Quelle  div_nat.prf   Sprache: Lisp

(div_nat
 (div_TCC1 0
  (div_TCC1-1 nil 3507028517
   ("" (skosimp*) (("" (rewrite "floor_max") nil)) nil(div_nat
   ((floor_max formula-decl nil floor_more nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl"[rational -> boolean]" integers niljava.lang.StringIndexOutOfBoundsException: Range [66, 67) out of bounds for length 66
    ( nonempty-type-declnil booleans niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    ( nonempty-type-eq-decl nil
    (>= const-decl "bool" reals nil)
    n nonempty-type-eq-decl  nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
nil)
 (div_nat_TCC1 0
  (div_nat_TCC1-1 nil 3507028517 ("" (subtype-tcc) nil nil)
   ((boolean     (ationalnonempty-type-from-declnilr nil)
java.lang.StringIndexOutOfBoundsException: Range [40, 4) out of bounds for length 49
> bool"booleansnil)
    (number nonempty-type-decl nil numbers nil)
    ( const-decl "number -> boolean]"number_fields
     niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    ( nonempty-type-from-decl number_fields )
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl    ))
    (> const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    ( const-decl"[ -> boolean]" integers nil
    (int nonempty-type-eq-declnilintegers)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl     bool nilbooleans)
    (posnat nonempty-type-eq-decl nil integers nil)
   nat nilnaturalnumbersnil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 47
real_props)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (div_nat 0
  (div_nat-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand )
      (("" (lift-if    (real nonempty-type-from-decl nilreals)
        ((" ground
          (("1"    rational_predconst-decl"[real - boolean] rationals)
           ("2" (lemma "floor_plus_int")
            (2"(inst 1"1 "n!1-m!1/m!1)
              (((intnonempty-type-eq-decl nilintegersnil
    nil)
   ((int_minus_int_is_int application-judgement "int real_lt_is_strict_total_ordername-judgement
(  "(n)" nil
    (rat_div_nzrat_is_rat    (real_ge_is_total_ordertotal_order?[real]"
     real_props nil)
   (nnrat_div_posrat_is_nnrat application-judgement"onneg_rat"
     rationals nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    posnatnonempty-type-eq-declnilintegers)
    (>   nil)
    (nonneg_int nonempty-type-eq-declnil integersnil)
    (> const-decl"" realsnil
(boolnonempty-type-eq-decl booleans nil
    (int nonempty-type-eq-decl nil integers nil)
    (    ((" (expand "div)
java.lang.StringIndexOutOfBoundsException: Range [11, 4) out of bounds for length 56
(  [ - ]  nil
    (real nonempty-type-from-decl nil reals nil)
real_pred " -> boolean]" java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
    (number_field nonempty-type-from-decl nil number_fields nil)
(  "number- boolean] number_fields
     nil( application-judgementrat rationalsnil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    floor_small_nat  floor_more)
   nil))
 (div_value 0
  (div_value-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "div")
      (("" (typepred "floor(n!1 / m!1)")
        ((" (lemma "both_sides_div_pos_lt1)
          nals nil)
            ((" (lemma"both_sides_div_pos_le1)
              (("" (inst -1 "m!1" "k!1*m!1" "n!1")
                (("" (ground) nil)))    real_lt_is_strict_total_order
    nil)
   ((div const-decl " (natnonempty-type-eq-declnil naturalnumbers nil)
    ( formula-decl real_propsnil
    (both_sides_div_pos_le1 formula-decl nil    (> const-decl "bool" realsnil
    (posint_times_posint_is_posint application-judgement "posint"
     )
    (real_ge_is_total_order nonempty-type-eq-decl booleans)
    ( nonempty-type-eq-decl nil nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posrat_div_posrat_is_posrat    (integer_predconst-decl"rational->boolean"integersnil
     rationals nil)
    (real_lt_is_strict_total_order    (rational_pred const-decl "[eal ->boolean] rationals nil)
     "(strict_total_order?[real]) real_props 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)
    (nonneg_realnonempty-type-eq-decl nilreal_typesnil)
    (posreal nonempty-type-eq-declnil real_types )
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool] boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred    (numbernonempty-type-declnil numbers nil)
     niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl"number_field ->boolean]" realsnil
    (real nonempty-type-from-decl nil reals nil)
    < const-decl "bool"realsnil)
   ( const-decl " - boolean] rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_predconst-decl"[rational ->boolean" integers nil
    (            (" (lemma "both_sides_div_pos_le1
olbool )
    (< const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
                    ("() nil)))))
    (floor {i  i = x&x<i+1 floor_ceilnil
    (=const-declboolean notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-declboth_sides_div_pos_le1formula-decl  real_propsnil
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    cl "bool" reals nilnil)
    (posnat nonempty-type-eq-decl nil integers nil))
   nil))
 (div_sum_nat 0
  (div_sum_nat-1 nil 3507028517
   ("" (skosimp*)
    ((" []"
      (("" (lemma "floor_plus_int")
        (("" (      )
    nil)
   (      nil)
    (div const-decl "upto(n)" div_nat nil)
    ( application-judgement"nonneg_rat"
     rationals nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_predconst-decl"[number -> ]" number_fields
     nil)
    (     (strict_total_order[real" real_propsniljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
(  " - boolean]"rationals)
    (rational nonempty-type-from-decl nil rationals nil)
    ( const-decl"rational ->boolean] integersnil)
( nonempty-type-from-decl integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (=const-declboolean notequalnil
          nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (bool nonempty-type-eq-decl    nonneg_floor_is_natapplication-judgementnatfloor_ceilnil)
    (= const-decl b" java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
    (nat nonempty-type-eq-decl nil    numbernonempty-type-decl numbers)
    ( nonempty-type-eq-declnil integers nil)
    (> const-decl "bool niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
(  nilintegersnil)
    (    (real nonempty-type-from-declnil reals)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props)
    (rat_div_nzrat_is_rat(rational_pred  "real- boolean"nil
(  nil nil)
    (mult_divides2     (integer_pred const-decl "rational - boolean] integersnil)
    (mult_divides1 application-judgement "(divides(n))" divides nil))
   nil)
 (    ( const-decl"bool,bool - bool]" booleans nil)
 (div_multiple-1 nil3070857 ("(rind nil nil)
   ((booleannonempty-type-decl nilbooleans nil)
    (bool nonempty-type-eq-declnil booleansnil
    NOTconst-decl "[bool - bool"booleansnil
    ( nonempty-type-decl nilnumbersnil
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (/ const-decl"numfield,nznum ->numfield]"number_fieldsnil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred    (intnonempty-type-eq-declnilintegersniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    (rational nonempty-type-from-decl nil rationals nil)(nonneg_int nonempty-type-eq-declnil  nil
    (integer_pred    posnatnonempty-type-eq-decl nil nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil)
  (div_sum_nat-1 nil 35702857
    (posnat nonempty-type-eq-declnilintegersnil)
( name-judgement"total_order[])"
     real_props nil)
al_gt_is_strict_total_orderjava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
     "(strict_total_order[real]) real_props nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nnrat_div_posrat_is_nnrat application-judgement    nil)
     rationals nil)
    (div const-decl "upto(n)" div_nat nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    mult_divides1 application-judgement"divides(n))" dividesnil)
    (mult_divides2 application-judgement(divides()) divides))
   nil))
 div_is_00
  (div_is_0-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "div")
      (("" (prop)
        ("" (typepred"loor(!1 /m!))
          ("1 ( -4)
            (("1" (hide -1 -3 -4)
              ("1 (lemma"both_sides_div_pos_lt1)
                (("1" (inst?)
                  ("" ( -1"m!1) (""assert nil))))))))
         ("" ( "floor_small_nat")nil)))java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
    nil)
(( const-decl"(n)" iv_natniljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
floor_small_nat  floor_more )
    (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)(umfield  nil  niljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (>= const-decl "bool" reals 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)
    (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (< const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
(nonempty-type-from-decl  nil
    (integer_pred const-decl " (>const-decl "bool realsniljava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
java.lang.StringIndexOutOfBoundsException: Range [37, 4) out of bounds for length 56
    (rational_pred application-judgement"rationals )
    (<= const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (umber_fieldnonempty-type-from-decl number_fields nil
    (number_field_pred const-decl "[number mult_divides2application-judgement "(dividesm)"divides nil)
     nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> nil))
    (bool nonempty-type-eq-decl nil div_multiplejava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
    (( nonempty-type-eq-declnil nil
    (nonneg_floor_is_nat application-judgement ""floor_ceilnil)
    (nnrat_div_posrat_is_nnratapplication-judgementnonneg_rat"
     rationals nil
    (posreal nonempty-type-eq-declnilreal_typesnil)
    (nonneg_real nonempty-type-eq-declnil real_typesnil)
    (posrat_div_posrat_is_posratapplication-judgement"posrat
     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
  (div_smaller-1 nil 3507028517
   (""(skosimp)
    ((" (expand "div")
      ((" (typepred "(n! / m1)")
        (("" (    (rational_pred const-decl[real- boolean"rationals )
          ((" ( both_sides_times_pos_le1)
            (("" (inst -1 "m!1" "floor(n!1 / m!1)" "n!1/m!1")
              (" () nil))))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
nil
   (> "bool realsnil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (real_le_is_total_order    (nonempty-type-eq-decl  niljava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
     real_props      (strict_total_order?[real)"real_propsniljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (nnint_times_nnint_is_nnint     (nnrat_div_posrat_is_nnrat application-judgement
     integers nil
( application-judgement"dividesn)"dividesnil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nnrat_times_nnrat_is_nnratintegers nil)
     rationals nil)
( formula-declnilreal_propsnil
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"    ( application-judgement))
     rationals div_is_00
nonneg_floor_is_nat ""  )
    (boolean nonempty-type-decl nil booleans nil)   "
    (bool nonempty-type-eq-decl nil booleans nil      (()
    NOTconst-decl[ - bool]booleansnil
    (number java.lang.StringIndexOutOfBoundsException: Range [0, 30) out of bounds for length 28
    ( const-decl " -> ]"number_fields
     nil)
    ( nonempty-type-from-decl  number_fieldsnil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil                  (1 inst!)("())))))java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
   ( const-decl"(n) div_nat niljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
    (rational_pred const-decl "[real -> boolean]" rationals( nonempty-type-eq-decl integersnil
    (rational nonempty-type-from-declnil rationalsniljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    integernonempty-type-from-decl nil integersniljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
, - ]  niljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
( bool nil
    (numfield     (/ const-decl "[numfield, nznumconst-decl[, nznum>numfield"number_fieldsnil)
(+const-decl[,>numfieldnumber_fieldsnil
    (floor const-decl " (= const-decl"boolean notequalnil
equalniljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
( nonempty-type-eq-declnumber_fields)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    intnonempty-type-eq-declnilintegersniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    > const-decl""realsnil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil))
   nil)
 (iv_rem_small 0
  (div_rem_small-1nil 3070851
   (""(skosimp)
    (<=const-decl "bool" reals nil)
      (("" (lemma "both_sides_times_pos_lt1")
        (("" (inst -1 "m!1"   nil
("()nil))))
    nil)
((  "" )
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil
mult_divides1 application-judgement "dividesn)"divides
( application-judgementdivides)  nil
( const-decl"() )
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnrat_div_posrat_is_nnrat nilbooleansnil)
     rationalsniljava.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_predconst-decl[number- ] number_fields
     nil)
    (number_field nonempty-type-from-decl nil java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 19
    (real_pred const-decl "[java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 18
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>=  div_smaller-1 57257
    (nonneg_real nonempty-type-eq-decl("(expand div)
    (> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl  nil)
(  [ -boolean nil
   rational nilrationals)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl((" (inst-1"!1 "floor(!1/ !1)""!1m!)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    numfieldnonempty-type-eq-decl nil number_fields nil)
    (/= const-decl " nil)
    ( nonempty-type-eq-declnilnumber_fields)
    (/    posrealnonempty-type-eq-decl real_typesnil
    natnonempty-type-eq-decl naturalnumbersnil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    ( nonempty-type-from-decl integersnil)
real_propsnil)
    <=const-decl"ool" reals nil) ( const-decl"ool"realsnil)
    (floor const-decl "(mult_divides1 application-judgement (divides()) divides nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil    mult_divides2application-judgement"dividesm))"dividesnil
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
   nil))
 (div_mult_lt 0
1nil35070251java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
(  "bool->bool]"booleansjava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (("" (expandnumber_field_predconst-decl "number-> boolean" number_fields
      ((""( "div_mult_pos_lt1"
        (("" (inst?)
          (""(assert
            ((" real nonempty-type-from-decl nil
              (1"() nil)("" () ))))))))
    nil)
   ((div const-decl "upto(n)" div_nat nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_predconst-decl"number - boolean]"number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
   (real_pred  "[number_field > boolean] reals nil)
    (eal nilreals)
    (bool nonempty-type-eq-decl nil booleans nil)
    ( ( nonempty-type-from-decl integersnil
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]"nznumnonempty-type-eq-decl nilnumber_fields niljava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
(  nilintegers)
    (nonneg_int nonempty-type-eq-decl    nat   nil
    (posnat "realsniljava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])"java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
( "
     rationals nil)
    (nnint_times_nnint_is_nnint application-judgement    )
     integers nil)
(ult_divides1application-judgement(()  nil
    mult_divides2application-judgement"()"divides)
    (nonneg_floor_is_nat application-judgement " )
    (div_mult_pos_lt1 formula-decl nil real_props nil))
java.lang.StringIndexOutOfBoundsException: Range [50, 8) out of bounds for length 8
rationals)
  (div_by_one-1 nil 3507028517 ("" (grind) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    ( const-decl  >bool"booleansnil
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]"( const-decl"number_field- boolean] )
     nil)
(   java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (real_pred const-decl "[ (rational nonempty-type-from-decl nilrationalsniljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
    (real nonempty-type-from-decl nil    nonneg_intnonempty-type-eq-decl nil
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl  =const-declbooleannotequal)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]"   number_fields)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationalsjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
    (div const-decl "upto(n)" div_natreal_lt_is_strict_total_order
   nil))
iv_zero0
  (div_zero-1 application-judgementnonneg_rat
   ((boolean nonempty-type-decl nil    posint_times_posint_is_posintapplication-judgement"posint"
    (bool nonempty-type-eq-decl     integers)
    (NOT const-decl "[bool -> )java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
    (number nonempty-type-decl("(*
    ( const-decl"number - boolean number_fields
     nil)
number_field nilnumber_fields)
    (real_pred const-decl "[number_field (" ()
    (real nonempty-type-from-decl nil reals nil)
    ( const-declbool"reals )
    (rational_pred const-decl "[real -> boolean]" rationals nil    niljava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational (umber_field_pred const-decl"number>boolean 
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (osnat nonempty-type-eq-declnil integers nil)
    (real_gt_is_strict_total_order name-judgement
"(trict_total_order?[eal)"real_propsnil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nnrat_div_posrat_is_nnrat application-judgement " nonneg_real nilreal_typesnil
     rationalsposreal  real_types)
    (div const-decl "upto ( -"nil
nil
div_eq_arg
  (posnat   )
   ((boolean nonempty-type-decl nil booleans nil)
    (bool     (real_lt_is_strict_total_order
    (NOT const-decl "( application-judgementnonneg_rat
    (number application-judgementnonneg_int
    ((  (n  )
     nil)
    nil )
    (real_pred const-decl "[number_field -div_mult_pos_lt1 )
   reals
 nonempty-type-eq-decl
    (rational_pred( const-decl"-bool]"booleansnil
    (rational nonempty-type-from-decl nil rationals nil)
    integer_pred [ >boolean ntegersnil
    (int nonempty-type-eq-decl nil integers nil nil
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat  const-decl"real->boolean"rationalsnil

     "(strict_total_order?[real])" real_props(  "rational - ]"  nil
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
p application-judgementposrat
     rationals nil)
    (div const-decl  nat )
   nil))
 
  (div_one-1 nil 35070( application-judgement"
   ("" (skosimp*    ( const-decl "pto()" div_nat ))
    (("" (expand "div")
      (("" (rewrite "floor_small")
        (("1" (lift-ifdiv_eq_arg0
          ("" ( "quotient_pos_le")
            (("1" (oolean nilbooleans niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
("expandabs)(""() nil))))
    nil)
   ((div const-decl "upto(n)" div_nat nil)
    (abs const-decl "{n: nonneg_real ( const-decl [number- ]"number_fields
         nil)
     nil)
    ( name-judgement"total_order?real]"
     real_props nil)
    (quotient_pos_le formula-decl nil real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order ( nonempty-type-from-decl nil nil)
    (nzint_abs_is_pos application-judgement "{j
real_defsjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
| j >= i}"
     real_defs nil)
    (nzrat_abs_is_pos application-judgement "{r: posrat int nonempty-type-eq-decl nil integers )
     real_defs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order? (>= const-decl "" reals nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (inus_odd_is_oddapplication-judgement"" integersnil
    (real_ge_is_total_order name-judgementjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
nil
    (posnat(posrat_div_posrat_is_posrat application-judgement posrat
    (     rationalsn)
        ( const-decl"() div_nat ))
    (>= const-decl "bool nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (nonzero_integer nonempty-type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (int nonempty-type-eq-decl nil integers 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(div_one-1 nil3072851java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
    (realnonempty-type-from-declnilrealsnil)
    (real_pred const-decl "[number_field -> boolean] (" ( "floor_small"java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
    (number_field nonempty-type-from-decl           ("1" ( "quotient_pos_le)
    ( const-decl"number > boolean" number_fields
     nil)
( nonempty-type-decl nil nil)
    (  upto  nil
    floor_small   niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
)
 (div_even 0
  (div_even-1  nil nil
   ("" (skosimp*)
    (("" (expand "div")
      (" rewrite")(" (ssert ))))
    nil)
  (( application-judgement"" )
      "j j >= i}java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
     integers nil)
    (mult_divides1 application-judgement "(divides(n))"strict_total_order )
    (mult_divides2 application-judgement "(divides(m))" divides nil)
(div const-decl"upto(n)"div_natnil)
    (nnrat_times_nnrat_is_nnrat application-judgement( application-judgement"osrat
     rationals nil)
    (rat_minus_rat_is_rat application-judgement "rat" rationals nil)
ers nil)
    (> const-decl "bool"     real_ge_is_total_ordername-judgement "total_order?real]"
    (onneg_intnonempty-type-eq-declnil integersnil
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl booleans)
    (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" notequalnil)
    (numfieldnonempty-type-eq-declnil number_fieldsnil)
    (integer nonempty-type-from-decl nill
( const-decl [rational - boolean" nil)
    (rational nonempty-type-from-decl nil rationals nil    integer nonempty-type-from-decl nilintegersnil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)

    (real_pred const-decl "[number_field -> (ational_predconst-decl "real>boolean rationals nil)
     nil number_fields nil)
    (number_field_pred const-decl "[ ( const-decl "number_field- boolean"realsniljava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
 nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationalsnil)
   nil)))