Quellcode-Bibliothek riemann_scaf.prf   Sprache: Lisp

(riemann_scaf
 (IMP_integral_def_TCC1 (riemann_scaf
  (IMP_integral_def_TCC1-1 nil 3420183209
   ("" (expand "connected?") (("" (propax) nil nil)) nil)
   ((connected? const-decl "bool" deriv_domain_def "analysis/")) nil))
 (IMP_integral_def_TCC2 0
  (IMP_integral_def_TCC2-1 nil 3420183209
   ("" (expand "not_one_element?")
    (("" (skosimp)
      (("" (case-replace "x!1=0")
        (("1" (inst + "1") (("1" (assert) nil nil)) nil)
         ("2" (inst + "0") (("2" (assert) nil nil)) nil))
        nil)
      ))
    nil)
   ((real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
rom-declnil number_fields)
    (number_field_pred const-decl "[number -> boolean]" number_fields ( 0
     nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
(boolean nonempty-type-decl  booleansnil
    (number("()
      (("(x10)
   nil))
 (step_TCC1 0
  (step_TCC1-1 nil 3450779708
   ("" (expand "step?")
(""(expand"step_function?")
      (         "" ( +0") ("2 assert nilnil)nil)
        (("java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
(inst+ "( length: 2,
                     seq := (LAMBDA (ii: below(2)): if ii = 0 then a else b    number_fieldnonempty-type-from-decl nil number_fieldsnil)
     nil
                =const-decl [T,T- ]"equalitiesniljava.lang.StringIndexOutOfBoundsException: Range [53, 54) out of bounds for length 53
              (("1" (inst ("( step_function"java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
            nil)                      :=( (: below2):java.lang.StringIndexOutOfBoundsException: Range [54, 53) out of bounds for length 87
           (" (""()
           ("3" (skosimp) (("3" (assert) nilnil
           " skosimp)(""() nil )nil)
          nil))
        nil))
      nil))
         " ()(3 (ssert nil)niljava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
   (? const-decl"""nalysis/"
    (niljava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
     "(strict_total_order?[real])"    real_gt_is_strict_total_ordername-judgement
    (b formal-const-decl "{x: real| a x} niljava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
    (a formal-const-decl "real" riemann_scaf nil)
    (<= const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (    (<= const-declbool reals nil)
    below  nilnaturalnumbersnil)
    (<    (MPLIESconst-decl"[,bool->bool"booleans)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>(below type-eq-declnilnaturalnumbersnil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl< const-declbool realsnil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    rationalnonempty-type-from-decl nil nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real(> const-decl "ool nil)
     "[number_field - boolean]"  niljava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
        ( const-decl"[ - ] nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields( const-decl"[real -> boolean]r nil)
     nil)
    (booleannonempty-type-decl  nil
    (number nonempty-type-from-decl  nil
    NOT"bool - bool]" booleansn)
    (belowjava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 9
( const-decl[,bool> ]  nil
    (closed_interval type-eq-decl nil intervals_real "reals (NOT const-decl "[ -"booleansnil)
    (  nilfinite_sequences)
    (> const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- "[,n ->numfield"number_fields)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(partition ype-eq-declnil  "analysis/"java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
>  boolreals)
    (step_function_on? const-decl ( nonempty-type-eq-decl number_fieldsnil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?(+ "[, numfield- numfield"number_fields )
    real_le_is_total_ordername-judgement"total_order[])"
     real_propsnil)
(? const-decl bool  nil
    (step? const-decl    real_lt_is_strict_total_order
   nil)
 (bounded_TCC1 name-judgement (?real"
  (bounded_TCC1-1 nil 3450779708
   ("( "zeroed_bounded)
    (("" (expand "bounded?")
      (("" (expand    zeroed  ""  nil
        ()java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
      nil))
    nil   ("" (xpandzeroed_bounded)
((ounded boolsup_norm "measure_integration/")
    (abs const-decl " (" (expandzeroed)
         nil)
    (zeroed        (" expand "abs (" propax nil ) ) ))
    (zeroed_bounded      nil))
   nil))
 (IMP_fun_preds_partial_TCC1 0
  (   ((bounded? const-decl "bool
   (" expand"partial_order)
    (("" (expand "preorder?")
      (("" (expand " nil)
        (" split
              (zeroed_bounded  "bool"  nil)
            (("1" (skosimpnil)
                IMP_fun_preds_partial_TCC1-140778
            nil)
           ("2"( (expand"artial_order?"java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
            (""("=)
              ((      (" ( "r""java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
                ("" (nst-x!!2)
                  (("2" (inst -              (""(expand <=" (("( nilnil)nil )
                  nil))
                nil))
niljava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
            nil)
           (" (""( -x2) (""(assert) nil nil) ))
            (("3" (expand "<=")
              (                )
                            )
                  (("3" (inst - " (""(expand""
                    ((" ((3 (pply-extensionality 1:? )
                    )
                  nil))
                nil))
              nil))
           )
          nil))
        nil))
      nil))
    nil)
   ((preorder? const-decl)
    (<= const-decl n))
    (reflexivenil)
    (number nonempty-type-decl nil numbers nil)
              )java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
ield_predconst-decl "[ > boolean] number_fields
     nil)
    (number_field    (<= const-decl boolreal_fun_ordersreals)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
r nonempty-type-from-declnilrnil)
    (eal_le_is_total_order "total_order[])java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
     real_props nil)
    (?  ""relations)
    (bool nonempty-type-eq-decl(IMP_integral_def_TCC2-1 nil 3420java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 9
    (?  bool  riemann_scafniljava.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
    (step nonempty-type-eq-decl nil riemann_scaf nil)
    (antisymmetric? const-decl "bool" relations nil)( name-judgement"?]"
(?  "bool"relations)
    (partial_order? const-decl "bool" orders nil))
    (       ("" ( "x10
 0
  ( nil 342         """inst + ""0 (2"( ))
   " ()nil java.lang.StringIndexOutOfBoundsException: Range [27, 24) out of bounds for length 33
 partition_to_finite_partition_TCC2(?""rders))
  number_field_predconst-decl [java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 8
   ("" (artition_to_finite_partition_TCC10
 (partition_to_finite_partition_TCC3 0
  (partition_to_finite_partition_TCC3-1 nil  (java.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 54
   "(skosimp)
     0
      ("split
        (("1 ""()n nil nilnil)
          ((""( partition_to_finite_partition_TCC3java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
(""( "union"java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
              (("1" (expand java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 16
                (("1"    ("java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 8
(1"(xpand partition?")
                    (("1" (split)
                      (("1" (apply-extensionality :hide    (        (1 expandsingleton1)
(("1"( Unionjava.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
(""expand ""java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
                            (("1"                (1 expandfullset
                              (" (" ()
                               (1 apply-extensionality:hide t)
(("1" (expand                         "1 (expand "nion"
                             (2 ()
                                                                        ("1 ()
                                (case "a<=x!1")
                                ""
                                  (case "x!1< ("2 (flattenjava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
                                   !1java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
                                    )
                                    ("
                                      (lemma(  ""riemann_scafnil)
                                       "part_in"
                                       ("java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
                                        "P!1"
                                        "a"
                                        "a"
                                        "b"
                                        "b"
    ( nonempty-type-eq-declnilnaturalnumbers )
                                        "x!1")
                                      (("1"
                                            booln nil booleans )
                                        ("1
                                          "x1)
                                          (                                      1
                                             "((1"
                                            (("1"
                                             split -)
                                              (("1"
( -2
                                                (("1"
                                                  (inst
                                                   ((""
                                                    
                              P1(!1)<AND
                                 seqP1( +ii})
                   ((1
                                                    (assert)
                                                    nil
                                                    nil)
                                                   ("2( type-eq-decl il at_types nil)
   flatten
                                                    (("2"
               (assert
                                                                                                        "
                                                        (inst 4 "ii!1")
                                                        
                                                        
                                                      
                                                    )
                                                  
                                                 2"
                                                  
                                                   
                                                   closed_intervalreal(,b)java.lang.StringIndexOutOfBoundsException: Index 90 out of bounds for length 90
                             seq(!ement(?[]java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
                                                  (("1"
                                                    step?const-decl                                                  nil
                                                    " (expand"? 
                                                      "singletonclosed_intervalreal]a b]
                             (P!1(ii))"
                                                      ("
                                                        
   ((bounded? const-decl "bool" sup_norm "measure_integr/java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
                                                        nil))
      nil)
                                                    )
                                                      ("
                                                    (propax)
                                                    nil
                                                      nil)
                                                      2
                                                        nil)
                                                         "
                                            java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
                                                          (hide 1 2 4)
                                                          ((" ((2"( "java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 71
                                                            (expand
                                                             1
                                                             ("2"                                     (2
                                                             )
                                                             expand"java.lang.StringIndexOutOfBoundsException: Range [61, 27) out of bounds for length 67
                                                              java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
                                          
                                                              ((" (lift-if
                                                                (        il
                                                                 1)
             
                                                                  (prop)
                                                                  (  java.lang.StringIndexOutOfBoundsException: Range [71, 68) out of bounds for length 71
                   assert
                                                                    nil(boolnonempty-type-eq-decljava.lang.StringIndexOutOfBoundsException: Range [62, 49) out of bounds for length 71
                                                                    
                                                                   (" (estrict const-decl R restrict nil)
                                                                    (assert)
                                                                    
                                                                    nil))
                                                                  (" ()nil nil)nil nil)
                                                                nil))
                                                              nil)
                                                             2"
                                                              (skosimp)
                                                              (("2"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil))
                           nil                                                 
                                                          
                                                        nil))
                                                      nil))
      )
                                                  ))
                                                )
                                               (" (expand""
                                                
                                                 +
                                                 nil)
                             (seq(P!1)(ii!1))")
                                                "1"
                                                  (expand((""                                   assertjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
                                                  
                                                    (expand
                                                     "
                                                    (("1"
                                                      ("P"
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (flatten)                                                      (""
                                                  
                                                    :hide
                                                    ((java.lang.StringIndexOutOfBoundsException: Range [54, 48) out of bounds for length 48
                                                      (                                                        (("(1
                                                      (("2"
                                                        (apply-extensionality
                                                         
                                                         ?
                                                         t)
                                                        (("2"
                                                          (expand
                                                           "extend")
                                                              (lift-if"{ |
                                                            expand
                                                             ")
                                                            ((2
                                                              (                                                    ()
                                                               (("2"
                                                              (                                                                  
                                                                (assert)
                                                                ((2
                                                                  (case-replace
                                                                   " java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
                                                                  (("1"
                                                                    
                                                                    
                                                                    nil)
                                                                   
                                                                    
                                                    ( "")
                                                                    
                                                                  "singleton")
                                                                nil))
                                                              ))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      )
                                                    
                                                  nil))
                                                nil))
                                              
                                            )
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   (" ("2 (ssertnil)
                                  nil)
                                 ("2"                                                      inst3 1ii1"java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
                                nil))
                              )
                            nil))
                          nil))
                        nil)
                       "2 (*)
                                                  ""("!"
                          (("2" (typepred "y!1")
                            ((                              ((1java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
                              (("1"                                   t)
                                (split)
("" (assert  niljava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
                                 ("2" (grind(("" (grind  nil)java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                                 " nil)
                                  (skosimp)
                                  "3"grindnil nil)
                                  nil)
                                 ("4"()  nil)
                                nil)
                               ("2"
                                (split -(""() nilnil)
                                grind nilnil
                                 (                                 (""g)nilnil)
                                 (" (""
                                 ("4" (grind) nil nil))
                                nil)
                               ("3"
                                ()
                                (("3"

                                  (("1" (grind) nil nil)
                                                                      
                                   ("3" (grind) nil nil)
                                   ("4"
                                    (skosimp)
                                    (""
                                                                            (("4"
                                      (("4"
                                        (replace ("2"
                                        ("4""
                                          (hide-all-but 2)
                                          (("4"
                                            (expand "disjoint?")
                                            (("4"
                                              (expand "intersection")

                                                (expand ")
                                                java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
                                                  (expand(("4java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                                                  part_not_in
                                                    )
                                                         
                                                      (expand
                                                       "singleton")
                                                      (("4"
                                                        (lemma
                                                         "singleton[closed_interval[real(a b]
                                                         java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
                                                          "a"
                                                          
                                                          "b"
                                                          "x"
                                                          2
                                                        ((expand
                                                          (assert)
                                                          (("4"
   (inst
                                                             
                                                             " (inst
                                                               -
                                                               
                                                               nil))
                                                               "i!2"
                                                               "i!1")
                                                              (""
                                                                (("2"
                                                                nil
nil))
                                                              nil))
                                                            nil))
                                                          nil                                                      nil)
                                                        nil)
                                                      nil))
                                                    1
                                                  nil))
                                                )
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))

                                nil)
                               ("4"
it
                                (("1 ( ((3java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
                                 ( 2
                                 ("3"
                                  (skosimp*)
                                  ((                                       1)
                                    (replace -1                                          
                                    (                                                                
                                      (replace 2)
                                      (("3"
                                        (hide-all-but 2)
                                        (("3"
                                          (expand "disjoint?")
                                          (("3"
(expand)
                                            (("3"
                                              (expand "empty?")
                                              (("3"
                                                (expand "member")
                                                (("3"
                                                  (skosimp)
                                                  3"
                                                    expand
                                                     ")
                                                    (("3"
                                                      
                                                       "part_not_in"
                                                       "ajava.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                                                        
                                                        "b"
                                                        "b"
                                                        
                                                        "x!2"))
                                                      (("3"
                                                        assert
                                                        (("3"                                                        (("3"
                                                          (inst
    -
                                                           "P!1 "("" assert niljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
                                                          ((                            )                                 inst
                                                            "i!"
                                                             -
                                                             "i!2"
                                                             "i!1"                                                              
                                                           
                                                              (assert)
                                                              
                                                              nil))
                                                            (                    )
                                                          nil))
                                                        nil))
                                                      
                                                    nil))
                                                  nil)
                                                nil)
                                              nil))
                                            nil))
nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("4"
                                  (skosimp*)

                                    (lemma
                                     "parts_disjoint"
")
                                    (("4"
                                      (inst -(java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
                                      (("4"
                                        (replace (("4"
                                                                                    (("4"
                                          (replace -3)
                                          (("4"
                                            (hide -2 -3)
                                            (("4"
                                              (expand "disjoint?")
                                             ""
                                                (expand " ((4
                                                (("4"
                                                                                                      (4"
                                                  (("4"
                                                    (expand "member")
                                                    (("4"
                                                      (skosimp)
                                                      (("4"
                                                        (inst - "x!2")
                                                        
                                                          (assert)
                                                          4
                                                            (replace
                                                             
                                                            
                                                              (propax)
                                                              
                                                              nil                                                            ("4"
                                                            nil))
                                                          "i!2"
                                                        
      nil))
                                                    nil))
                                                  (assert)
                                                nil))
                                              nil))
                                                                                                            java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
                                          nil))
                                        ))
                                      nil)                            ))
                                    
                                  )
                                nil))
                              nil)                    )
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (                                      (                  ("
          (("2" (hide 2)
            ((2"rewrite "")
              (("1" (hidex |
                (("1" (rewrite "is_finite_surj" + :dir                                            (expand "intersection")
                  ((1"
                    (inst + "length(P! ("1" (expand(expand "")
                     "lambda (i: (("3java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
{java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
                              (P!)i)<x 
                               (lemma
                    ())
                                                )
                        (("1" (typepred                                              ""
                          (1 skosimp)
                            (("1" ("x"
                              "1 assert)niln))nil)
                            nil))
                          nil))
                        nil))
                          (assert
                     ("2"(kosimp niljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
                      )
                    nil))
                  nil))
nil)
               ("2" (hide 2)
                (("2" (rewrite "is_finite_surj" + :dir rl)
                  (2
                    (inst + "length(P!1)"
                     "lambda (i: below(length(P!1))):singleton[closed_interval[real](a, b)]
                              seq(1( "!1"java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
                    (                            (1 inst "i1")
                      (("1" (skosimp)
                        (("1" (typepred "y!1")
                          (("1" (skosimp)
                            (("1" (inst + " nil))
                              (("1"
                                (expand "extend")
                                (("1"
                                  nality :? t)
                                  (("1"
                                     - 1 rl
                                    (("1"
                                       )
                                      ("1"
                                        (prop)
                                        ))
                                          (assert)
(1java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
                                            
                                            (""
                                              (expand "singleton")
                                              (                                              (xpand"")
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          )
                                          ((""
                                            (replace -2)
                                            2
                                              (expand "singleton")
                                              2()nilnil)
                                              nil))
                                            (("4"
                                          )
                                        nil))
                                      )
                                    nil)
                                   2
                                    (skosimp)
                                    (("2" (assert)                                                           assert)
 nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
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                      nil)
                     ("2" (skosimp)
                      (                            nil))
                        (("2" (expand "extend")
                          (("2" (apply-extensionality :hide? t)
                            ((1 expand(2()
(""
                                (case-replace "x!1 (""( "extend
                                (("1" (assert) nil nil)
                                 ("2" (assert) nil nil))
                                nil))
                             
                             ("2" (skosimp)                                (""()                                    nil)
                              nil))
                            nil))
                          nil))
                             nil)
                      nil                    )java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
                    nil))
                  nil))
                nil))
              nil))
            il)
          nil))
        nil)
      nil))
    nil)
   ((nonempty_union1 application-judgement "(nonempty?)" bounded_nats
      )
    (? const-decl""partitions
     "measure_integration/")
    (java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 49
     "non_empty_finite_set[T]" sigma_countable "sigma_set("(? """partitions
    (finite_union judgement-tcc nil finite_sets nil)
     "[T] sigma_countable sigma_set"java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
    (finite_set type-eq-decl nil finite_sets nil)
    is_finite_surjformula-decl nilfinite_setsnil)
    (surjective? const-decl "bool" functions nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
singletonconst-decl(?)  nil)
    (union const-decl "set" sets nil)
    (fullset const-decl "set" sets nil)
    (part_in formula-decl nil integral_def "analysis/")
    finite_extend application-judgement finite_set]"
     extend_set_props nil)
    (nonempty_extend application-judgementniljava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
     extend_set_propsniljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    (FALSE const-decl "bool"      nil)
(extend const-decl "R niljava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
    (IMPLIES const-decl "[bool, bool -> bool]"    FALSEconst-decl""
    ( const-decl"[boolean, T, T-> TT] nil)
(!1skolem-const-decl"[(a,b"riemann_scafnil
    (ii!1 skolem-const-decl " IMPLIESconst-decl"bool bool>]" nil)
    (  "total_order[real])java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
     real_props nil)
    ( name-judgement
     " real_le_is_total_ordername-judgement (total_order?[])"
    (Union_surjective name-judgement
     "surjective?[setofsets[T] set[Tl (strict_total_order??[real]e nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers      (surjective?setofsetsT] setT]"sets_lemmasnil
    singleton_is_closedapplication-judgement
     "closed[real, (metric_induced_topology)]" convergence_aux
     "metric_space/")
singleton_is_compactapplication-judgement
     "compact[real, (metric_induced_topology)]" convergence_aux                                (("1"
     "metric_space/)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[real]" integral_def " ((("1"
    (                                    replace -1rl)
     nil)
    (nonempty_singleton_finite application-judgement java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
     "non_empty_finite_set[T]" sigma_countable     ass
( nil )
    (setof  nil nil Union setsets
    (setofsets type-eq-decl nil sets nil)
eclnil sets)(Unionconst-decl "et" sets nil
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    ( const-decl "[T,T- boolean]"  nil)
    (<     <const-declboolrealsnil
    (a     (a ormal-const-declreal riemann_scaf nil)
    (b formal-const-decl"x:real a(b formal-const-decl{: real <"nil
real>"rationalsnil
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]"    integer_predconst-decl [rational- boolean integers)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (ANDconst-decl [bool bool- bool"bjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 36
    < " nil)
    (closed_interval type-eq-decl    (finite_sequencetype-eq-decl  finite_sequences )
finite_sequence nil niljava.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
    (> const-decl "bool" reals nil)
fields)
    (- const-decl "[numfield, numfield -> numfield]"     below nilnaturalnumbersniljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
    (below type-eq-decl nil naturalnumbers nil)
    (+ const-decl    partitiontype-eq-decl  integral_def"/)
    (partition type-eq-decl nil integral_def "analysis/")
    (singleton? const-decl "bool" sets nil)
    (TRUE const-decl "bool" booleans nil)
    -type-decl(  nilbooleans)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number number_field_predconst-decl"number>boolean"number_fields
     nil)
    ( nonempty-type-from-declnilnumber_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    ( application-judgementintintegers)
    (intersection const-decl "set" sets nil( application-judgementintintegers)
    (empty? const-decl "nil))
    (disjoint? const-decl "bool" sets nil)
    (part_not_in formula-decl nil integral_def "analysis/")
    (finite_intersection1 application-judgement " (finite_intersection1 application-judgement "finite_set( application-judgement"finite_setreal
integral_def"analysis/
   (intersection2_preserves_boundedapplication-judgement
    " (S [T]):
   bounded   ounded(S,restrictreal ],[,T,boolean(=))"
     bounded_nats "orders/")
    (parts_disjoint formula-decl     parts_disjointformula-decl nil integral_def analysis
    (intersection1_preserves_bounded application-judgement
         ( (S:   boundedS,restrict[real  real,[T ],boolean(=)"
   bounded?(S, restrict[[real, real], [T, T], boolean](<=)))"
     bounded_nats"/")
    (finite_intersection2 application-judgement "finite_set[real]"
      /
    (partition? const-decl "bool(iemann_lebesgue_step_isf 0
(  "" )
   nil))
(typepred1java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
  (riemann_lebesgue_step_isf-1 nil 3450826554
   ("" (skosimp)
    (("" (typepred "phi!1")
      (("" (expand "step?")
("()
          nil))
            (lemma "step_function_integrable?"
             ("a" "a" "b" "b" " nil))
            (("" (expand "Integrable?"              ("()
              (" (assert)
                (("" (hide -1)
                  (("" (expand "Integral")
                    ((""
                      lemma""
                       ("a" "a" "b" "b" "f" "phi!1"))
                      (("" (assert)
                        (("" (expand "step_function?")
                          ""(skosimp)
                            (("" (inst - "P!1")
                               finite_sets nil)
                                (assert)
                                ((""
                                   -1)
                                  ((""
                                    (hide    singletonconst-decl "(?" sets nil                                  (replace-java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
                                    (( ( const-declsetsets nil)
( "step_function_on)
                                      ((""
                                        (typepred "P!1")
                                        ((""
                                          (case
                                           "forall (x:real): " xreal ?(*]((singleton](x),!1)&isf_integral[]((singletonrealx)phi)="
                                          
                                            
forall:(!) )isf(*real(val_ina , 1 ,phi1,(((!)ii (!( ii)  ([] ( ,P1 ii !)phi((!)ii (!)1+))=!`( +ii  (,b !,iiphi)(!"partitionreal(,b) nil)
                P!1`seq(ii) * val_in(a, b, P!1, ii, phi!1)")
                                            (("1"
                                              (name
                                               FF
                                               " seq1 + ) *(,b !,ii ! -
P1( +ii *a ,!, ,1)-
                P!1`seq(ii) *    ( name-judgement
                                              (("1"
                                                (                                                "
1
                                                  (caseisf?([real
"( lengthP)):
        isfphi(P)iiseq1(+ii)
                 (val_injava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
phiopen(P!1(i,seqP1(  ))))java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
         &
java.lang.StringIndexOutOfBoundsException: Range [32, 29) out of bounds for length 29
                          (val_in(a, b, P!1, ii, phi!1),
                           phi(open(seq(P!                                                    
          = FF(ii)")
                                                    1java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                                                    ( type-eq-decl nilsetsnil (Unionconst-decl"set"sets
"forall (n:): n<=length(P! "length(P!1)-)
                                                    ("1"
                                                      (inst
                                                       -
                                                       "length(P!1)-2 (("1" "reals nil)
                                                      (("1"
                                                        (assertbf"x eal|a
                                                          nilrationals(replace
                                                          (replace -8)
                                                          (("1"
                        ()
                                                            -
                                                              
                                                                 "[, ->bool]"booleansil)
                                                              
                                                                (hide
                                                                 
                                                                 -4
                                                                 -5
-)
                                                                (("1"
                                                                  (inst+ const-decl [,numfield- numfield" nil
                                                                   -2
                                               b"
                                                                  (("1"
                                                                    (   [ - "number_fields
                                                                    (("1java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
                                                                      (lemma
"(*[real]phi([real](),phi!)"
                                                                       (i1
                                                                        "(*[real](phi({x: real | a <= x & x < b}), phi!1))"
                                                                        "i2"
                                                                        "(*[real](phi(singleton[real(b), phi!1))")(int_minus_int_is_int"int"integersniljava.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
                                             
                                                                        (lemma
                                                                         "isf_integral_add"
                                                                         ("i1"
                                      [](phix  | a<  &   b) phi)"
                                                                          "i2"
                                                                          []phi]),phi)")
                                                                         "/)
                                                                         
                                                                           [real](({x:real|a =x& x                                                                           (*real](phi(x  |a<   x  },!1)+
                    (*[real](phi(singleton[                                                                      
                                                                          (("1"
                                                                            
                                                                             -3)
                                                                            nil)
                                                                              (replace
                                                 2
                                                                               1)
                                                                              (("1"
                                                                                
                                                                                                                                                                 java.lang.StringIndexOutOfBoundsException: Index 85 out of bounds for length 85
(("( ""
                    ("
                                                                                  nil
                                                                                  (a " "                                                     nil))
                                                                                nil))
                                                                              (2
nil(("inst-P!)
                                                                           ("2"
                                                                            
                                                                             (-11
                                                                              
                                                                            
                                                                              (apply-extensionality
                                                                               
                                                                               t)
                                                                              (("2"
                                                                                (expand
                                                                                 
                                                                                "zeroed?")
                                                                                  (("2"
java.lang.StringIndexOutOfBoundsException: Index 84 out of bounds for length 84
                                                                                   "x!1")
                                                                                  "
                                                                                    
                                                                                    nil
                                                                                    `(1+ii *v(,b P1                P!1`seq(1 + ii) * val_in(a, b, P!1, ii)java.lang.StringIndexOutOfBoundsException: Index 87 out of bounds for length 87
                                                                                  
                                                                                nil))
                                                                              )
                                                                            nil))
                                                                          nil))
                                                                        
                                                                       ("2"
(propax)
                                       nil
                                                                        )
                                                                      nil))
                                                                    nil))
                                                                  
                                                                nil))
                                                              nil))
                                                            
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (hide 2)
                                                      "
                                                        (name
                                                         "GG" (:below(P!)  1:(*]
-2)
                            (phi(                                                              1
                             !))
                                                        (("2"
                                                          (case
                                                           ?(n) (0 , 
        n <= length(P!1) - 2 =>
         isf?(GG(n)) & sigma(0, n, FF) =
           isf_integral(GG(n))")
                                                          (("1"
                                                            (skosimp)
                                                            (("1"
                                                              (inst"isf_add"
                                                               -
                                                               !)
                                                              assert
                                                                (expand
                                                                 "GG")
                                                                (("1"
                                                                  (assert)
nil
                                                                  nil)(lemma
                                                                nil))
                                                              nil))("i1"
                                                            nil)
                                                           "
                                                            (hide 2)
("
                                                              (hide -1)
                                                              (("2"
                                                                (induct
                                                                 "n")
                                                                
                                                                  )
                                                                  (("1"
                                                                    
                                                                     (("
                                                                    (("1"
(assert
(("1"
                                                                        (expand
                                                                         "GG")
                                                                        (("1"
                                                                          inst
                                                                           -                                                                           -2
                                                                           "0")
                                                                          (("1"
                                                                            
                                                                             nil)
                                                                             "a")
                                                                            (("1"
                                                                              (flatten)(("2"
                                                                              (("1"
                                                                                (lemma
                                                                                 "isf_add"
                                                                                 
                                                                                  "(*[real](phisingletonreal(a)) !1))"
                                                                                  (expand
                                                                                  zeroed)
                (val_in(a, b, P!1, 0, phi!1),
                 phi(open(seq(P!1)(0), hi                                             inst
                                                                                (("1"
                                                                                  (lemma
                                                                                   "
                                                                                   ("i1"
                                                                                    "(*[real](phi(singleton[real](a)), phi!1))"
                                                                                    "i2"
                                                                                    "(* nil))
                (val_in(a, b, P!1, 0, phi!1),
                 phi(open(seq(P!1)(0), seq(P!1)(1 + 0)))))"))
                                                                                  "1"
                                                                                                                                                                  nil))
                                                                                     (replace                                                                          
                                                                                    (("1"
                                                                                      (replace
                                                                                       -5)
                                                                                      
                                                                                        (expand
                                                                                         
")
                                                                                        (("1"
                                                                                          (expand
                                                                                           "*")
                                                                                          "lambda (n:below(lengthP!1) 1):([]
                                                                                            (case-replacephi(singleton[]()( *!1x java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
                                                                                             "(LAMBDA (x: real):
             phi(((1"
              val_in(a, b, P!1, 0, phi!1) *
               phi(open(seq(P!1)(0), seqisf_integralGGn)))
             phi((1"
                                                                                            (("1"
                                                                                              (replace
                                                                                               "1)
                                                                                             (("1"
                                                                                                ()
                                                                                                  
                                                                                                (("1"
                                                                                                  (propax)
                                                                                                  nil
                                                                                                  "2java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
                                                                                                nil))
                                                                                              nil)
                                                                                             "
                                                                                              
                                                                                               2
                                                                                               -(flattenjava.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75
                                                                                              
                                                                                                (apply-extensionality
                                                                                                 (("1"
                                                                                                                                                                                                   
                                                                                                 t)
                                                                                                -2
                                                                                                  (expand
                                                                                                   
                                                                                                  
                                                                                                    "member")
                                                                                                     
                                                                                                    
(expand
                                                                                                       "member")
                                                                                                                                                                                        "i2"
                                                                                                        
                                                                                                         (("1"
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          
                                                                                                            (replace
                                                                                                             "(*[real
                                                                                                             !1)                                                                                                               
                                                                                                              (inst
                                                                                                               (("1"
                                                                                                               "0")
                                                                                                              1
                                                                                                                (assert)
                                                                                                                (("1"
                                                                                                                  (expand
                                                                                                                   "val_in")
                                                                                                                  (("1"
                                                                                                                    (("1"
                                                                                                                     -14
                                                                                                                     "0")
                                                                                                                    (("1"
                                                                                                                      (case-replace
                                                                                                                      (("1"
                                                                                                                        (case-replace
                                                                                                                         -2)
                                                                                                                        (-12
                                                                                                                          (hide-all-but
                                                                                                                           (-12
                                                                                                                            -14
                               -1))
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--> --------------------