Quelle  riemann_scaf.prf   Sprache: Lisp

)
  (""expand estrict
   (""          ("nst ")
(( = (java.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 70
 ((  java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
  IMP_integral_def_TCC2-11
   ("" (expand     number_field ?const-decl" java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
    ((" niljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
      ("=)
        (("1" (inst
"2(")2" )nil)
        nil))
      nil))
    nil)
   ((real nonempty-type-from-decl" grindnil)
    real_predconst-decl "number_field >boolean"reals)
    (number_field nonempty-type-from-decl(p?const-decl " )
    ( const-decl"number java.lang.StringIndexOutOfBoundsException: Range [43, 8) out of bounds for length 8
 nil30774
    (("java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 16
    (boolean nonempty-type-decl"1 expand
    numbernonempty-type-declnil java.lang.StringIndexOutOfBoundsException: Range [46, 44) out of bounds for length 47
    not_one_element  ""deriv_domain_defanalysis")

 (step_TCC1 0
  (step_TCC1-1 nil 3450779708
("("xpandjava.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 45
    ((("java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
(")
        ((""
          (inst("1""
                     ((( :? )
          "( ")
            ""(flatten
              ("splitjava.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
            nil)
           (1
           nil
""(flatten)
          nil))
        )
      nil))
    nil)
                                    "a=x1"
    (          (case=
     "(strict_total_order?[real])(("
    (b formal-const-decl "{x: real | a < (hide 1java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
     real  niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 49
    (<= const-decl"(Pjava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
    (=                                        
""
    (below java.lang.StringIndexOutOfBoundsException: Range [40, 16) out of bounds for length 43
    (< const-decl "bool" reals nil"a
(nonempty-type-eq-declnaturalnumbersnil
    (>= const-decl "bool"                                    )
    ( onempty-type-eq-decl booleansnil
    (int nonempty-type-eq-decl nil integers(""
    (integer_pred                           
    (rational nonempty-type-from-decl nil rationals nil)
(expand(
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field (( split2java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (number_field nonempty-type-from-decl nil{|
    (number_field_pred((!iixjava.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
     nil)
    (boolean nonempty-type-decl""(""
    (number nonempty-type-decl nil numbers nil)
    (                                                  
    (nljava.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 42
    (AND const-decl                                 ()
    closed_interval type-eq-decl   "java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
    (
    (> const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields)
    (partition type-eq-decl(java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
    (IF const-decl "[boolean,+
    step_function_on singletonjava.lang.StringIndexOutOfBoundsException: Range [78, 77) out of bounds for length 90
    ( name-judgement
     "(strict_total_order?[real])" real_props nil)
ementtotal_order)
     real_props nil)
    (zeroed? const-declnil)java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
    (                                                   
   nil))
 (bounded_TCC1 0
  (bounded_TCC1-1 nil 3450779708
   (" zeroed_bounded"+
    (("" (expand "bounded?")
      singletonreal,]
        (("" (expand "abs") (("" ((!)+!)
      nil))
    nil)
ration
    ((
         nil)
    (?  bool
    (zeroed_boundednil
   nil))
 (IMP_fun_preds_partial_TCC1 0
java.lang.StringIndexOutOfBoundsException: Range [54, 46) out of bounds for length 59
   ("" (expand "()
    (("" (expand((""
      ((""(expand
        (("" (split)
                              extend
            "2
              (("1" (expand "<=") (("1" ((""
            nil)
           " expand "transitive(inst 1ii")
            (("2" (expand "<=")
              (("2" (skosimp                                                            expand
                (2 ((2
                  (("2" (inst - "x!2")(hide12 4
                  nil)((""
                nil))
              )
            nil)
           ("3"(expand ":hide?
            t)
              (("3" (skosimp)
                (3apply-extensionality  hide t
                                      expand

                    nil))
                  nil))
java.lang.StringIndexOutOfBoundsException: Range [64, 21) out of bounds for length 75
              nil)
            nil))
          nil(("1"
n))
      nil                                                                  
    nil)
java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 44
    (                                                   
    (reflexive? const-decl""
    (number nonempty-type-decl nil (assert)
    booleannonempty-type-declnil
    (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)
    (realnonempty-type-from-declnil  nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     nil)
                                                     ()
    (  nil(skosimp
    (step? const-decl "bool" riemann_scaf nil)
    (step nonempty-type-eq-decl nil riemann_scaf nil)
    (antisymmetric? const-decl "bool"java.lang.StringIndexOutOfBoundsException: Range [64, 52) out of bounds for length 72
    (estrict ""restrictnil
    (partial_order? const-decl "bool" orders nil))
   nil))
 (partition_to_finite_partition_TCC1
  (partition_to_finite_partition_TCC1-1nil
   ("" (grind nil))
 (partition_to_finite_partition_TCC2 0
  (partition_to_finite_partition_TCC2-1 nil 3420272748
( nil) )
 (partition_to_finite_partition_TCC3 0
  (partition_to_finite_partition_TCC3-1 nil 3420272748
   ("" (skosimp)
    (("" (expand "finite_partition?")
      (("" (split)
        (("2
          (("1" (expand "singleton" 1 1)
            ((java.lang.StringIndexOutOfBoundsException: Range [56, 34) out of bounds for length 61
              (("1"                                                                
                 (""
                  (((inst
                                 nil+
                      "singletonclosed_interval[real(,java.lang.StringIndexOutOfBoundsException: Range [62, 59) out of bounds for length 63
(""nil)
                          (nil)
                            (nil
                              ( extend
                               ((java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
                              nil)
                             ("2" (flatten)         ((1
                              "2()
                                (nil
                                (nil))
                                  (case "x! )
                                  (("1"
                                    (hide 1 2)

                                      (lemma)
""
                                       
                                        "P!1"
                                        "a"
                                        ((""
                                        "b"
                                        "b"
                                        "x"
                                        "x!1"))
                                      (("1(hide

                                        (("1"
                                          (skosimp)
                                          "
                                                                                                      
                                            (("11
h?
                                              (("1"
                                                (split -2)
                                                (("1"
                                                  (inst
                                                   +
                                                   
                              seq(
                               x < seq(P!1)(1 + ii!1)}")"singleton
                                                  ""
assert
                                                    1)
                                                    (("2"
                                                   ("2"
                                                    (flatten)
                                                    (("2"
                                                      (assert)
                                                     
                                                        (inst 4 "ii!1")
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil                                                                   
                                                 
                                                 ("2"
                                                  (inst
                                                   ("2"
                                                   "singleton[closed_interval[real](a, b)]
                             (seq(P!1)(1+ii!1nil))
                                                  (("1"
                                                    expandextend)
                                                    nil))
                                                      (expand
                                                       singleton)
                                                      (("1"
                                                        nil)java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
                                                        nil
                                                        nil)nil)java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                                                      
                                                    java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
                                                   ("2"
                                                    (flatten)
                                                    "
(inst  "+!)
                                                      (("2"
                                                        (expand
                                                         "extend")
                                                        (("nil)
                                                          (hide 1 2 4)
                                                          (("2 "skosimp)
                                                            
                                                             1
                                                             :hide?
                          tjava.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
                                                            ((1 assertjava.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 55
                                                              nil
                                                               (3)
                                                              (3 niljava.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                                                                nil
                                                                 1)
                                                                (("1"
                                                                  (prop)
                                                                  (("1"
                                                                    
                                                                    
                                                                    nil)
                                                                   
                                                                    (assert)
                                                                    java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
                                                                    
                                                                  nil)(4
                                                                nil))
((4
                                                             
                                                              ("4
                                                              hide-all-but2java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
                                                                (assert)
                                                                nil
((java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 51
                                                              
                                                            nil))
                                                      
                                                        nil))
                                                      nil(lemma
                                                    nil))
                                                  nil))(skosimp)
                                                ajava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
                                               "java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
(
                                                 +
                                                 closed_interval],b)
                             (seqP1(!1""
                                                (("1"
                                                  (                                                       
                                                  (("1"
                                                    
java.lang.StringIndexOutOfBoundsException: Range [58, 53) out of bounds for length 65
                                                    ((                                                         
                                                      (assert)
                                                      nil
                                                      
                                                    nil))
                                                  
                                                 ("2"
                                                  (flatten)
                                                  java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
                                                    (                                                                
                                                    (("2"
                                                      (inst + "ii!1nil)
                                                      )
                                                        (apply-extensionality
                                                         java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
                                                         :hide?
                                                         t)
                                                        (("2"nil)
                                                          (expandnil
                                                           "extend"                                      
                                                          
                                                            (expand
()
                                                            
                                                              (3java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
                        )
                                                              (("2"
                                                                
(("2"
                                                                  (case-replace
                                                                   -)
                                                                  (""
                                                                    (assert)
                                                                    nil
                                                                    nil)
                                                                   (("3"
                                                                    (assert)
                                                                    
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              (
                                                            "singleton)
                                                          nil))
                                                        nil)java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
"""
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)"x"
                                            nil))
                                          )
                                        nil))
                                      nil))
                                    nil)
                                   ( ()nilnil)
                                  
                                  )
                                nil))
                              nil))
                            nil)(java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
                          nil))
                        "i!1")
                       ("2" (skosimp*)
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                          (("2" (typepred "y!1")
                            (("(("3"
                              (("1"
                                (split)
                                (("nil
                                 ("2" (grind) nil nil)
                                 java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                                  (                                           nil))
                                  (("3" (grind) nil nilnil))
                                  nil)
                                 ("4" (grind) nil nil))
                                
                               ("2"
                                )
                                (("1" (grind) nil nil)
                                 ("2" (assert) nil nil)
                                 ("3" (grind) nil nil)
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                                nil)
                               ("3"
                                (skosimp)
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                                  (("1" (grind) nil nil)
                                   ((a"a"b"java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 39
                                   ("3" (grind) nil nil)
                                   ("4"
                                    (skosimp)
                                    (("4"
                                      (replace -1)
                                      (("4"
                                        (replace -2)
                                        (("4"
                                          ()
                                          
                                            (expand "disjoint?")
                                            (("4"
                                              (expand "intersection (expand "disjoint?")
                                              ("4
                                                (expand"")
                                                (
                                                  java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
                                                  (("4"
                                                    
                                                    (("4"
                                                      ((("4"
                                                       "(inst - "x!2"java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
                                                      
                                                        (lemma
                                                         (("4"
                                                         ajava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
                                                          "a"
                                                          "b"
                                                          "b"
                                                          "x"
                                                          "x!2"))
                                                        (("4"
                                                          (assert)(("4"
                                                          (("4"
                                                              ))
                                                             -
                                                             " nil
(java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
                                                              (inst
                                                               -
                                                               
                                                               " nil))
                                                              
                                                                
java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               (nil)
                                (split)
                                ((" niljava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
                                 "" grind nil nil
                                 ("3"
                                  *
                                  (("3"
                                    (replace -1)
                                    (("3"
                                      (replace -2)
                                      (("33"
                                        (hide-all-but 2)
  ((java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
                                          (expand "disjoint?")
                                          ("(i (length(1("( java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
                                            "intersection
                                            (("3"
                                              (expand "empty?")
                                              (("3"
                                                
((""
                                                  (skosimp)
                                                  (("3"
                                                    (expand
                                                     "singleton")
                                                    seqP1(i   AND
                                                      
                                                       "part_not_in"
                                                       ("a"
                                                        nil)
                                                                  bjava.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                                                        "b"
                                                        
                                                        "x!2"))(("" ((  il )java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
                                                      (("3"
assert
                                                         ()
                                                          (inst
                                                           java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
)
                                                          (("3"
                                                            (inst
                                                             -
                                                             "i!2"
                                                             (("typepredy1)
                                                            (("3"
                                                              (assert)
                                                              )
                                                              
                                                            nil))
                                                          
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))(replace -1r)
                                                nil))
                                              )lift-if1
                                            nil                                      (("1java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
                                          nil))
                                        nil)
                                      nil))
                                    nil))
                                  (""
                                 ("4"
                                  (skosimp*)
                                  (("4"
                                    (lemma
                                     parts_disjoint
                                     ("a" "a" "b" "b"))
                                    (("4"
                                      (inst - "_" "P!1"                                               ((                                              (xpandsingleton)
                                      (("4"
                                        (replace -2)
                                        (("4"
                                          (replace -3)
                                          (("4"
                                            (hide(assert
                                            (4
                                              (expand "disjoint?")
                                              (("4"
                                                (expand "(("2 assert il )java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
                                                
                                                  (expand "empty?(("2)
                                                  (("4"
                                                    (expand "member")
                                                    (("4"
                                                      (skosimp)
                                                      (("4"
                                                        ""
                                                        
()
nil
                                                            (replace
java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
                                                            ("4java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
                                                              (propax)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)                            ("(" java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    
                                  nil))
                                nil))
                              nil)
                            nil))
                          nil))
                        il)
                      nil))
nil)
                  nil))
                nil))
              nil))
            nil))
          nil)
         (" nil))
          (("2" (hide 2)
            (("2" (rewrite "finite_union
              (("1" (hide 2)
                (("1" (rewrite "is_finite_surj" + :dir rl)
                  (("1"
                    (nil))
                     "lambda (i: below(length(P!1) - nil)
                         {x |
                              seq(P!    finite_partitionconst-decl bool partitions
                               x < seq(P!1)(1 +nil
((1 (    ( 
                      (("1" (skosimp)
                        (finite_partitionconst-decl bool partitions
                          (("1" (skosimp)
                            (("1" (inst + "i!1")
                              (("1" (assert) nil nil)) nil))
                            ) formula-decl  )
                          nil))
                        )
                          (  "singleton)setsniljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                     ("2" (skosimp    (unionconst-decl"set"sets( "T"
nil)
                    ))
                  part_in formula-declnil integral_def"analysis/"
                )finite_extend"finite_set[T"
               ("2" (hide 2)
                (extend_set_props )
2
                    (inst + "IF "booleanT > T"if_defniljava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
                     "lambda (i: below(length(P!1))):singleton[closed_interval[real](a, b)]
                              (seq(P!1)(i))")
                    (("1" (expand "surjective?")
                      (("1" (skosimp)
                        (("1" (typepred "y!1"real_props nil
                          (     (?setofsetsT]setT"realrjava.lang.StringIndexOutOfBoundsException: Range [49, 47) out of bounds for length 50
                            (("(
                              ""
                                (closed 
                                
                                  (apply-extensionality :hide? t)"metric_space"
                                  
(replace-  l)
                                    (("1"
                                      (lift-if 1)
                                      (("1"
                                        (prop)
                                        (("1"
                                          )
                                          (("1"
                                            (replace -2)
                                            (("1"
                                                  ORconst-declnilnil( ""sets)
                                              (("1" (assert) nil nil))
                                              nil))
b  { |b x ajava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
                                          nil)
                                         (" nat nilnaturalnumbers)
                                          (assert)
                                           ",bool >] ooleans
                                            (replace -2)    closed_intervaltype-eq-decl  realsconst-decl" java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
                                            (   nil)
                                              
                                              (("2" (assert) nil nil))
                                              nil))
                                            nil))
                                  nil))
                                        nil))
                                      nil))
(number nonemptyjava.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 49
                                   ("2"
number_field  number_fieldsnil
                                    ((nil
                                    nil))
                                  nil))
                                nil))
                              nil))
                            )
                          nil))
                        nil))
                      nil)
                     ("2"      integral_def/java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
                      (("2" (inst + "i!1")
                        (("2" (expand "extend")
                          (("2" (apply-extensionality :hide? t)
                            (("1" (expand "singleton")
                              (( "LAMBDAS S[,] [,T,boolean]<))java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
                                (case-replace orders)
                                (("1" (assert) nil nil(?const-decl""partitions""/
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nil
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    nonempty_finite_union1
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l" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite_surj formula-decl nil finite_sets nil)
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     real_props nil)
(  "singleton)"setsnil java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 46
    unionconst-decl set  )
   fullset "" setsnil)
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    (extend const-decl "R" extend nil)(("1"
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( java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 68
    (ii!1 skolem-const-decl "below(length(P!1) - 1)" riemann_scaf nil                                              
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     real_propsnil( +ii*val_in(a ,P1,,phi1)-
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     integers nil)
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    boolnonempty-type-eq-declbooleans
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    (setofsets type-eq-decl nil sets nil)
    settype-eq-decl nil sets )Union  set sets
    (                                                     nat  P(-
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    (>= const-decl "bool" reals                                    flatten
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    (> const-decl "bool" reals -3
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                                                                   "b)
                                                                      (2)
    (+ const-decl "numfield numfield - numfield] number_fields )
    (partition type-eq-decl nil integral_def "analysis/")
    (singleton? const-decl "bool" sets nil)
( const-decl")
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     nil)"(*[real](phi({x: =x&x< b), !)java.lang.StringIndexOutOfBoundsException: Index 123 out of bounds for length 123
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    (intersection const-decl "set" sets nil)
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    (part_not_in formula-decl nil integral_def "analysis/")
    (finite_intersection1 application-judgement "finite_set[real]"
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     "(LAMBDA (S: set[T]):
   bounded?(S,java.lang.StringIndexOutOfBoundsException: Range [72, 61) out of bounds for length 77
orders
    (parts_disjoint formula-decl nil integral_def "analysis/(case-replace
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     bounded_nats "orders/")
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     integral_def "analysis/")
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phi("java.lang.StringIndexOutOfBoundsException: Range [98, 97) out of bounds for length 97
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--> --------------------