Quelle  div_nat.prf   Sprache: Lisp

java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
 ( rational )
  (div_TCC1-1 nil 3507028517
   ("" (skosimp*) (("" (rewrite "floor_max") nil)) nil)
   ((floor_max formula-decl nil floor_more nil)
    (number nonempty-type-decl nil numbers nil)
boolean nilbooleans)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fieldsboolnonempty-type-eq-decl nil booleans)
    ((onneg_int nilintegersjava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
   )
 (div_nat_TCC1java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
r   ationals
    (integer_pred const-decl "[rational (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool"     (NOT const-decl "[bool -]  nil)
    (nonneg_intnumber_field_pred[ >] 
    (> const-decl " )
    (posnat nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers    number_field nilnil
niljava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
 (div_nat_TCC1integer_pred rationalbooleanintegers)
  (div_nat_TCC1-1 nilint   nil
   ((boolean nonempty-type-decl nil booleans nil)
    ( nonempty-type-eq-decl  niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
        ( nonempty-type-eq-decl  niljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
          niljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    (real_pred const-decl "[number_field -> boolean]" reals nil
nonempty-type-from-decl  nil
    (> const-decl "bool" reals"()
(  "real- " nil
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl(" inst- "(!-!)m"
     nonempty-type-eq-decl  )
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
( 
     "(strict_total_order?[real])" real_props nil)    divconst-declupton) div_nat)
    ( name-judgement "(?)
nil
    (  "java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
     "(strict_total_order?[real(osnat nil)
   )
 (div_nat  
  (div_nat-1= bool )
   ("" (      nil)
"""
      ((""    (rational nonempty-type-from-decl nil rationals nil)
        (("" (ground)
          (("1" (rewrite    rational_predconst-decl"real-boolean"rationals)
           ("2" (lemma "floor_plus_int")
            (("2" (inst -1    ( const-decl[number_fieldbooleanreals nil)
              (("2" (assert) nil))))))))))))
    nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
        number_field_predconst-decl[ -"
    (rat_div_nzrat_is_ratapplication-judgement "rat"  niljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (int_plus_int_is_int application-judgement( formula-declnil nil)java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (nnrat_div_posrat_is_nnrat" "
 nil
    (nonneg_floor_is_nat" "java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
( name-judgement
     "(strict_total_order?[real])" real_props nil)
     naturalnumbers
    (posnat     both_sides_div_pos_lt1 nil )
> bool )
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl " integersnil)
    (bool nil nil
int  integersjava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
  [ >]  )
    (rationalrationals
rational_pred[>"
    (realstrict_total_order" java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
           )
    (number_field nilniljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
(  java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
(   numbers
    (floor_small_nat formula-decl nil )
   nil))
 (div_value 0
  (div_value-1 nil 3507028517
nonempty-type-from-decl 
    ((""     [>"reals )
(=const-decl  )
        (("" (rational_pred [real>"rationals)
          (  rational ]integers)
(""")
              (("" (inst -1 " (AND const-decl "[bool, bool -> bool]" booleansniljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
("" ground)))))))))
    nil)
   ((div const-decl "upto( const-decl"|<       1" )
    /  ""notequaljava.lang.StringIndexOutOfBoundsException: Range [42, 43) out of bounds for length 42
    ( formula-declnil nil)
    (    (> const-de java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
"(expand "div")
    (real_ge_is_total_order name-judgement "(total_order?real)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
     real_propsnil
    (posint_plus_nnint_is_posint application-judgement "posint"
integers
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posrat_div_posrat_is_posratnnrat_div_posrat_is_nnrat java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
     rationals  numberboolean 
    (real_lt_is_strict_total_order
"?]) )
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields    rational_predconst-decl[real-boolean rationals nil
    (nnint_plus_posint_is_posint application-judgementinteger_pred [ >] )
     integers    integer nilintegersniljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (    /  "" )
     rationalsjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
(  ""  nil
    (boolean nonempty-type-decl> const-decl"oolrealsnil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
(  nil nil
    (number_field_pred const-declnonneg_int nil integers nil)
     )
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field posnatnonempty-type-eq-decl integers nil)
real nil niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    (<      nil
    rational_predconst-decl" >boolean] rationals )
    (rational nonempty-type-from-decl nil rationals     floor_plus_intformula-decl floor_ceil)
    (integer_pred const-decl [rational>" java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
)
AND  ",>"booleans
    (  521 " ()nil
    (numfield nonempty-type-eq-decl( 
    (+    (bo    )
    (floor( const-decl[-]  )
    (/= const-decl "boolean"number   )
    (nznum )
 [  >" java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    )
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    nonneg_int nilintegers)
    (> const-decl "bool" reals nil)
( nonempty-type-eq-decl integers)java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
   nil))
 (div_sum_nat 0
 01
    nil
    (("" (    real_ge_is_total_order (?real
      ( name-judgement
        (("" (inst -1 "i!1" "n!1/m!1") (("" (assert) nil))?"
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
   integers
    ( ( 
    (nnrat_div_posrat_is_nnrat "(" nil
( java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
    (number(1( "n !"
    (boolean(""replace
    (number_field_pred (" "
     nil)
    (number_field(1 inst m"(1 ())))))
    (real_pred const-decl         2 rewrite)))))
    (real nonempty-type-from-decl nil reals nil)
    (   div uptod )
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)    ( formula-declnilfloor_morenil
    (integer nonempty-type-from-decl nil integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    numfieldnonempty-type-eq-declnumber_fields)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (bool
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (nonneg_int     (nteger  nilintegers)
>" )
    (posnat nonempty-type-eq-decl nil integers nil)
    (rat_plus_rat_is_rat application-judgement "rat" rationals nil)
    (nonneg_floor_is_nat     (rational nonempty-type-from-decl nil rationals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (rat_div_nzrat_is_ratapplication-judgement "at" rationals niljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (floor_plus_int formula-decl nil floor_ceiln  nil )
( application-judgement()  nil
    (mult_divides1 application-judgementjava.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 9
niljava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
( 0
  (div_multiple-1 nil 3507028517 ("" (grind) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    boolnonempty-type-eq-decl  booleans)
    (NOTnonneg_floor_is_natapplication-judgement"nat floor_ceil nil)
    (      ""
    (number_field_pred const-declrationals )
     nilposreal   )
      )
    (real_pred const-decl "[( ""
    (real"*
    " (expand "div"floorn! !)"
  " >boolean]"nil
    (rational nonempty-type-from-decl nil          " lemma""java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    (integer_pred               ("assert nil))))))
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil     )
    ( const-decl"" java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    (nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat  nilintegers)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
"?[]"  )
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
 "nonneg_rat"
     rationals nil)
      )
    mult_divides1 "() java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
     integersjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
    (mult_divides1 application-judgement     both_sides_times_pos_le1   )
mult_divides2 "(divides(m))" divides nil)
   nil))
 ( 0
  (div_is_0-1 nil 35070285    (nonneg_floor_is_nat application-judgementnat floor_ceilnil
   (" (skosimp*)
    (("" (expand "div")
("" (prop
        (("1" (typepred(  "bool>bool] booleans )
          (("1" (replace -4)
            (number_field_pred [number>boolean 
     )
    number_fieldnil java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
                  ("" ( -1 "m1") (1" assert nil))))))))))
         ("2" (rewrite "floor_small_nat") nil))))))
    nil)
   (div upto) )
    (floor_small_nat formula-decl nil floor_more nil)
    posnat nil )
    (> const-decl "bool" realsrational   )
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil ( onempty-type-from-decl )
    (>= const-decl " (AND const-decl "[bool,bool->bool"booleans)
    (int nonempty-type-eq-decl nil integers    ( const-decl"" realsnil)
    (/  "numfield - ] )
    (nznum nonempty-type-eq-decl nil number_fields    + "numfield numfield - numfield]"  )
   / " )
    (floor const-decl "{i | i <= )
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield    nznum nil  nil
    (< const-decl "bool" (    )
    (AND const-decl "[bool, bool ->(=const-decl bool niljava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
    (integer)
(java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
    (rational  501
    ( *
< const-decl"java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
    (real nonempty-type-from-decl nilreals)
    (real_pred const-decl "[number_field -> boolean]"          (" assert ))))
    (number_field nonempty-type-from-decl    (nonneg_floor_is_nat application-judgementnat floor_ceilnil
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number    (mult_divides1application-judgement"() nil)
    mult_divides2 "((m)"divides)
    (bool nonempty-type-eq-decl nil    div upton"div_natniljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
l  )
    (nonneg_floor_is_nat )
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 47
    (posrat_div_posrat_is_posrat  " >boolean"java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
     rationals nil)
    (odd_plus_even_is_odd application-judgement "odd_int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (both_sides_div_pos_lt1 formula-decl nil real_props nil))
   nil))
 (div_smaller 0
( nil 307081
   ("" (skosimp*)
    (" expand""java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
      ((     nilreal_types
        ((    (ational_predconst-decl "real - boolean]" rationals)
          (( ( nonempty-type-from-decl  niljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
            (( 1m""( m1"n/!"java.lang.StringIndexOutOfBoundsException: Range [61, 62) out of bounds for length 61
              (("" ((   nil
    )
   ((div const-declnznum   nil
(  nil )
    (nonneg_real(  nil niljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (real_le_is_total_order name-judgement "(total_order?[realinteger nil )
      )
    (nnint_times_nnint_is_nnint(= ""reals)< "" )
     integers nil)
    mult_divides1"dividesn)dividesniljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
(  (()"divides )
    (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (both_sides_times_pos_le1 formula-decl    formula-declreal_props)
    (nnrat_div_posrat_is_nnrat div_mult_lt
     rationals   5787
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    NOTconst-decl[ - ]  nil)
    (number nonempty-type-decl nil numbers nil)
    ( const-decl[ >] number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)( lemma)
    (real_pred const-decl "[number_field -> ( assert)
( nilreals)
    (<= const-decl "bool (" assert 2assertnil)))))java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
    (rational_pred const-decl "[number_field_pred [ >boolean"java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
    ((real_predconst-decl"number_field- boolean"reals
    (integer_pred const-decl "[rational (eal nonempty-type-from-decl nil niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
   integer nil )
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
    (/= const-decl "boolean" notequal nil)
    ( nonempty-type-eq-decl number_fields )
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool"    intnonempty-type-eq-decl  nil
    ( nonempty-type-eq-declnilnaturalnumbers)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl"bool reals nil)
    (posnat nonempty-type-eq-decl nil integers nil))
   nil))
 (div_rem_small 0
  (div_rem_small-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "div")
      (("" (lemma "both_sides_times_pos_lt1")
        (("" (inst -1 "m!1" "n!1 (nrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
          (("" (assert) nil))))))))
niljava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
       (ult_divides1 application-judgement "dividesn)"divides)
    (nnint_times_nnint_is_nnint(mult_divides2  "(dividesm)"  nil
     integersnil
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides
    (div const-decl "upto(n)" div_nat nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
      niljava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred     NOT"[bool- ] )
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    real_predconst-decl [ >"realsnil
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-declnil real_typesnil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    ( nonempty-type-from-decl  )
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers)
    (posnat nonempty-type-eq-decl nil integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    /  ""  niljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
    (znumnonempty-type-eq-declnil niljava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (integer nonempty-type-from-decl nil integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool"      nil)
    (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
    ( name-judgement
     "(strict_total_order?[real])" real_props nil)
 (d 0
mes_nnrat_is_nnrat ""
     rationals nil)
(  "posintjava.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
 nil
    (both_sides_times_pos_lt1 formula-decl nil real_props nil))
   nil)
 (div_mult_lt 0
  (div_mult_lt-1 nil 3507028517
   " skosimp)
    (("" (expandnumber_field_pred " >boolean]" number_fields
      (("" (lemma "div_mult_pos_lt1")
        ((""     ( nonempty-type-from-decl  nil
          ("assert
            (("" (prop)
              (("1" (assert) nil) ("2 > "bool  nil
    nil)
   ((div const-decl "upto(n)" div_nat nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (umber_field_pred [ - boolean]"number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
(  integers
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil      (trict_total_orderr]" niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (>= const-decl "bool" reals nil)
   ( nonempty-type-eq-declnil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-declnilreal_types nil)
    (rational_pred const-decl"[real - boolean] rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil   nil))
    (int nonempty-type-eq-decl (div_eq_arg 0
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-declnil integersniljava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
     name-judgement
     "(strict_total_order?[real])" real_props nil)
    nnrat_div_posrat_is_nnrat ""
     rationals nil)
    (nnint_times_nnint_is_nnintapplication-judgement "nonneg_int"
     integers nil)
    mult_divides1application-judgement"(divides(n))"dividesniljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (mult_divides2 application-judgement "(divides(m))" divides  (number_fieldnonempty-type-from-decl  number_fieldsnil
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (div_mult_pos_lt1 formula-declnil real_propsnil)
   nil))
 (div_by_one 0
      (realnonempty-type-from-declnil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    NOT "bool - bool] booleans )
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil( const-decl"rational- ]"i nil)
umber_fields)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
l_predconst-decl [ - ] rationals nil)
    (rational nonempty-type-from-decl nil rationals
    integer_predconst-decl[ -boolean integersnil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_ge_is_total_order name-judgement "( (osrat_div_posrat_is_posrat application-judgement ""
     real_props nil)
    (nonneg_floor_is_natapplication-judgement "nat" floor_ceil nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (div const-decl "upto(n)" div_nat nil))
   nil))
 (div_zero 0
  (div_zero-1 nil 3507028517 ("" (grind) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number (div_one0
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    nnrat_div_posrat_is_nnrat "nonneg_rat
     rationals nil)
div"n niljava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
   nil))
 ( 
  (div_eq_arg-1 nil 3          (1 lemmaquotient_pos_le
   (( nonempty-type-decl ooleans)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil          "2" ( "" (2 assert))))java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
number_field_pred" >boolean] java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
nil
    real_le_is_total_order (?)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    realrealsniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48

    (rational_pred const-decl     real_defs nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]"     (int_abs_is_nonneg application-judgement "{j: nonneg_int 
(nonempty-type-eq-declnil
  booljava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
    (nonneg_int nonempty-type-eq-decl(  odd_int )
    (posnat nonempty-type-eq-decl nil integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nonneg_floor_is_nat application-judgement "nat real_props )
    posrat_div_posrat_is_posratapplication-judgement""
 il
    div "upton"nil
)
 (div_one 0
  div_one-1 5081
   ("" (skosimp*)
    (("" (expand    )
("(rewrite")
        (("1" (lift-if)
(1 lemma"
            (("1" (inst?) (("1" (assert)    number_field_pred "number- ]
    booleannonempty-type-decl booleans
    nil)
   ((ivconst-decl "(n)"div_nat)
    (abs    (floor_small formula-declnil floor_ceil))
         nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (real_le_is_total_order name-judgement "(total_order nil)
     real_props nil)
_pos_leformula-decl real_props)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nzint_abs_is_pos application-judgement       ("( floor_int" ("()nil))
     real_defs nil)(nonneg_floor_is_nat nat floor_ceilnil)
(int_abs_is_nonnegapplication-judgement{:nonneg_int|j>i"
     real_defs nil)
    (nzrat_abs_is_pos application-judgement "{r: posrat | r >= q}"
     real_defs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_propsniljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (nonneg_floor_is_nat     div upto  nil
    posrat_div_posrat_is_posrat ""
     rationals nil)
    (minus_odd_is_odd application-judgement
( ([)
     real_props nil)(  nil )
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "boolbool nil nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl/ boolean )
    (nonzero_integer (  nil )
)
    (    integer_pred"-]"integers
(    nil
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals 
    r  " - ]"rationalsnil
    (real nonempty-type-from-decl     (number_field nonempty-type-from-decl
real_pred [ >]  )
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers
    (floor_small formula-decl nil floor_ceil nil)) )
   nil))
 (div_even 0
  (div_even-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "div")
      (("" (rewrite "floor_int") (("" (assert) nil))))))
    nil)
   ((nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (div const-decl "upto(n)" div_nat nil)
    (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (rat_minus_rat_is_rat application-judgement "rat" rationals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (integer nonempty-type-from-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (floor_int formula-decl nil floor_ceil nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil))
   nil)))