skosimp*)
(("" (typepred "seq2set(fs!1)" )
(("" (typepred "length(fs!1)" )
(("" (expand "seq2set" )
(("" ( ("
(("" (lemma "seq2set_lem" )
("" inst
(("" (assert )
("expand" java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
(("" (expand +
lemmaCard_injection
(("" (expand "injective?" )
((""
(inst -1
s: T| EXISTSkk lengthfs1):fs1seq) = s"
"length(fs!1)"
(("" (assert )
((expand )
java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
+
"LAMBDA (f: {s: (skosimp*)
(("1"
(skosimp*)
(("1" (assert (2
nil )
("2"
(skosimp*)
(("2"
(expand "nonempty?" )
(("2"
(typepred f1)
(("2"
(skosimp*)
(("2"
(expand "empty?" )
(("2"
(expand "member" )
(("2"
(inst -2 "kk!1" )
nil
nil ))
)java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
nil ))
nil ))
(seq2setconst-decl"[T]" fseq2set)
nil ))
ype-eq-declnil "/)
nil ))
nil ))
nil )) const-decl"" finite_sets)
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
nil )
nil ))
nil ))
nil )
unchecked
((seq2set (below type-eq-decl nil
(finite_set nil nil
fseqtype-eq-decl structures"
(barray type-eq-decl (=const-declbool nil java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(is_finite const-decl "bool" finite_sets nil )
set nil sets
( type-eq-decl naturalnumbersjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(injective? const-decl[
(empty nil
(memberconst-decl"bool niljava.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
(below type-eq-decl nil nat_types nil )
(AND const-decl "[bool, bool -> bool]" number_field_pred [ >
,>"nil
<"" realsjava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
( { ()( :S)IMPLIES=x}"
min_nat nil
nonemptyconst-decl"" nil
(= const-decl "[T, T -> boolean]" equalities ((" (emma " seq2set_lem)
(below type-eq-decl nil naturalnumbers nil )
(< const-decl "bool" reals nil )
( nonempty-type-eq-decl nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
(rational nonempty-type-from-decl nil rationals nil )
( const-decl"real ->boolean" rationalsnil
(Card_injection formula-decl((" (expand " ?)
(real_ge_is_total_order name-judgement "(total_order?[real] ((" "
real_props nil )
( inst1
real_props nil )
(seq2set_lem formula-decl nil
(number nonempty-type-decl nil numbers nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(real nonempty-type-from-decl nil reals nil )
(= "" realsnil )
231 190 t shostak)
(card_seq2set-1 nil 3282918983 3283085680
("" (skosimp*)
("(expand seq2set)
(("" (lemma "seq2set_lem" )
(("" (inst?)
(" (assert)
(("" (expand "seq2set" )
(("" (expand "finseq_appl" )
((" lemma " )
(("" (expand "injective?" )
("
(inst -1
"{s: T | EXISTS (kk: below(length(fs!1))): fs!1`seq(kk) = s}"
"length(fs!1)" )
(("1" (assert )
"min({kk below(lengthfs!)) |fs!`seq(kk)=x21}" )
(("1"
(inst +
"LAMBDA (s: {s: T | EXISTS (kk: below(length(fs!1))): fs!1`seq(kk) = s}): min( {kk: below(length(fs!1)) | fs!1`seq(kk) = s}nil)
((
(skosimp*)
(("1"
(inst-cp
-2
"min({kk: below(length(fs!1)) | fs!1`seq(kk) = x1!1})" )
(("1"
(inst
-2
"min({kk (skosimp)
(("1"
( ((""
(("1" (assert ) nil nil ))
nil )
("2"
(skosimp
(("2" (assert ) nil
nil ))
nil nil ))
("2" (assert
nil ))
nil )
("2"
(skosimp*
(("2"
(reduce nil 222834720
(("2" (( )
(grind)
( (" (expand seq2set)
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (postpone) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
nil ))
nil ))
nil ))
nil )
nil ))
nil )
unfinished nil 506 real_lt_is_strict_total_order
(minmax_seq2set_TCC1 0
(minmax_seq2set_TCC1-1 nil rational_predconst-declnil java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
("" (skosimp*)
(("" (expand "empty?" )
(" expand member)
(("" (expand "seq2set" )
(("" (inst - "ne_fs! ( nil " "
(("" ( (real nonempty-typ java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
(("" (assert
(("" nil "" java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
)
nil ))
nil ))
nil )
nil ))
nil ))
nil ))
nil )
((empty? const-decl " (" ( ne_fs1"
(seq2set const-decl "finite_set[T]" fseq2set nil )
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real] (" " expand seq2set)
(rational_pred const-decl "[real -> boolean]" rationals nil )
(rational nonempty-type-from-decl nil rationals nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
(int nonempty-type-eq-decl nil integers nil )
(>= const-decl "bool" reals nil ) (< const-decl "bool" reals nil )
(below ("" inst
( type-eq-declnil fseqs structures"
(> const-decl "bool" reals nil )
(nonempty-type-eq-decl )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(boolean nonempty-type-decl nil booleans nil )
( nonempty-type-decl numbersnil )
(fseq type-eq-decl nil fseqs "structures/" )
(barray type-eq-decl nil mm
(nat "[T <=({s: |EXISTS(: below(length(ne_fs!)): !1`seq(kk) s}" java.lang.StringIndexOutOfBoundsException: Index 117 out of bounds for length 117
(T formal-type-decl nil fseq2set nil )
(member const-decl "bool" sets nil ))
1 2 tshostak
java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
(minmax_seq2set-2 "" 3283271310 3440772898
" skosimp*)
(("" (typepred "seq2set(ne_fs!1)" )
(("" (typepred "ne_fs!1" )
(("" (split)
(("1" (typepred "min(ne_fs!1)" )
(("1" (expand "seq2set" )
(("1" (assert )
(("1" (skosimp*)
(("1" (expand "finseq_appl" )
(("1" (inst?)
(("1" ( 1 < mmjava.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
(("1" (inst?)
(("1" (expand "seq2set" )
(("1" (expand "finseq_appl" )
(("1"
(inst?)
(("1"
(lemma "min_seq_lem" )
(("1"
(name
mm
"min[T, <=]({s: T | EXISTS (kk: below(length(ne_fs!1))): ne_fs!1`seq(kk) = s})" )
((""
(expand
(
(typepred "mm" )
(("1"
(skosimp*)
(("1"
(case "mm <= min(ne_fs!1)" )
(("1"
(assert )
(("1"
(case
"min(ne_fs!1) <= mm" )
(("1"
(assert )
(("1"
(typepred "<=" )
"
(java.lang.StringIndexOutOfBoundsException: Range [67, 61) out of bounds for length 82
"total_order?" )nil
(("1"
(("1"
(expand
"dichotomous?" )
(("1"
(expand
"partial_order?" )
nil ))
(expand
"antisymmetric?" )
(("1"
( java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
(("1"
(inst
-2
"mm"
"min(ne_fs!1)" )
(flatten
(assert )
nil
nil ))
nil ))
-8
"ne_fs!1"
)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(assert )
(("2"
(typepred "<=" )
(("2"
(expand
"total_order?" )
(("2"
(expand
("" ( nil java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
(("2 nil)
(expand
"partial_order? nil)
(assert
(flatten)
(("2"
(expand
"antisymmetric?" )
(("2"
(inst
-8
"ne_fs!1"
"kk!1" )
(("2"
nil
nil
nil ))
nil ))
nil ))
nil ))
nil ))
java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
nil ))
nil ))
*
nil ))
nil )
(2
(inst? -2)
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(assert )
(("2"
(skosimp*)
(("2"
(expand "empty?" )
(("2"
(expand "member" )
(("2"
(inst?)
m max )
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
nil ))
nil ))
nil ))
nil )
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (typepred "max(ne_fs!1)" )
(("2" (expand "seq2set" )
(("2" (assert )
(("2" (skosimp*)
(("2" (expand "finseq_appl" )
"?" )
(("2" (lemma "seq2set_lem" )
(("2" (inst?)
(("2" (expand "seq2set" )
(("2" (expand "finseq_appl" )
(("2"
(?)
(("2"
(lemma "max_seq_lem" )
((
(name
mm
" max[T, <=]
({s: T |
EXISTS "mm"
(("1"
(replace -1)
(("1"
(typepred "mm" )
(("1"
(*)
(("1"
(case "mm <= max(ne_fs!1)" )
(("1"
)
(("1"
(case
"max(ne_fs!1) <= mm" )
(("1"
(assert )
(("1"
(typepred "<=" )
(("1"
(expand
"total_order?" )
(flatten)
(("1"
(expand
"dichotomous?" )
(expand
(expand
(("1"
(expand
"antisymmetric?" )
(("1"
(flatten)
(("1"
(inst
-2
"mm"
"max(ne_fs!1)" )
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(assert )
(("2"
(typepred "<=" )
(("2"
( flatten
"total_order?" )
(("1"
(expand
"dichotomous?" )
(("2"
"partial_order?" )
(("2"
(flatten)
(("2"
(expand
"antisymmetric?" )
(("2"
(expand
"preorder?" )
(("2"
( (inst
"reflexive?" )
(("2"
(expand
"transitive?" )
(("2"
(flatten)
("2
(lemma
"max_lem" )
(("2"
(inst?
-1)
(("1"
(replace
-9)
(("1"
(("1"
)
(("1"
(skosimp*)
(("1"
(inst?)
nil
nil nil
nil ))
nil ))
nil ))
nil )
nil )
(expand
(("2"
(inst?)
(("2"
("
"member" )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(inst?)
(("2"
(inst
-4
"ne_fs!1"
( nil "structures/)
(("2"
(assert )
nil
nil " java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
nil ))
nil ))( nonempty-type-declbooleansjava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
nil ))
nil ))
nil )
(finite_sets_minmax/)
(2java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
)
dichotomousconst-decl"" orders)
(expand "empty?" )
(("2"
(inst?)
(("2"
(expand rational_pred [>" nil)
rational java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
(inst 1 "jj!1" )
(("2"
(assert )
nil
( min_fseqstructures)
nil ) AND "[ool, >bool]" )
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((ne_fseq type-eq-decl nil fseqs(skosimp
(> ("( " (!))
(real nonempty-type-from-decl ("( ne_fs!1" java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number ((" " assertjava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
nil )
(number nonempty-type-decl nil numbers nil )
(seq2set const-decl "finite_set[T]" fseq2set nil )
(finite_set type-eq-decl nil finite_sets nil )
(fseq type-eq-decl nil fseqs "structures/" )
(barray type-eq-decl nil fseqs "structures/" )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
("" ( "finseq_appl" )
(set type-eq-decl nil sets nil )
(inst
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(seq2set_lem formula-decl nil fseq2set nil )
(empty? const-decl "bool" sets nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
( const-decl
"{a: T | SS(a) AND (FORALL (x: T): SS(x) IMPLIES a <= x)}"
finite_sets_minmax "finite_sets/" )
(partial_order? const-decl "bool" orders nil )
(antisymmetric? const-decl "bool" relations nil )
(dichotomous const-decl boolordersnil )
(member const-decl "bool" sets nil )
(min_seq_lem formula-decl nil min_fseq "structures/" )
(below type-eq-decl nil naturalnumbers nil )
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(rational_pred const-decl "[real -> boolean]" rationals nil )
(rational nonempty-type-from-decl nil rationals nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
( nonempty-type-eq-decl java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
(>= const-decl "bool" reals nil ) (< const-decl "bool" reals nil )
(pred type-eq-decl nil defined_types nil )
total_orderconst-decl "" orders nil java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
(<= formal-const-decl "(total_order?[T])" fseq2set nil )
(dom
(AND const-decl "[bool, bool -> bool]" booleans nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(in "t:T|
(FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_fseq
"structures/" )
(max const-decl
"{a: T | SS(a) AND (FORALL (x: T): SS(x) IMPLIES x <= a)}"
finite_sets_minmax "finite_sets/" )
(preorder? const-decl "bool" orders nil )
(transitive? const-decl "bool" relations nil )
(max_lem formula-decl nil finite_sets_minmax "finite_sets/" )
(reflexive? const-decl "bool" relations nil )
(max_seq_lem formula-decl nil max_fseq "structures/" )
(dom type-eq-decl nil max_fseq "structures/" )
(max const-decl "{t: (" 1"
(FORALL (ii: dom(s)): seq(s)(ii) <= t) AND
(EXISTS (jj: dom(s)): seq(s)(jj) = t)}" max_fseq
"structures/" ))
861 760 t shostak)
(minmax_seq2set-1 nil 3283098598 3283255060
("" (skosimp*)
(("" (typepred "seq2set(ne_fs!1)" )
(("" (typepred "ne_fs!1" )
(("" (split)
(("1" ( "inne_fs1"
(("1" (
(("1" (assert )
(("1" (skosimp)
(("1" (expand "finseq_appl" )
(("1" (inst?)
(("1" (lemma "seq2set_lem" )
(("1" (inst?)
"" ( seq2set
(("1" (expand "finseq_appl" )
(("1"
(inst?)
(("1"
(lemma "min_seq_lem" )
nil ))
(skosimp*)
(("1"
mm
,{ EXISTS!))`() }))
(("1nil))
(replace -1)
(("1"
(typepred "mm" )
(("1"
(skosimp*)
(("1"
(case
"mm <= min(ne_fs!1)" )
(("1"
(assert )
(("1"
"min(ne_fs!1) <= mm" ) java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
(("1"
(assert )
(("1"
(typepred "<=" )
(("1"
(expand
"total_order?" )
(("1"
(
(("1"
(expand
"dichotomous?" )
)
(expand
"?)
(("1"
"antisymmetric?" )
(("1"
(flatten)
"
(inst
-2
"mm"
"min(ne_fs!1)" )
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil boolean nil booleans)
("2"
(("2"
(inst?)
(("2"
()
nil
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(postpone)
nil
nil ))
nil ))
nil ))
nil ))
nil )
("2" (postpone) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (postpone) nil nil ))
nil ))
nil ))
nil ))
nil )
unfinished nil 3562301 6490 t shostak))
(seq2set_TCC2 0
(seq2set_TCC2-1 nil 3282912778 3440772507
("" (skosimp*)
(("" (expand "nonempty?" )
(("" (lemma "minmax_seq2set_TCC1" )
(("" (inst?) (("" (assert ) (("" (postpone) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((nonempty? const-decl "bool" sets nil )
(ne_fseq type-eq-decl nil fseqs "structures/" )
(> const-decl "bool" reals nil )
(bool nonempty-type-eq-decl nil booleans nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(boolean nonempty-type-decl nil booleans nil )
(number nonempty-type-decl nil numbers nil )
(fseq type-eq-decl nil fseqs "structures/" )
(barray type-eq-decl nil fseqs "structures/" )
(T formal-type-decl nil fseq2set nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(minmax_seq2set_TCC1 subtype-tcc nil fseq2set nil ))
30 10 t shostak))
(set2seq_TCC1 0
(set2seq_TCC1-2 nil 3440770694 3440772890
(""
(inst + "(LAMBDA (S: finite_set[T]):
choose({fs: fseq[T] |
length(fs) = card[T](S) AND
(FORALL (ii: below(length(fs))):
S(fs`seq(ii))) AND
(FORALL (x: T):
S(x)
IMPLIES
(EXISTS
(ii: below(length(fs))):
fs`seq(ii) = x))
AND
(FORALL (ii, jj: below(length(fs))):
ii /= jj
IMPLIES
("(*java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
(("" (skosimp*)
(("" (name "F" "ibij(S!1)" )
(("1" (typepred "ibij(S!1)" )
(("1" (replace -2 * lr)
(("1" (hide -2)
(("1" (expand "nonempty?" )
(("1" (expand "empty?" )
(("1" (expand "member" )
(("1"
(inst -2 "(# length := card(S!1),
seq := (LAMBDA (i: nat): IF i < card (1
ELSE default
ENDIF)
#)")
(("1" (prop)
(("1" (ground) nil nil )
("2" (skosimp*)
(("2" (inst + "bij(S!1)(x!1)" )
(("2" (lift-if)
(("2"
(ground)
(("2"
(expand "F" )
(("2" (rewrite "ibij_bij" ) nil nil ))
nil ))
"java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
nil ))
nil ))
nil )
)
(("3" (lift-if)
(("3" (ground)
(("3"
(expand "bijective?" )
(("3"
(flatten)
(("3"
(expand "injective?" )
(("3"
(inst?)
(("3" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (skosimp*)
(("2" (lift-if) (("2" (ground) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil )
nil ))
nil ))
nil )
("2" (expand "nonempty?" )
(("2" (lemma "empty_card" )
(("2" (inst?)
((2" (assert)
(2( -1*lr
(("2" (hide -1)
(("2" (hide -1)
(("2" expand ?"
(("2" (expand ))
(("2"
(inst -
#:,seq=(LAMBDA (: nat: default)#))
(("2" (prop)
(("1" (skosimp*) nil nil )
("2"
(skosimp*)
(("2"
(assert )
(("2"
(reveal -2)
(("2"
(expand "empty?" )
(("2"
(expand "member" )
(("2" (inst?) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("3" (skosimp*) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((empty_card formula-decl nil finite_sets nil )
(IF const-decl "[boolean, T, T -> T]" if_def nil )
(default const-decl "T" fseqs "structures/" )
(injective? const-decl "bool" functions nil )
(ibij_bij formula-decl nil fseq2set nil )
( name-judgement
"(strict_total_order nil)
(bij const-decl "{f: [(S) -> below(card(S))] | bijective?(f)}"
fseq2set nil )
(real_ge_is_total_order name-judgementnil ))
real_props nil )
(member const-decl "bool" sets nil )
(ibij const-decl "{f: [below(card(S)) -> (S)] | bijective?(f)}"
fseq2set nil )
(bijective? const-decl "bool" functions nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(empty? const-decl "bool" sets nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(choose const-decl "(p)" sets nil )
(nonempty? const-decl "bool" sets nil )
(/= const-decl "boolean" notequal)
IMPLIES ",bool - bool" nil
( type-eq-decl naturalnumbersnil java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
(< const-decl "bool" reals nil )
(card const-decl "{n: nat | n = Card(S)}" java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 8
(Card const-decl "nat" finite_sets nil )
(>= const-decl "bool" reals nil )
( nonempty-type-eq-decl nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
(rational nonempty-type-from-decl nil (defaultconst-decl"T fseqs structures/"
(rational_pred const-decl "[real -> boolean]" rationals nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(= const-decl ( const-decl "{f (S - (()) |bijective?()"
(number nonempty-type-decl nil numbers nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(fseq type-eq-decl nil fseqs "structures/" )
(barray type-eq-decl nil fseqs "structures/" )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(finite_set type-eq-decl nil finite_sets nil )
(is_finite const-decl "bool" finite_sets nil )
(?const-decl"functionsniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
(bool empty "" setsnil
(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil fseq2set nil ))
365426 390 t nil )
(set2seq_TCC1-1 nil 3280842302 344077067 below nil )
(""
(inst + "(LAMBDA (S: finite_set[T]):
choose({fs: fseq[T] |
> "" )
(FORALL (ii: below(length(fs))):
S(fs`seq(ii)) AND
rational_pred [ >] nil
S(x)
IMPLIES
(EXISTS
(ii: below(length(fs))):
fs`seq(ii) = x))
AND
(FORALL (ii, jj: below(length(fs))):
ii /= jj
IMPLIES
fs`seq(ii) /= fs`seq(jj)))}))")
(("" (skosimp*)
(("" (name "F" "bij(S!1)" )
(("" (typepred "bij(S!1)" )
(("" (replace -2 * lr)
(" hide-)
(("" (expand "nonempty?" )
(("" (expand "empty?" )
(("" (expand "member" ) (("" (postpone) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unfinished ((nonempty? const-decl "bool" sets nil )) 116 80 t
shostak))
(set2seq_length 0
(set2seq_length-1 nil 32810989Sxjava.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
("" (induct(EXISTS
(("1" (expand "set2seq" )
(("1" (expand "fseq1" )
(("" ( "o " java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
(("1" (ground)
(("1" (case "empty?[T](emptyset[T])" )
(("1" (assert )
(("1" (rewrite "card_emptyset[T]" )
(("1" (assert )
(("1 (" " skosimp*java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
nil ))
nil ))
nil ))
nil )
("2" (hide 2) (("2" (grind) nil nil )) nil ))
nil ))
nil ))
nil )
nil ))
nil )
("2" (skosimp*)
(("2" (expand "set2seq" 1)
(("2" (expand "o " )
(("2" (expand "fseq1" )
(("2" (assert )
(("2" (rewrite "card_rest" ) (("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((finite_rest application-judgement " ((finite_rest application-judgement "finite_set
(finite_emptyset name-judgement "finite_set" finite_sets nil )
(finite_emptyset name-judgement "finite_set[T]" fseq2set nil )
(finite_set_induction_rest formula-decl nil finite_sets_inductions
"finite_sets/" )
(T formal-type-decl nil fseq2set nil )
(set2seq const-decl "{fs: fseq[T] |
length(fs) = card(S) AND
(FORALL (ii: below(length(fs))): S(fs`seq(ii))) AND
(FORALL (x: T):
S(x) IMPLIES
(EXISTS (ii: below(length(fs))): fs`seq(ii) = x))
AND
(FORALL (ii, jj: below(length(fs))):
ii /= jj IMPLIES fs`seq(ii) /= fs`seq(jj))}" fseq2set
nil )
(/= const-decl "boolean" notequal nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
)
< boolrealsnil
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil )
(Card const-decl "nat" finite_sets nil )
(>= const-decl "bool" reals nil )
(int nonempty-type-eq-decl nil integers nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
( nonempty-type-from-declnil java.lang.StringIndexOutOfBoundsException: Range [51, 43) out of bounds for length 56
(rational_pred const-decl "[real -> boolean]" rationals nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(fseq ))
(barray type-eq-decl nil fseqs "structures/" )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(number nonempty-type-decl nil numbers nil )
(pred type-eq-decl nil defined_types nil )
(finite_set type-eq-decl nil finite_sets nil )
(is_finite const-decl "bool" finite_sets nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
84 70 t shostak))
(set2seq_lem 0
(set2seq_lem-1 nil 3280846807 3440772898
("" (skosimp*)
(("" (assert )
(("" (skosimp*)
(("" (typepred )
(("" (inst?) (("" (flatten) nil nil )) nil )) nil ))
nil )
nil ))
( name-judgementfinite_set finite_sets nil java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
unchecked nil 28 20 t shostak))
(set2seq_exists 0
( "/" java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
("" (skosimp*)
(("" (assert )
(("" (flatten)
((" ( " set2seq(!1")
(("" (inst -3 "x!1" ) FORALL(:T:
nil ))
nil ))
nil )
unchecked
((set2seq const-decl "{fs: fseq[T] |
length(fs) = card(S) AND
(FORALL (ii: below(length(fs))): S(fs`seq(ii))) AND
(FORALL (x: T):
S(x) IMPLIES
(EXISTS (ii: below(length(fs))): fs`seq(ii) = x))
AND
(FORALL (ii, jj: below(length(fs))):
ii /= jj IMPLIES fs`seq(ii) /= fs`seq(jj))}" fseq2set
nil )
(/= const-decl "boolean" notequal nil )
IMPLIESconst-decl[bool,bool>bool"booleansnil
(below type-eq-decl nil naturalnumbers nil )
(< const-decl "bool" reals nil )
(card ( const-decl "number_field >boolean" realsjava.lang.StringIndexOutOfBoundsException: Range [63, 61) out of bounds for length 64
( number_field_pred " - boolean]"
(>= const-decl "bool" reals nil )
(int nonempty-type-eq-decl nil integers nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
(rational nonempty-type-from-decl nil rationals nil )
(rational_pred const-decl "[real -> boolean]" rationals nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
( type-eq-decl finite_sets nil
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
--> --------------------
--> maximum size reached
--> --------------------
quality 100%
¤ Dauer der Verarbeitung: 0.25 Sekunden
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*© Formatika GbR, Deutschland
2026-03-28