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.nprems_of st then Seq.empty
  else Seq.single (Conv.gconv_rule cv 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 se Seq.ingle Conv cv);
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

fun transitive'eqeq'=Thm.ransitive eqeq.eq

fun type_of_eqn(onv Thm eqn1(.rhs_of))

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

fun cong1
      T
  in
mtransitive(Thm.ombination (hm. (Thm. (Thmlhs_of) eqn1         eqn2
(.combination. ct) eqn
      (conv' (Thm.rhs_of eqn))
  fun args2 conv ct =conv.dest_arg1ct.dest_arg);

fun cong2 conv1 conv2\<close>
  Thmstrip_numeralctcase strip_app
    \<^const_name>\<open>uminus\<close>, [n]) => (case strip_app n of
       (Thm.reflexive (Thm.dest_fun2      >",[)
       (conv1 .dest_arg1)))
    (conv2 (Thm.dest_arg

fun cong2
  let
    fun i = case iof
    valeqn2 =conv2 Thm ct
  in
    Thm.transitive   (\<^const_name>\<open>one_class.one\<close>, []) => @{thm nat_one_as_int [meta, symmetric]}
      (.combination
         (Thm.combination (Thm.reflexive (Thm\^>\<open>uminus\<close>, [b]) => (case strip_app b of
         eqn2)
      (conv (Thm\<close>
  end;

fun cong2'' conv eqn1 eqn2 =
  let val eqn3 = conv (Thm.rhs_of eqn1) (Thm.rhs_of eqn2)
  java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
    Thm.transitive
      (Thm.combination
         (       [] [] @thm add_num_simps2 [eta
         eqn2
      eqn3
  end;

fun args1transitive
fun conv = conv.dest_arg1)(.dest_arg);
\<close>

ML (args2))
fun ct =( strip_appof
    (\<^const_name>\<open>uminus\<close>, [n]) => (case strip_app n of
      (\<^const_name>\<open>numeral\<close>, [b]) => (\<^const_name>\<open>uminus\<close>, [b]) (
    | _ => ("", []))inst[]@thm(4) [meta}
  | x => x);
\<close>

lemma nat_minus1_eq: "nat (- 1) = 0"
  by simp

ML \<open>
fun nat_conv i = (case strip_app i of
    (\<^const_name>\<open>zero_class.zero\<close>, []) => @{thm nat_0 [meta]}
  |         [] [m,n] @thm(6) [meta
  | (\<^const_name>\<open>numeral\<close>, [b]) => inst [] [b] @{thm nat_numeral [meta]}
  | (\<^const_name>\<open>uminus\<close>, [b]) => (case strip_app b of
      (\<^const_name>\<open>one_class.one\<close>, []) => @{thm nat_minus1_eq [meta]} [[]@thm(7) meta
    | (\<^const_name>\<open>numeral\<close>, [b']) => inst [] [b'] @{thm nat_neg_numeral [meta]}));
\<close>

ML \<open>
fun add_num_convinst,]@ add_num_simps[]})
    ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>args2add_num_conv
      @{thm add_num_simps(java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 17
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
       ] [n { add_num_simps
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
   transitive'
        (fun m = ( strip_app
        (cong1 ( add_num_conv
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst'
  |(nst [ n {thm BitM(2)[]})
      transitive'
        (instm n] { add_num_simps]})
        (cong1 (<const_name>\<open>Num.Bit1\<close>, [n]) =>
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      transitive
        (inst [] [m, n] @{thm add_num_simps
        (cong1Num( Num.numeral .numeral k)
|(\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      transitive'
        (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        (cong1 (args2 dbl_neg_numeral_a [a ]@thm [metajava.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
  | (\^const_name><pen.\<close[],(^const_name>\<open>Num.Bit0\<close>, [n])) =>
      transitive
        (inst
        (cong1 n=java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      transitive'
        (inst [] [m, n] @{thm add_num_simps (<const_name>
        (cong1   ;
\<close>

ML \<open>
fun BitM_conv =(ase m of
    (\<^const_name>\<open>Num.One\<close>, []) => @{thm BitM.simps(1) [meta]}dbl_inc(- Num.numeral k) = - Num.numeral (Num.BitMjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
>, [n] =
      transitive'
        (inst dbl_inc_0_a [a][@thm(2) [olded , meta}
        cong1 (rgs1))
  |  in
inst[ @thm .simps
\<close>

dbl_neg_numeral
  "Num.dbl (- "Num.dbl (- Numname><>zero_class.zero\, []) => dbl_inc_0_a
  by simp

ML \<open>
fun dbl_conv a =
  let
    val dbl_neg_numeral_a = inst [a] [] @{ |(
    val dbl_0_a'
    valinst dbl_inc_neg_numeral_a
  in
     n =>
      case strip_numeral
        (\<^const_name>\<open>zero_class.zero\<close>, []) => dbl_0_a
      | (\<^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>

dbl_inc_neg_numeral
(- Num k)   .numeral.BitM
  by simp

ML dbl_dec_neg_numeral_a [a]@thm [meta
fun    val dbl_dec_0_a =inst [ ]@thm dbl_dec_simps2 folded, ]};
     dbl_dec_numeral_ainst@thm(5) meta
    val = inst[ {thm dbl_inc_neg_numeral[]};
    val dbl_inc_0_acase strip_numeralnof
    val
  in
    fn n =>
      case  n of
        (<const_name
      | (\<^const_name>\<open>numeral\<close>, [k]) => inst [] [k] dbl_inc_numeral_a
      | (\<^const_name>\<open>uminus\<close>, [k]) => [] []dbl_dec_numeral_ajava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
          transitive
             [] [k]dbl_inc_neg_numeral_a
            (ong1 ( (args1)))
         sub_Bit0_One,sub_Bit1_One,sub_Bit0_Bit0java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
\<close>

lemma (inst[)@thms [meta];
  "Num.dbl_dec (- Num.numeral k) = - Num.numeral (Num.Bit1 k)"
  bysimp

ML
fun val =dbl_dec_conva
  let
    val dbl_dec_neg_numeral_aconv( ( m, strip_appof
    val dbl_dec_0_a = inst [a] [] @{thm        (
    val dbl_dec_numeral_a
  in|(\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>'
    fn n =>
       strip_numeral
        (\<^const_name>\<open>zero_class.zero\<close>, []) => dbl_dec_0_a
      | (\<^const_name>\<open>uminus\<close>, [k]) => inst [] [k] dbl_dec_neg_numeral_a
      |(<>\<open>numeral\<close>, [k]) =>
          transitive'
            (inst [] [k] dbl_dec_numeral_a)
            (cong1 >\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.One\<close>, [])) =>
  end
\<close>

ML \<open>
fun sub_conv a =
  let
    val [sub_One_One, sub_One_Bit0, sub_One_Bit1\<>\<open>Num.Bit1\<close>, [k]), (\<^const_name>\<open>Num.One\<close>, [])) =>
         sub_Bit0_One, sub_Bit0_Bit0
         sub_Bit0_Bit1, sub_Bit1_Bit0, sub_Bit1_Bit1] =
      map (instinstk,l])
    val dbl_conv_a(cong1'dbl_conv_a( conv))
    val       (<const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
    valdbl_dec_conv_a = a;

    fun convinst,l )
        ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>' dbl_dec_conv_a (args2 conv)
          sub_One_One
      |(
          transitive
            (inst [] [l] sub_One_Bit0)
            ( (cong1args1)))
      | ((            (cong1' dbl_inc_conv_a (args2 conv))
          inst [] [l] sub_One_Bit1
      |'
          transitive(inst ][ l]sub_Bit1_Bit1
            (inst]sub_Bit0_One
            (cong1 conv;
\<close>
          inst \<open>
      | ((\<^const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>let numeral_1_eq_1_a [a][ @thmnumeral_One [, symmetric
          transitive
            (inst [] [k, l] sub_Bit0_Bit0)
            (cong1' dbl_conv_a (args2 conv))
      | ((\<^const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
          transitive'
            ( [] [k l )
            (cong1' dbl_dec_conv_a (args2 | \<^Const_>\zero_class.zero _\ => Thm.reflexive n
      | ((\<^const_name>\<open>Num.Bit1\<close>, [k]), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>
          transitive'
            (inst [ k l]sub_Bit1_Bit0)
            (cong1' dbl_inc_conv_a (args2 conv))
      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
         '
            (inst
            (    neq=
  in end;
\<close>

ML \<open>
fun expand1 a =
         <^Const_>\<open>uminus _ for \<^Const_>\<open>Num.numeral _ for \<^Const_>\<open>Num.One\<close>\<close>\<close> =>
  in
                  (hm. (.reflexive.dest_fun. eq)))
      case Thm.term_of                 )
  end
      | \<^Const_>\<open>uminus _ for \<^Const_>\<open>one_class.one _\<close>\<close> =>
          Thm.java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      | <Const_
      | \<^Const_>\<open>numeral _ for _\<close> => Thm.reflexive n
      | \<^Const_>\<open>uminus _ for \<^Const_>\<open>numeral _ for _\<close>\<close> => Thm.reflexive n = inst { add_0_right]};
      |_=  "expand1" n
  end;

fun norm1_eq a =
  letval numeral_1_eq_1_a inst [][ @thm numeral_One meta
  in
    fn =java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
      case Thm.term_of (Thm.rhs_of eq_,\<>\<open>zero_class.zero\<close>, [])) => inst [] [m] add_0_right_a
        \<^Const_>\<open>Num.numeral _ for \<^Const_>\<open>Num.One\<close>\<close> => Thm.transitive eq numeral_1_eq_1_a
\<^Const_>\<open>uminus _ for \<^Const_>\<open>Num.numeral _ for \<^Const_>\<open>Num.One\<close>\<close>\<close> => = '' (fconv m) ( n))
            Thmval nat_plus_conv =plus_conv Ijava.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
              (.combinationreflexive. (Thm.hs_of )))
                 numeral_1_eq_1_a)
      |_= java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
  end;
\<close>

ML \<open>
fun plus_conv f a =
  let
    val add_0_aval =
    val [a] [ { add_neg_numeral_simpsmeta
numeral_plus_numeral_a [a] []@thm [meta
val = expand1

    fun conv [][ { neg_numeral_plus_neg_numeral]};
((\<^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'
            ( [] [m,n numeral_plus_numeral_a)
            (          Thm
|  = '' (f conv)( m) (expand1_a
  in f conv             sub_conv_a n)

val  |((<const_name
\<close>

lemma neg_numeral_plus_neg_numeralThm
  " Num.numeral m -.numeral ( Num. (m + n):':neg_numeral"
  by simp( nmjava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28

ML \<open>
fun plus_neg_conv
  let
val =
      inst [a] [] @{thm (cong1 add_num_conv
    val =
      inst [a] [] @{thm add_neg_numeral_simps
    valplus_conv'a =norm1_eq ooplus_conv (( a) a;

    val int_plus_conv' \<^ctyp>\int\;
  in
    fn
      case( m, strip_numeral
        ((
          Thm.transitive
            java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
            fun a =
      |      minus_zero_a [a] []@thm [meta
          .transitive
            (inst [val = inst]{ minus_numeral]};
            (sub_conv_a
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) => n >
          transitive'
            ( [] [m ]neg_numeral_plus_neg_numeral_a)
            (      |(^const_name
      | _ => conv m n
  endjava.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6

fun plus_conv' a = norm1_eq a oo plus_conv (plus_neg_conv a) a\

val int_plus_conv = plus_conv a =
\<close>

minus_one    " by simp
lemma minus_numeral: "- numeral, neg_numeral_minus_neg_numeral_a] =

ML \<open>
fun (inst ] { diff_numeral_simps]};
  let
    val = inst]@thm [meta
    val sub_conv_a a;
    val uminus_conv_a a;
         expand1_aexpand1 a
      val norm1_eq_a = a;
    fn n
      case m n =c (strip_numeralstrip_numeral
        (<const_name
      | (\<^const_name>\<open>one_class.one\<close>, []) => minus_one_a
      | (\<^const_name>\<open>Num.numeral\<close>, [m]) => inst [] [m] minus_numeral_aThm.ransitive ( [] []diff_0_a n)
      | (\<^const_name>\<open>uminus\<close>, [m]) => inst [] [m] minus_minus_a
  java.lang.StringIndexOutOfBoundsException: Range [109, 5) out of bounds for length 6

val int_neg_conv = uminus_conv [] [m,n]numeral_minus_numeral_a
\<close>

ML (<const_name><pen>umnumeral
fun minus_conv a =
  let
    val, numeral_minus_neg_numeral_a
         neg_numeral_minus_numeral_a             [] [,n numeral_minus_neg_numeral_a
      map (inst [a] []) @{thms       (\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
    valinst,n]neg_numeral_minus_numeral_a
    val diff_0_right_a = inst (cong1 add_num_conv)java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    val sub_conv_a = sub_conv a;
    val uminus_conv_a = uminus_conv a;
     expand1_aexpand1 ajava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
    val norm1_eq_a = norm1_eq a;

    fun conv m n = (case (strip_numeral m, strip_numeral n) of
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) =>
          Thm (inst[ ) (uminus_conv_a

      |ML\<open>
          Thm
            (
( m n)
      | ((\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          transitive'
            (inst nat_minus_convn  (ase(strip_app , strip_appnof
            (cong1 (args2 add_num_conv))
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          transitive'
            (inst,n eg_numeral_minus_numeral_a)
           cong1( (args2)))
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>(\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          Thm.transitive
            (inst [] [m, n] neg_numeral_minus_neg_numeral_a >cong2' nat_minus_conv( m)expand1_nat );
            (sub_conv_a n m)
      | _ => cong2'' conv (expand1_a m) (expand1_a n))
  in norm1_eq_a oo conv end;

val int_minus_conv = minus_conv \<^ctyp>\<open>int\<close>;
\<close>

ML \<open>
val int_numeral = Thm.    (,\^>\<open>Num.One\<close>, [])) =>

val nat_minus_refl|(\<^const_name>\<open>Num.One\<close>, []), _) =>

val = expand1

fun nat_minus_conv   (
    ((\<^const_name>\<open>zero_class.zero\<close>, []), _) =>
      inst [] [n        inst ][,n]{thm mult_num_simps]})
  _(<const_name
      inst [] [m] @{thm minus_nat.diff_0  |(
  | ((      transitive'
      transitive
        (instcong1 mult_num_conv
java.lang.StringIndexOutOfBoundsException: Range [48, 8) out of bounds for length 48
  | _ => cong2'' nat_minus_conv (expand1_nat m)         cong1 mult_num_conv
\<close>

ML
fun mult_num_conv m n = (case (strip_app (cong2
    (,(<const_name><pen.One>, []) =
      inst [] [m] @{thm mult_num_simps(( (args2)))));
  | ((\<^const_name>\<open>Num.One\<close>, []), _) =>
      inst@thm(2 meta
  | fun  f a =
      transitive
        (inst  = inst]@thm [meta;
        (cong1 (args2)))
  | (
      transitive'
        (inst [] [mv expand1_a a;
        (cong1 mult_num_conv
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m']), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>fun m n  ( strip_app n) of
      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])) =>|(\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
transitivejava.lang.StringIndexOutOfBoundsException: Range [17, 18) out of bounds for length 17
        (inst [] [m, n] @{thm|_>cong2) (expand1_aexpand1_a
        ( (cong2add_num_conv
           (args2 add_num_conv)
           (cong1 (args2 nat_mult_conv I \<^ctyp>\<open>nat\<close>;
\<close>

ML \<open>
fun mult_conv f a =
  let
    mult_zero_left_a [a ]@{ mult_zero_left]};
    val mult_zero_right_a = inst numeral_times_neg_numeral_a] =
    val = inst [ { numeral_times_numeral]};
    val  java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
    val norm1_eq_a = norm1_eq a;

    fun conv m n = (case (strip_app
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) => inst [] [n] mult_zero_left_a
      | (, java.lang.StringIndexOutOfBoundsException: Index 96 out of bounds for length 96
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive'
            (transitive'
(cong1 args2
      | _ => cong2fconv m) ( n))
  inooconv ;

val nat_mult_conv = mult_conv I \<^ctyp>\<open>nat\<close>;
\<close>

ML \<open>
java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 21
  let;
    val [neg_numeral_times_neg_numeral_a, fun
         numeral_times_neg_numeral_a]=
map[][){thms}
  in
    fn => m
       (strip_numeral
        ((
          transitive
            (inst [] [m, n] neg_numeral_times_neg_numeral_a(\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>fun 'convct =
            cong1))
|(\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) => []  ;
          transitive [] n]{ eq_num_simps]}
            (inst><pen<close,m,(java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
(ong1( (hm );
      |  java.lang.StringIndexOutOfBoundsException: Range [5, 6) out of bounds for length 5
          '
            inst,] numeral_times_neg_numeral_a
            cong1
      | _ => conv m n
  end;

fun mult_conv  )

val.   (\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
\<close>

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  |fun  ct. ct ct\<close>
(const_name.\<> ],<><>.One
      @{thm eq_num_simps((^><>
  |T.
      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])) =>
      inst \<close>
  | ((  | (\<^const_name>\<open>one_class.one\<close>, []) => @{thm nat_one_as_int [meta, symmetric]}
      inst [] [  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
  |(^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst name
(
      Thm.transitive
meta
        (eq_num_conv
  |        inst[] [] @{hmadd_num_simps()[       [a] [ {thm[Eq_FalseI
      inst]{eq_num_simps
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>    al a;
      inst ][,n { eq_num_simps []}
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
     .transitive
        (inst(\^onst_name
        (q_num_conv      '
\<close>

ML \<open>
       [ n
       ( (args2)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
    val   [][@hm ,THEN}
    val zero_neq_numeral_a(\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) => mn@hm[])
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    val numeral_neq_zero_a
      instjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
   [a ]{numeral_eq_iff
val expand1_a args1java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33

     dbl_neg_numeral
        ((java.lang.StringIndexOutOfBoundsException: Range [2, 110) out of bounds for length 9
          java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      | (
           [] [n] zero_neq_numeral_a
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          inst]        (\<^const_name>\<open>zero_class.zero
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>      | \<eq_neg_conv
          Thmjava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
            (inst [] [m, nr"umk) -.(Num. k"
            (eq_num_convbysimp
      | _ =>fun dbl_inc_c a inst@neg_numeral_neq_numeral Eq_FalseI
f end

val      dbl_inc_numeral_a[ ]@hm[];
\<close>

ML
fun conv fn mjava.lang.StringIndexOutOfBoundsException: Range [21, 22) out of bounds for length 21
  end
    val. -. )-.umeral
           [] [m
    val =
      inst [a  let
    val neg_numeral_neq_numeral_a =
       a ]{  [THEN]java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
    val numeral_neq_neg_numeral_a
      inst strip_numeral
    val neg_numeral_eq_iff_a = inst(<^>\<open>uminus\<close>, [k]) => inst [] [k] dbl_dec_neg_numeral_a
  in
fn m=   =
      case (strip_numeral
        (     [sub_One_One, sub_One_Bit1
          inst sub_Bit0_Bit1, sub_Bit1_Bit1
      val =  a;
|_= m n
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
          java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          inst [] [m, n] java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 8
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
Thmjava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
            (instm n )
            (eq_num_conv m n)
mn
  ;

'a (eq_neg_conva ;

          transitive            inst,]sub_Bit0_Bit0)
\<close>

\<open>
mn=case
(
      inst
   java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
java.lang.StringIndexOutOfBoundsException: Range [10, 6) out of bounds for length 47
  |(\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst(<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
|(java.lang.StringIndexOutOfBoundsException: Range [0, 66) out of bounds for length 0
         (<const_name
        instm,n]@thm(4) meta
        le_num_conv
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      Thm.transitive
        (inst [] [m,    (java.lang.StringIndexOutOfBoundsException: Range [0, 76) out of bounds for length 75
        (le_num_convn)
      |\<^Const_>\<open>zero_class.zero _\<close> => Thm.reflexive n
      Thm
        (inst[] [m,n]@{thmle_num_simps(6) [        less_num_conv
        (le_num_conv        > less_num_conv( strip_app n) of
|(java.lang.StringIndexOutOfBoundsException: Range [0, 35) out of bounds for length 6
       [[ { less_num_simps
        java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
        (less_num_conv

andless_num_conv (casestrip_app
    (_, (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst  java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 99
  |.transitive(Thm (Thm (Thm (Thm inst]@thm(4 meta
][]@thm[]}
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>  java.lang.StringIndexOutOfBoundsException: Range [3, 2) out of bounds for length 6
      inst [] m,n @thm less_num_simps5 meta
( m n)
      .transitive
[] [m, n] @thm(4)    al   [a][{add_0_right
        (less_num_conv [] [,n]@thm(6) [     expand1_a a
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      Thm.transitive
        (inst [] [m, @{thm less_num_simps]})
        (le_num_conv m n)
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      Thm.transitive
        (inst
        (less_num_conv
^ le_conv
convjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
             zero_le_zero_a  [a] ]@thm\<close>
  n)
\<close>

ML \<open>
funle_conv
  let
  = [a [@  [of, THENEq_TrueI}val  inst]]thm]}java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    inst@ add_neg_numeral_simpsjava.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
      insta] []@{thmzero_le_numeral
    valjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
inst{hm  [ Eq_FalseI

    valexpand1_ajava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24

    fun conv m n = (case (strip_app|(\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
        (\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          zero_le_zero_a
      | ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>numeral\<close>, [n])) =>
inst]
      |(java.lang.StringIndexOutOfBoundsException: Range [0, 78) out of bounds for length 48
          inst  > m n
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>oo);
          Thm.transitive
            lemma: "- 1=val nat_le_conv=le_convI\^ctyp><>nat\;
            (le_num_conv
      | _ => cong2'' (f conv) (expand1_a a =
  infconvendjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16

val nat_le_conv = le_conv [][{ not_zero_le_neg_numeral]};
\<close>

fun le_neg_conv a =
  let
    valneg_numeral_le_zero_a
      inst]@  [ Eq_TrueI
      java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
      inst [a] []java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    val neg_numeral_le_numeral_a numeral_minus_numeral_a(\const_name><uminus[)<java.lang.StringIndexOutOfBoundsException: Index 107 out of bounds for length 107
       [a] [ { neg_numeral_le_numeral Eq_TrueI
    valmap [a] []) @ diff_numeral_simpsmeta
      inst[@ [ Eq_FalseI
    valinst [a] [] @{thm neg_numeral_le_iff [meta
    |(\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
fn =>fn>  n =>
      case (strip_numeral]m,n]not_numeral_le_neg_numeral_a
                    expand1_a ;
          inst [] [m]    fun n( m  n) of
      | ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>uminus\<close>, [n])) =>
           ] n
|(\<
           [][,n]
       (
          inst [] [m, n] neg_numeral_le_numeral_a
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          Thmtransitive
[m, n]neg_numeral_le_iff_a
(  m)
                  cong1 add_num_conv  ;

fun' a =le_conv (le_neg_conv )aval int_le_conv=le_conv'\<^ctyp>\<open>int\<close>;

val = le_conv
\<close>

MLval = inst[][ {  norm1_eq_a;
fun  f a=
  let
valinst thm of THEN];
    val =
      inst [a] [valnat_minus_refl       [] ]thm [THEN;
valval=expand1
      inst nat_minus_conv= case     expand1_ajava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
val =inst ]{ numeral_less_iff;
java.lang.StringIndexOutOfBoundsException: Range [8, 4) out of bounds for length 30

    un mn=case m       \const_nameopenzero>],(
(<
          not_zero_less_zero_a
(<const_name
          inst [] []not_numeral_less_zero_a\<close>
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          instfunmult_num_conv    ( ( m, strip_app][,  java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
java.lang.StringIndexOutOfBoundsException: Index 101 out of bounds for length 101
          Thmjava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
            (inst [] [m, n] val nat_less_conv = less_conv I \<^ctyp
                    ( []java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
      | _ => cong2'' (f conv) ('
  incong1 mult_num_conv

val (args2)
\<close>

ML \<open>
less_neg_conv
cong1'add_num_conv
    val =
      inst [ neg_numeral_less_numeralEq_TrueI
    valval =
            inst \<open>
    val neg_numeral_less_iff_a   java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      instfn=  m = fn
    val numeral_times_numeral_a ]{  [meta
      inst(^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
    val convase  n of
  in
       (\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>uminus\<close>, [n])) =>
      case ( m  n) of
        (\<
          inst ] [ n]java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 41
      |(^><>\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          inst [] [n] not_zero_less_neg_numeral_a
      ((\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          inst [] [m, n] not_numeral_less_neg_numeral_a
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          inst [ [,n
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          .transitive
            (inst [] [m, n] neg_numeral_less_iff_a

      | _ => conv m n
  end;

fun     conv>fn int_less_conv'\<^ctyp>\int\;

val = java.lang.StringIndexOutOfBoundsException: Range [0, 29) out of bounds for length 10
\<close>

MLal=inst]{ if_False}
fun If_conv a =
  let
    val     fn p =f x y = fn'
    val            (cong1cong1))
  in(
fn  x =  y =>fn =>
case  ct
        (|   m n
          let
            val p_eq
            valjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49


                  val x_eq = x cx;
                  val cx = Thm cx[ [n thm []}
                in
                 Thm
                    Thm.combination
(Thm eq)
                       . java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
                    (inst|(^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
                java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
            | \<^Const_>\<open>False\<close> =>inst@ eq_num_simps [meta
                letval [ mn { eq_num_simps
                  val = Thm
                   cy .rhs_of;( m;
                in

                    (Thm zero_neq_numeral_a(.combination Thm cx[] { zero_neq_numeral];
                       (Thm       [a] [] {thmnumeral_neq_zero[HEN]};

                    (inst [] [cx    valend
                java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
             _>err
          end
  end;
\<close>

ML \<open>
fun drop_conv=

val      =  a[{  []};
           )
    val>'fconv)(xpand1_a )expand1_a)

    fun  ys. n of
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      | = (ase ys neg_numeral_neq_zero_a
(<\<open>Cons\<close>, [x, xs]) =>
                        transitive
(inst[ x,xs
               neg_numeral_neq_numeral_a
                 Thm.reflexive(*  Title:      HOL/Decision_Procs/Conversions.thy  =
                 (cong2' conv (args2 nat_minus_conv) Thm.reflexive))))
  in conv end;
\<close>

ML \<open>
fun nth_conv a =
  let
    val nth_Cons_a = inst [a] [] @{thm nth_Cons' [meta]};
    val If_conv_a = If_conv a;

    fun conv ys n = (case strip_app ys of
        (\<^const_name>\<open>Cons\<close>, [x, xs]) =>
          transitive'
            (inst [] [x, xs, n] nth_Cons_a)
            (If_conv_a (args2 nat_eq_conv)
               Thm.reflexive
               (cong2' conv Thm.reflexive (args2 nat_minus_conv))))
  in conv end;
\<close>

end

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