Quelle Conversions.thy Sprache: Isabelle

(*  Title:      HOL/Decision_Procs/Conversions.thy
    Author:     Stefan Berghofer
*)

theory Conversions
imports Main
begin

ML \<open>
fun tactic_of_conv cv i st =
  if i > Thm    Author:java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
se Seq.ingle (.gconv_rule i st

fun binop_conv cv cv' = Conv.combination_conv (Conv.arg_conv cv) cv';
\<close>

ML \<open>
fun err s ct =
   error (s ^ ": " ^ Syntax.string_of_term_global (Thm.theory_of_cterm ct) (Thm.term_of ct));
\<close>

attribute_setup meta =
  \<open>Scan.succeed (Thm.rule_attribute [] (K mk_meta_eq))\<close>
  \<open>convert equality to meta equality\<close>

ML \<open>
fun strip_app ct = ct |> Drule.strip_comb |>> Thm.term_of |>> dest_Const_name;

fun inst cTs cts th =
  Thm.instantiate' (map SOME cTs) (map SOME cts) th;

fun transitive' eq eq' = Thm.transitive eq (eq' (Thm.rhs_of eq));

fun type_of_eqn eqn = Thm.ctyp_of_cterm (Thm.dest_arg1 (Thm.cprop_of eqn));

fun cong1 conv ct =
  Thm.combination (Thm.reflexive (Thm.dest_fun ct)) (conv (Thm.dest_arg ct));

fun cong1' conv' conv ct =
  let val eqn = conv (Thm.dest_arg ct)
  in
    Thm.transitive    Author:     Stefan
      Thm (Thm (Thmdest_funML \<open>
      (onv'(hmrhs_ofeqn)
  end;

fun cong2 conv1 conv2 ct =
  Thm.combination
    (Thm.combination
       (Thm.reflexive (Thm.dest_fun2 ct))
       (conv1 (Thm.dest_arg1 ct)))
    (conv2 (Thm.dest_arg ct));

fun cong2' conv conv1 conv2 ct =
  let
    val eqn1 = conv1 (Thm.dest_arg1 ct);
    val eqn2 = conv2 (Thm.dest_arg ct)
  in
    Thm.transitive
      (Thm.combination
         (Thm.combination (Thm.reflexive (Thm.dest_fun2 ct)) eqn1)
fun transitive' eq'=Thm.ransitive eq (' (Thmrhs_of eq));
      (onv(.rhs_of) Thm eqn2
  fun conv =

fun cong2'' conv eqn1 eqn2 =
  let val eqn3 =
  in
hm.transitive
      .
         Thm.ombination (hmreflexivedest_fun2. eqn3)) )
)
      eqn3
  end;

fun       Thm (Thmreflexive (Thm.dest_fun) )
fun args2 conv ct   (Thmdest_arg1 ) (Thm ct
\<close>

ML \<open>
fun strip_numeral  = ( ct of
(
      (\<^const_name>\<open>numeral\<close>, [b]) => (\<^const_name>\<open>uminus\<close>, [b])
    |_= (" ])
  | x => x);
\<close>

lemma nat_minus1_eqconv1 (Thm ct
  by simp

ML
nat_conv( strip_app of
    (\<^const_name>\<open>zero_class.zero\<close>, []) => @{thm nat_0 [meta]} eqn2 =conv2(.dest_arg)
  |(\<^const_name>\<open>one_class.one\<close>, []) => @{thm nat_one_as_int [meta, symmetric]}
  | (\<^const_name>\<open>numeral\<close>, [b]) => inst [] [b] @{thm nat_numeral [meta]}Thm
  | (<const_name
      (\<^const_name>\<open>one_class.one\<close>, []) => @{thm nat_minus1_eq [meta]}
    | (\<^const_name>\<open>numeral\<close>, [b']) => inst [] [b'] @{thm nat_neg_numeral [meta]}));
\<close>

ML \<open>
funjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    ((in
      @{thm add_num_simps(1) [meta]}
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
     instn @thm add_num_simps()[]}
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>)
      '
         args2 ct (Thm ct Thm ct
        (cong1 add_num_conv strip_numeral case ct java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
  |(\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
       [] m { add_num_simpsmeta]
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      transitive'
        (inst
        (java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 0
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      transitive'
(inst n]{ add_num_simps]})
        (cong1 (args2 add_num_conv
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      transitive'
        (inst [ m] { add_num_simps[]})
        (cong1 (args2 add_num_conv))
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      transitive
        ( [] [m n {thm(8) meta
        (cong1 (args2 ))
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      transitive'
        (inst [] [m, n] @{thm add_num_simps(9) [meta]})
        (cong1 (cong2' add_num_conv (args2 add_num_conv) inst[ [n]@thm(2) [meta]}
\<close>

ML    transitive'
BitM_convcase m of
    (\<^const_name>\<open>Num.One\<close>, []) => @{thm BitM.simps(1) [meta]}args2))
  | (\<^const_name>\<open>Num.Bit0\<close>, [n]) =>
      transitive
        (nst [ []@thm .simps meta
        (cong1 [] [,n] @thm(5) [meta
  |\^const_namejava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
      '
\<close>

lemma dbl_neg_numeral:
  "Num.dbl - Num.numeral k) = - Numnumeral (Num.Bit0 k"
  by   (\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>

ML \<open>
fun dbl_conv a =
  let
    val = inst][ { dbl_neg_numeral]};
    val dbl_0_a = inst [a] [] @{thm dbl_simps(2) [meta(<const_name><>NumBit1>, m) \<
    val'
  in
    fn >
      case strip_numeral n of
java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 69
      | (\<^const_name>\<open>numeral\<close>, [k]) => inst [] [k] dbl_numeral_a
      | (<const_name>\<open>uminus\<close>, [k]) => inst [] [k] dbl_neg_numeral_a
  end
\<close>

lemma fun BitM_conv m=( strip_app
  "Num. k)"
  by simp

ML \<open>
fun dbl_inc_conv a =
  let
    val dbl_inc_neg_numeral_a = inst [a]  | (\<^const_name>\<open>Num.Bit0\<close)>
    val = inst]] { dbl_inc_simps fnumeral_One];
    val(cong1 ( BitM_conv
  in
       [] []@thm BitM(3) [meta]});
      case lemma:
_>open
      | (\<^const_name>\<open>numeral\<close>, [k]) => inst [] [k] dbl_inc_numeral_ajava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
      \<^const_name>\<open>uminus\<close>, [k]) =>
          transitive
            ( [] [k])
            fn
  end      case strip_numeralnof
\<close>

lemma dbl_dec_neg_numeral
  "Num.dbl_dec (- Num.numeral \<^const_name>\uminus\, [k]) => inst [] [k] dbl_neg_numeral_a
  by simp;

MLlemma:
fun   "Num.dbl_inc.numeral=-Num (Num k)"
  let
    val = inst [] @ dbl_dec_neg_numeral]};
    valdbl_dec_0_a =inst[][ {thm dbl_dec_simps()[ numeral_One meta
val =  [a] [] { dbl_dec_simps[]};
  in
    fn dbl_inc_neg_numeral_a [a] [@thm dbl_inc_neg_numeral meta
      case strip_numeral  of
        (\<^const_name>\<open>zero_class.zero\<close>, []) => dbl_dec_0_a
      casestrip_numeral
      (<>\<open>zero_class.zero\<close>, []) => dbl_inc_0_a
          transitive'
            (inst[ dbl_dec_numeral_a)
            (cong1 (args1 BitM_conv))
  end;
\<close>

ML \<open>
fun sub_conv a(inst )
  let
    val(ong1 cong1 BitM_conv
         sub_Bit0_One,sub_Bit1_One,sub_Bit0_Bit0,
         sub_Bit0_Bit1, sub_Bit1_Bit0, sub_Bit1_Bit1] =
      map [a] ] { sub_num_simpsmeta}java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
    val dbl_conv_a simp
    val \<open>
dbl_dec_conv_a dbl_dec_conv ;

    fun  m n = casestrip_app n) java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
(\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>
          sub_One_One
       (
          transitive
            (inst [] [l] sub_One_Bit0)
            case n of
      | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
          inst [] [      |(^const_name
name
          transitive'
            (inst []   ;
java.lang.StringIndexOutOfBoundsException: Range [0, 12) out of bounds for length 0
      | ((^const_name
          inst [] [k] sub_Bit1_One
      | ((\<^const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>, sub_Bit1_One,
          transitive'
            ( [] [,l]sub_Bit0_Bit0
            (cong1  (rgs2
|(\^const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
          transitive dbl_dec_conv_a  dbl_dec_conv
            ( [] [k ]sub_Bit0_Bit1
            (cong1dbl_dec_conv_a)
      | ((\<^const_name>\<open>Num.Bit1\<close>, [k]), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>
      |(\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>'
            (inst [] cong1 ( BitM_conv
java.lang.StringIndexOutOfBoundsException: Range [48, 12) out of bounds for length 48
      | ((\<^const_name>\<open>Num.Bit1\<close>, [k]), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
          transitive
            inst[][, )
            (cong1' dbl_conv_a ( [] [k )
  in end
\<close>

ML\<open>
fun expand1 a =
   val = inst ]@thm numeral_One[eta]}
  in
    fn n =>
      case Thm.term_of n of'
        \<^Const_>\<open>one_class.one _\<close> => numeral_1_eq_1_a
      | \<^Const_>\<open>uminus _ for \<^Const_>\<open>one_class.one _\<close>\<close> =>
          Thm.combinationinst,]sub_Bit0_Bit1
      |
      | \<^Const_>\<open>numeral _ for _\<close> => Thm.reflexive n
      | \<^Const_>\<open>uminus _ for \<^Const_>\<open>numeral _ for _\<close>\<close> => Thm.reflexive n
      | _ => err[[,l sub_Bit1_Bit0java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
  end;

fun norm1_eq a =
  let val numeral_1_eq_1_a  transitive
  in
f eq >
      case Thm conv
        java.lang.StringIndexOutOfBoundsException: Range [0, 106) out of bounds for length 0
|java.lang.StringIndexOutOfBoundsException: Index 124 out of bounds for length 124
            Thm.transitive eq
              (hm.ombinationThm (Thm (Thmrhs_of
numeral_1_eq_1_a
      | _ => eq
  ;
\<close>

ML \<open>
fun plus_conv f a =
  let
    val add_0_a = inst [a] [] @{thm add_0 [meta\^>\<open>zero_class.zero _\<close> => Thm.reflexive n
    val add_0_right_a [a] []@thm [meta
    val numeral_plus_numeral_a = inst [a] [] @{thm| >err java.lang.StringIndexOutOfBoundsException: Range [28, 29) out of bounds for length 28
    val val numeral_1_eq_1_a = inst []] {thm numeral_One[]}

     eq>
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) => inst [] [n] add_0_a
      | (,(<const_name
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive'
            (inst [] [m, n] numeral_plus_numeral_a)
      |
      | _ =cong2 ) (expand1_a(xpand1_a
  in f conv end;

val nat_plus_conv =plus_conv I <^ctyp>\<open>nat\<close>;
\<close>

lemma              Thm (Thm. (Thmdest_fun.hs_of eq
  "- Num.numeral >eq
  by simp

ML \<open>
fun plus_neg_conv a ML java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
  let
     numeral_plus_neg_numeral_a
      inst]@thm(1) []};
    val = inst { numeral_plus_numeral]};
     expand1_a a;
    val
      insta [ @@thm [meta

  in
    fn conv _ (^>\<open>zero_class.zero\<close>, [])) => inst [] [m] add_0_right_a
      case (strip_numeral m, strip_numeral n) of
        (            inst ]numeral_plus_numeral_a
          .transitive
            (inst [] [m, n]       _>cong2conv expand1_a n))
(sub_conv_a mnjava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
      (<>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          .transitive
            (inst  -Num +  Numn=( numeral :a:)
            sub_conv_a )
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          transitive a =
            (inst []     numeral_plus_neg_numeral_a
            (cong1 (args2)))
      | _ => conv neg_numeral_plus_numeral_a
  end;

fun plus_conv a = a  plus_neg_conv

val = plus_conv\<^ctyp>\<open>int\<close>;
\<close>

lemma strip_numeral n) of
lemma minus_numeral\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>

ML \<open>
uminus_conv
  let
val = inst { minus_zero]};
    val minus_one_a = instThm
     minus_numeral_a [a] []@thm [meta
    val n m)
  in
    fn=
      case strip_app n of
        (\<^const_name>\<open>zero_class.zero\<close>, []) => minus_zero_a
      |            inst,n neg_numeral_plus_neg_numeral_a)
      |\<>\<open>Num.numeral\<close>, [m]) => inst [] [m] minus_numeral_a
      | (end;
  end;

val int_neg_conv = uminus_conv \<^ctyp>\<open>int\<close>;
\<close>

ML \<open>
fun minus_conv
  let\<close>
    vallemma: "-1=-1 by simp
ral_ajava.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
      map [a][)@thms [meta
    val
         minus_zero_a [a] [ { minus_zero]};
    val = sub_conv
    val = uminus_conv
val = expand1 ;
    val norm1_eq_a  norm1_eq

nv =(ase m,  n) of
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) =>\<>\<open>zero_class.zero\<close>, []) => minus_zero_a
          Thm.ransitive(nstn ) (uminus_conv_a
      | (_, (\<^const_name>\<open>zero_class.zero\<close>, [])) => inst [] [m] diff_0_right_a
      | ((\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          Thm.transitive
            (inst n )
            (sub_conv_a\<close>
      |(\^const_name><pen>um.\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          transitive [numeral_minus_numeral_a,
(instm n] )
            (cong1 (args2 add_num_conv))
| (\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          transitive'
            ( [] [m,n]neg_numeral_minus_numeral_a)
            (cong1 (args2add_num_conv))
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          Thm.transitive
            (inst [] [m, val = expand1a;
            (sub_conv_a n m)
      | _ => cong2'' convjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  in norm1_eq_a oo conv end;

val int_minus_conv.transitive [] n]diff_0_a n)
\<close>

ML \<open>
val int_numeral.transitive

            sub_conv_a

val expand1_nat = expand1 \<^ctyp>\<open>nat\<close>;

fun  m n= (ase strip_appm strip_app ) java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
    ((\<^const_name>\<open>zero_class.zero\<close>, []), _) =>
      inst [] [n] @{thm diff_0_eq_0 [meta]}
  | ([] [m ]neg_numeral_minus_numeral_a
      inst [] [m] @{           (ong1 cong1 add_num_conv
  | (
      transitive'
        (inst [] [m, n] @{thm diff_nat_numeral [meta]})
        (cong1' nat_conv (args2 int_minus_conv))
  | _= cong2' nat_minus_conv expand1_natm)( n)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
\<close>

ML \<open>
fun mult_num_conv m n = (case (strip_app ML \<open>
    (,(<const_name
      inst [] [m] @{thm mult_num_simps(1) [meta
   (\<^const_name>\<open>Num.One\<close>, []), _) =>
      inst [] [n] @{thm expand1_nat \<^ctyp>\<open>nat\<close>;
  |(\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      transitive'
(inst[ m,n @thm (3) [meta
        (cong1 (cong1 (args2  |(, \^>\<open>zero_class.zero\<close>, [])) =>
  |(\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n'])) =>

        (inst [] [m, n']'
        ( (args2))
  | ((        (cong1' nat_conv (args2 int_minus_conv))
      transitive'
        (inst [] [m', n] @{thm mult_num_simps(5) [meta]})
        ( (args2))
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      transitive'
        (inst [] [m, n] @{thm mult_num_simps(6) [meta \<open>
        (cong1' add_num_conv
           (args2    _,(^const_name><>Num\<close)=
          cong1 mult_num_conv
\<close>

ML       [] [n] { mult_num_simps)[]}
funmult_conv
  let
    valmult_zero_left_a [a] [ { mult_zero_left]}
    val (cong1 mult_num_conv
    val(\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n'])) =>
    al = expand1
    val (args2))

     conv=case( m, strip_appjava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) => inst [] [n] mult_zero_left_a
      | (_,        cong1 mult_num_conv
      |(\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive'
            (      transitive'
            (cong1 (args2 mult_num_conv))
        = '' (f conv m) ( n))
  in(ong1' java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35

val = mult_conv
\<close>

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fun mult_neg_conv a =
  let
    val [ val = inst][ thm [meta
         numeral_times_neg_numeral_a =
       numeral_times_numeral_a [a]]@thm [meta
in
    fn conv => fn m => fn n =>
      case (strip_numeral m, strip_numeral
        ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          transitive'
            (inst_(<^const_name>\<open>zero_class.zero\<close>, [])) => inst [] [m] mult_zero_right_a
            (cong1 (args2 mult_num_conv))
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive'
            (inst [] [m, n] neg_numeral_times_numeral_a            cong1 ( mult_num_conv
            (cong1\<close> \<open>
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          transitive'
(inst ])
            (cong1cong1 (args2)))  a =
      | _=  m n
  end

val int_mult_conv = mult_conv' ap (inst a][ @thms mult_neg_numeral_simps [meta];
\<close>

MLcasestrip_numeral
fun eq_num_conv  case (trip_app n)           '
    (\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>'conv =
      @{thm
               args2
      inst
  |((
      inst[]@thm(3) [meta.
me\<>Numclose,m)] java.lang.StringIndexOutOfBoundsException: Range [97, 98) out of bounds for length 97
            ( (cong1 (hm );
  | (\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
    .transitive      Thm [][mn numeral_times_neg_numeral_a
>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
  end;
inst
        (njava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
   (\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      inst[m,n { eq_num_simps]java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  | args2= (Thm)Thm);
(^\openNumclose\const_nameopen
  | (\c\openuminus
transitive
        (inst>" )java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
          (^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
\<close>

ML \<open>
fun eq_conv f a =
  let
    val zero_eq_zero_a =  (^>\<open>numeral\<close>, [b']) => inst [] [b'] @{thm nat_neg_numeral [meta]}));\<close>
    val zero_neq_numeral_a []_>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>thm(1 meta
@{thm [THEN])
    valmnjava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
      inst[@ numeral_neq_zero Eq_FalseI
     numeral_eq_iff_a [a @thm [meta [,n  (7 meta
vexpand1_ajava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30

    funconv n=( ( m, strip_app
        ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          zero_eq_zero_a   (^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>(q_num_conv      '
ML
       ] [
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>] (8 ]})
          inst [    zero_eq_zero_aa ]{reflTHEN}
      | (\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) => [] ]{ (9) []java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
          Thm.transitive
ral_eq_iff_a] []};
    valexpand1_a args1)
      | _ =>instn {java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  injava.lang.StringIndexOutOfBoundsException: Range [2, 91) out of bounds for length 9

val nat_eq_conv = eq_conv I \<^ctyp>\<open>nat\<close>;(\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>numeral\<close>, [n])) =>
\<close>

ML            [] [m]        (\<^const_name>\<open>zero_class\<close>, []) => dbl_0_a
eq_neg_conv
  let
    val neg_numeral_neq_zero_a =
      inst\<close>
    val =
  "um.dbl_inc (- Num.umeral k) -Num NumBitM kjava.lang.StringIndexOutOfBoundsException: Range [62, 63) out of bounds for length 62
    val neg_numeral_neq_numeral_a
[][ { neg_numeral_neq_numeralEq_FalseI
valin;
      inst [a] [] @{thm numeral_neq_neg_numeral nat_eq_convdbl_inc_numeral_a ][{ (5) meta
    val
  in
    fn =>fn m'
      case (strip_numeral m, strip_numeral ( BitM_conv
val. -.) NumNum
instm]
      | ((java.lang.StringIndexOutOfBoundsException: Range [0, 35) out of bounds for length 20
           [] []zero_neq_neg_numeral_a
|       [][@thmTHEN}java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
           [] m ]numeral_neq_neg_numeral_a
      java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
          inst [] [m, n] neg_numeral_neq_numeral_a'
       (   conv>  =java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
          Thm.
            (instm ]neg_numeral_eq_iff_a
            (eq_num_conv( [a] ] @{thms [meta
      | >conv
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6

fun' a = eq_conv (eq_neg_conv )a;

int_eq_conv'\<^ctyp>\int\;
            (cong1 (cong1 (args1 BitM_conv)))

ML][]sub_One_Bit1
fun           .transitive
    ((\<^const_name>\<open>Num.One\<close>, []), _) => [] [,n]neg_numeral_eq_iff_a
      inst          '
end
      inst
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst []java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>|((^(^>>Num
      Thm.transitive
        ( \^>\<open>Num.Bit1\<close>, [k]), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>[ []@thm(2) [meta
        ( m n)
  | (\<
      Thm.transitive
   (java.lang.StringIndexOutOfBoundsException: Range [0, 29) out of bounds for length 0
        le_num_conv
|(\<const_name
      ( [] [m n @ le_num_simps[]})
( m java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
        (le_num_conv      | \<^Const_>\<open>uminus _ for \<^Const_>\<open>one_class.one _\<close>\<close> =>
  |(java.lang.StringIndexOutOfBoundsException: Range [0, 97) out of bounds for length 75
      Thm.transitive m njava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
        (inst [] [m, n] @{thm le_num_simps(7) [      .transitive
( m n))

  m n  case m, strip_appof
  |(java.lang.StringIndexOutOfBoundsException: Range [0, 37) out of bounds for length 6
instthm)[]}
java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
      instn { less_num_simps m n))
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>  m n = ( (or
      inst]@ less_num_simps]}
| ((<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
     Thm
(inst]java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 56
        (less_num_conv m       nst{less_num_simps
  end
      Thm.transitive \<open>
        (inst[,n]@thm less_num_simps()[]})
        ( m )
  Thm
              (inst{ less_num_simpsvaladd_0_right_a]   meta
        (instm n { less_num_simpsjava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 30
        (less_num_conv m n)
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
      Thm.transitive
        (inst
        (less_num_conv m n));
\<close>

ML m n)
fun f a =
       convjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
    val =inst[ { order_refl
    val zero_le_numeral_a" .numeral mmn);
       [a][@thm [THEN
    val not_numeral_le_zero_a =
      inst      numeral_plus_neg_numeral_a
val  =inst[  { [meta
    val expand1_a = expand1 a;

          [a][ thm2 meta
(\<
          zero_le_zero_a
      | ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>numeral\<close>, [n])) => sub_conv_a =
          inst []  case minst{hm  [ Eq_FalseI
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>  =Thm
ot_numeral_le_zero_a
      |      |(\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          Thm.transitive
            (inst [] [m, n] numeral_le_iff_a)
            (le_num_convmnjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
      | _ => cong2'' (      |(java.lang.StringIndexOutOfBoundsException: Range [0, 74) out of bounds for length 48
  in ;

nat_le_conv\opennat
\<close>

ML \<open>
fun le_neg_conv
  let
    val neg_numeral_le_zero_a =
       [][ { neg_numeral_le_zeroEq_TrueI
    val not_zero_le_neg_numeral_a =
      inst  thmTHEN;
    val neg_numeral_le_numeral_a =
      inst  n       case strip_app n of
    val =
      inst [
    inst[{neg_numeral_le_zero];
in
    fn conv = int_neg_conv \<^ctyp>\<open>int\<close>;
      case (strip_numeral a =
        \const_name\openuminus m)(const_name
          inst [] [m] neg_numeral_le_zero_a
      | ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>uminus\<close>, [n])) =>
          inst diff_0_a [a] []{ diff_0inst[@hm]}
      |(\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          inst [ [m  not_numeral_le_neg_numeral_a
| expand1_a ;
          inst [java.lang.StringIndexOutOfBoundsException: Range [16, 17) out of bounds for length 0
|           [ nn
       (<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
            (      |(      | ((\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
            (le_num_conv n m)
      | _ => ( [] m            nm)
  end

fun' =le_conv (le_neg_conv

val'\<^ctyp>\int\;
\<close>

ML int_le_conv' \<^ctyp>\int\;
\close>
  let
     not_zero_less_zero_a a ]@thm  conv
    val zero_less_numeral_a =
      insta ]@{hm [THEN  =  [a][@less_irrefl , THEN};
    val not_numeral_less_zero_a
inst[ {not_numeral_less_zero Eq_FalseI
    val numeral_less_iff_a = inst [a] [     not_numeral_less_zero_aexpand1_nat
val a;

    fun       [] n @ diff_0_eq_0java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
java.lang.StringIndexOutOfBoundsException: Range [8, 4) out of bounds for length 30
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(<\<java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 108
          inst' nat_conv args2 int_minus_conv(<
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          instm
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          Thm.transitive
            inst])
            (less_num_conv m n)
      |_       (<
  in f conv|(^const_name>\<open>Num.One\<close>, []), _) =>.transitive

>\<open>nat\<close>;|(java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 99
\<close>

ML \<open>
fun less_neg_conv( [][,n]@thm)[meta
  let
al_less_zero_a
      inst [a [ @thm [<close>
    val not_zero_less_neg_numeral_a =
inst  java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
    val neg_numeral_less_zero_a
inst[{thm [THEN]};
     not_numeral_less_neg_numeral_a
      inst \<open>
val  = inst
  in
    fn >fnfn
          val inst ]{numeral_times_numeral]}
(^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          inst     neg_numeral_less_iff_am ( (strip_app)of
|(\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>uminus\<close>, [n])) =>
          inststrip_numeral,strip_numeral
      |        (^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          inst[ [,n]java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 41
|(^>open
          inst [] [m, val = I
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          Thm.transitive
            (inst [] [m, n] neg_numeral_less_iff_a)
            (let
      | _ => conv m n
  end;

less_conv( java.lang.StringIndexOutOfBoundsException: Range [45, 31) out of bounds for length 31

val =less_conv
\<close>

ML \<open>
fun If_conv a =
  let
    val = inst
v if_False a]{ if_False]java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
  in
    fn p = n => fn>fn'
      case strip_app             (args2
        \<^const_name>\<open>If\<close>, [cb, cx, cy]) =>'
          let
            val p_eq = p cb>conv
            val eq = Thm            val  =p cb
          in
            case Thm.java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
              \<^Const_>\<open>True\<close> =>
                let
                  val x_eq=x cx
                  valinst]{eq_num_simpsjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
                in
                  Thm.transitive
                    (Thm.combination
                       (Thm.combination eq x_eq(Thm java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
                       .transitive
                    end
                end
            | \<^Const_>\<open>False\<close> =>
                let
                   y_eq][, thm8meta
                   cy= Thm
                val =Thm y_eqjava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
Thm

                       Thm eq(.reflexive []]thm THEN}java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                       y_eq)
                                           )

            | _ => err     fun                end
          end| =  java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
  end
\<close>

ML \<open>
fun drop_conv a =
  let
valinstdrop_0
        )
val>' (conv)e ( n)

    fun convconv term_of
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      |_= c strip_app of =
\const_name\^>
'
              ( [] nxs [] n x ] drop_Cons_a
              (If_conv_a (args2 a [{ neg_numeral_neq_numeralEq_FalseIjava.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
                 .eflexive
                 (cong2
  in conv      \<close>
\<close>

\<open>
nth_conv    val(  :".(theory_of_ctermct term_of);

    val nth_Cons_a = inst [a] [] @{thm    fun conv [][,]
    val If_conv_a = If_conv a;

    fun convfun eqn=Thm (Thm.java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 49
        ( ' a = (eq_neg_conv )ajava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
          transitive
             [ [x xs)
            ( args2)
               .reflexive
               (cong2' conv Thm.reflexive (args2 nat_minus_conv) inst[] [n] Thm. (.dest_fun2 ct))

    val eqn1 = conv1 (Thm.dest_arg1 ct);

end

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