Quelle Conversions.thy Sprache: Isabelle

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

theory Conversions
imports Main
begin(.combination.reflexive. ct)) eqn)

ML \<open>
fun tactic_of_conv cv i st =
        (onv'(hm. )
java.lang.StringIndexOutOfBoundsException: Range [5, 3) out of bounds for length 6

fun binop_conv| '' ( ) (expand1_aexpand1_a
\<close>

ML
fun err norm1_eq_a oo f convend
   error (      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
\<close>

attribute_setup             [] [m,n] numeral_times_neg_numeral_a
  \<open>Scan.succeed (Thm.rule_attribute [] (K mk_meta_eq))\<close> (cong1( mult_num_convfunmult_neg_conv
  \<open>convert equality to meta equality\<close>_>conv

ML \<open>
fun strip_app ct

funnumeral_times_neg_numeral_a java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
  Thm.instantiate' (map SOME cTs in

fun transitive' eq eq' =     conv>fn

fun \<open>

fun cong1 conv ct =
  Thm.combination\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) => m n=(case( m, strip_app

cong1
  let val eqn = conv (Thm.dest_arg ct)
  in
    Thm.transitive
      (Thm.combination (Thm( ( mult_num_conv
      (conv       (
  end

fun cong2 conv1 conv2 ct|((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
  Thmcombination
    (Thm.combination
       (Thm.reflexive (Thm..Bit0\>[m],) <^const_name>\<open>Num.One\<close>, [])) =>
       (conv1 (Thm.dest_arg1 ct)))
    conv2.dest_arg ct

fun cong2' conv conv1 conv2 ct =
  let
    val (
    val eqn2 transitive
  in
Thm
(.(   )
         (Thm.combination (Thm(  | ((\<^const_name
         eqn2)
      (conv
  end;

fun cong2
  let val eqn3 = conv (Thm mult_conv(eq_num_conv
  in
    Thm.transitive
      (Thm.combination
         (Thm|(\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
         eqn2)
      eqn3 [] [ ]@thm(7) [meta
  end;

fun args1 conv ct = conv (Thm.dest_arg ct);
conv = convdest_arg1 (.dest_arg;
\<close>

ML \<open>
fun strip_numeral ct = (case strip_app ct of    (<><>NumOne,[]),(^\<>Num\<close>, [])) =>
  \<onst_name\<close>, [n]) => (case strip_app n of
      (\<^const_name>\<open>numeral\<close>, [b]) => (\<^const_name>\<open>uminus\<close>, [b])|      hm
    |_=(,[)
  | x => x);
\<close>

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

ML \<open>
fun nat_conv i =         (eq_num_conv \<java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
    (\<^const_name>\<open>zero_class.zero\<close>, []) => @{thm nat_0 [meta]}
java.lang.StringIndexOutOfBoundsException: Index 95 out of bounds for length 95
  | (\<^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]}
    |(<const_name
\<close>

ML  |(\<java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
fun add_num_conv b b' = (case (strip_app b, strip_app b') of
name
      @{ add_num_simps) []}
  | (  |(\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      inst [] [n]      inst [] [n]  zero_neq_numeral }
  |          )
      transitive'
( [[ { 3 inst THEN]};
        (cong1 (args2 add_num_convval = inst] [] {thm numeral_eq_iff       [] m n@thm)[]}
  v  = expand1
      inst [] [m] @{thm add_num_simps(4) [meta]}
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>[ m ]@{hm(8)[etafun conv m  (casestrip_app n) of
      transitive'
         Thm
        (cong1 (args2 add_num_conv))
| \^>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
transitive
        (inst [] [m, n] @{\<close>
        (cong1 (args2 add_num_conv))
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>funinst]zero_neq_numeral_a
      transitive'
        (inst [] [m] @{thm add_num_simps(7) [meta]})
           (ong1args2 add_num_conv)

      transitive'
        (inst [] [m, n]@{thmadd_num_simps)[meta
        (cong1 (args2 add_num_conv))
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
           zero_eq_zero_a =inst {  [of0  Eq_TrueI]java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
        (inst[,n { add_num_simpseta
        (cong1 (cong2' add_num_conv (args2 add_num_conv) Thm.reflexive)));
\<close>

ML \<open>
fun BitM_conv m = (case strip_app m of
    (\<^const_name>\<open>Num.One\<close>, []) => @{thm BitM.simps(1) [meta]}
  | (\<^const_name>\<open>Num.Bit0\<close>, [n]) =>
      transitive'
        (inst [] [n] @{thm BitM.simps(2) [            =inst][@thm meta
        (cong1( BitM_conv))
  | (\<^const_name>\<open>Num.Bit1\<close>, [n]) =>
      inst [] [n]@thm
\<close>

lemma:
  "Num.dbl (- Num.numeral k) = - Num.numeral (Num.Bit0 k)"
  by simp

ML \<open>
fun dbl_conv a =
  let
    val dbl_neg_numeral_a = instjava.lang.StringIndexOutOfBoundsException: Range [0, 24) out of bounds for length 0
    instzero_neq_numeral_a
    val dbl_numeral_a = inst
  in
    fn n =>
      case strip_numeral n of
java.lang.StringIndexOutOfBoundsException: Range [40, 8) out of bounds for length 69
      (fun a =
      |java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
  end.transitive
\<close>

lemma  zero_neq_neg_numeral_a
umnk=numeral)java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
   java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9

ML \<open>
onv       a ]{hm [THEN]};
  let
    val dbl_inc_neg_numeral_a =    val     conv
    val dbl_inc_0_a =java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    val = inst a  {dbl_inc_simps];
  in
    fn n =>
      \<close>
        (\<^const_name>\<open>zero_class.zero\<close>, []) => dbl_inc_0_a
      | (\<^const_name>\<open>numeral\<close>, [k]) => inst [] [k] dbl_inc_numeral_a
      | (\<^const_name>\<open>uminus\<close>, [k]) =>
e
            (inst [] [k] dbl_inc_neg_numeral_a)
            (cong1(cong1 (args1)))
;
\<close>

lemma dbl_dec_neg_numeral:
  "Numbl_dec (Numnmeralk=-Num.umeral (.Bit1 k)"
  by simp

ML       inst [a] [] @{thm neg_numeral_neq_zero [THEN Eq_FalseI]};m]neg_numeral_neq_zero_a
fun zero_neq_neg_numeral_ajava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
  let
    val dbl_dec_neg_numeral_a = inst           instn zero_neq_neg_numeral_a
    val dbl_dec_0_a = inst [a      (inst {neg_numeral_neq_numeral Eq_FalseI;
    val dbl_dec_numeral_a = inst [a] [] @{thm dbl_dec_simps(5) [meta]};
  ininst[,n
    fn n =>
      case n of
        (\<^const_name>\<open>zero_class.zero\<close>, []) => dbl_dec_0_a
      | \<const_name
      | (\<^const_name>\<open>numeral\<close>, [k]) =>
          transitive
            (inst [] [k] dbl_dec_numeral_a
            (cong1 (args1 BitM_conv|((<   => fn  fn
  end;
\<close>

ML \<open>
fun sub_conv a =
  let
    val, sub_One_Bit0,
         sub_Bit0_Oneinst [] [,n )
         , sub_Bit1_Bit0] =
      map inst[)@{thms sub_num_simps]};
    val dbl_conv_adbl_conv
    val dbl_inc_conv_a = dbl_inc_conv a;
    val|_= conv

    fun conv m
        ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>
          sub_One_One
      |  eq_conv=eq_conva)java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
          transitive'
            (inst val = eq_conv \<^ctyp>\<open>int\<close>;
            (cong1 (cong1 (args1 BitM_conv)))
      | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
          inst [ l sub_One_Bit1
      | ((\<^const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.One\<close>, [])) =>
          transitive
            (inst  n
            (cong1 (args1 BitM_conv))
      | ((\<^const_name>\<open>Num.Bit1\<close>, [k]), (\<^const_name>\<open>Num.One\<close>, [])) =>
          instfun eq_conv  =eq_conv )a;
      | ((\<^const_name>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit0\<close>, [l])) =>
'
( [] [k l sub_Bit0_Bit0
            (cong1' dbl_conv_a (args2 conv))
\<close>
          transitive'
            (inst [] [k, l]ML
            (cong1' dbl_dec_conv_a funle_num_conv m = ( (strip_app m,strip_app n) of
      |(\<    \<const_name\<open.One\<close>, []), _) =>
transitive'
            (inst [] [k, l] sub_Bit1_Bit0|((<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
            (cong1' dbl_inc_conv_a (args2 conv))
      |((<const_name
      inst ] m { le_num_simps]}
            (inst [] [k, l] sub_Bit1_Bit1   (
            (cong1le_num_convjava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
  in conv end;
\<close>

ML \<open>
fun expand1 a =
  let val         ( m n)
  in
    fn
      casemn)
        \<^Const_>\<open>one_class.one _\<close> => numeral_1_eq_1_a
java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
          Thm.combination (Thm.reflexive (Thm.dest_fun n)) numeral_1_eq_1_a

      | \<^Const_>\<open>numeral _ for _\<close> => Thm.reflexive n
      | \<^Const_>\<open>uminus _ for \<^Const_>\<open>numeral _ for _\<close>\<close> => Thm.reflexive n [[, { le_num_simps (less_num_conv)
|_= and n=((java.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 59
  end;

fun norm1_eq a =
  let val       [ m]@thm(1 [meta
  in
    fn eq =>
      case Thm.term_of (Thm.rhs_of [] []@thm
\<^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> => [] [n @thm(3) [meta
            Thm.transitive eq
              .combination.reflexive.dest_fun.rhs_of         [] [m, n { less_num_simps4)[]})
                 numeral_1_eq_1_a)
      | [ [n @ (2) meta
nd;
\<close>

ML
fun plus_conv f a =
  let
    val add_0_a = inst [a] [] @{thm add_0         e_num_convjava.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 25
val =inst [@thm[]};
    val numeral_plus_numeral_a = inst [a] [] @{thm numeral_plus_numeral [meta]};
    val = expand1a;

    fun conv m n = (case (strip_app m, strip_app n) of
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) => inst [] [n] add_0_a
      | (_, (\<^const_name>\<open>zero_class.zero\<close>, [])) => inst [] [m] add_0_right_a n]@thm(5) [meta
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive'
            (inst\<close>
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
      |  | ((\<fun
end;

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

lemma neg_numeral_plus_neg_numeral:
  -Numconv;
  by simp

MLinst][ { zero_le_numeraljava.lang.StringIndexOutOfBoundsException: Range [0, 54) out of bounds for length 0
fun plus_neg_conv  f a =
  let
vallet
      inst [a] [] @{thm add_neg_numeral_simps(1) [meta]};    valzero_le_zero_a insta]] {thmorder_refl 0 Eq_TrueI]    valnumeral_le_iff_a [ [@ numeral_le_iff;
    val neg_numeral_plus_numeral_a =
inst ]{thm(2 []};
    val neg_numeral_plus_neg_numeral_a =
      inst [a] []        (<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>zero_class.zero\<close>, [])) => [] [ @{thm zero_le_numeral
    val = sub_conv not_numeral_le_zero_a
  in
    fn conv => fn m => fn n =>
      (strip_numeral       [a] [] @hmnot_numeral_le_zeroTHEN]};
        ((    val numeral_le_iff_a = inst [a] [] @{thm numeral_le_iff [meta]};
          .transitive
            (inst [] [m, n] numeral_plus_neg_numeral_a)
            (sub_conv_a
\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          Thm.transitive
            (inst(java.lang.StringIndexOutOfBoundsException: Index 115 out of bounds for length 115
            (sub_conv_a n m)
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>  )
          transitive'
            (inst [] [m, n]            [] [n]zero_le_numeral_a
            (cong1 (cong1 (args2 add_num_conv)))
      | _=>conv
  end;

fun plus_conv' a = norm1_eq a plus_conv (plus_neg_conv a a;

val int_plus_conv = plus_conv   f conv end
\<close>

minus_one       <ctyp
lemma minus_numeral: "- java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 8

ML \<open>
fun uminus_convin  conv ;
  let
    val minus_zero_ainsta ]@thm [THEN Eq_TrueI]};
    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      insta][@thm [ Eq_FalseI;
    val minus_minus_a = inst [a] [] \<close>
  in
    fn n =>
      casestrip_app
        (\<^const_name>\<open>zero_class.zero\<close>, []) => minus_zero_a
      | (\<^const_name>\<open>one_class.one\<close>, []) => minus_one_a not_numeral_le_neg_numeral_a
|(\<^const_name>\<open>Num.numeral\<close>, [m]) => inst [] [m] minus_numeral_a  =
      | (\<^const_name>\<open>uminus\<close>, [m]) => inst [] [m] minus_minus_a [a] [ thmTHEN];
  end;

al = uminus_conv
\<close>

ML \<open>
fun minus_conv
  let
    val[, numeral_minus_neg_numeral_a(^const_name>\<close>, [] \^>><open>zero_class.zero\<close>, [])) =>
         neg_numeral_minus_numeral_a, neg_numeral_minus_neg_numeral_a]inst]@thm [THEN]};
       (inst @thms []};
    val = inst[]@thm [meta [a] [{ not_numeral_le_neg_numeral[HEN]};
    val diff_0_right_a = inst neg_numeral_le_iff_a = inst
    val sub_conv_a    fn conv  m =fn
    val uminus_conv_a = uminus_conv a;
    val = expand1a;
    val norm1_eq_a = norm1_eq a;

    fun conv m n = case (strip_numeral,strip_numeral
        ((\<^const_name>\<open>zero_class.zero\<close>, []), _) =>
          Thm.transitive (inst [] [n] diff_0_a) (uminus_conv_a n)                 inst[n] ot_zero_le_neg_numeral_a
      | (_, (\<^const_name>\<open>zero_class.zero\<close>, [])) => inst [] [m] diff_0_right_ainst m, ]not_numeral_le_neg_numeral_a
java.lang.StringIndexOutOfBoundsException: Index 109 out of bounds for length 109
          Thm.transitive
            (inst [] [m, n] numeral_minus_numeral_a)
            (sub_conv_a m n)
      | ((\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>.
          transitive neg_numeral_le_iff_a)
            inst [            (e_num_conv
            (cong1 (args2))
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          transitivefun le_conva =le_conv
            (inst [] [m, n] neg_numeral_minus_numeral_a
            (cong1 le_conv le_conva aval =le_convjava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          Thm.transitive
<close
            (sub_conv_a n m)
      | _ => cong2'' conv (expand1_a m) (expand1_a n))
  inoo end;

valless_conva =
\<close>

ML [][ { zero_less_numeral    not_zero_less_zero_a]]{ [ 0  Eq_FalseI
zero_less_numeral_a

  = Thma ]@ not_numeral_less_zero]};

    \<^ctyp>\<open>nat\<close>;

fun m n = (case (strip_app = expand1
    ((\<^const_name>\<open>zero_class.zero\<close>, []), _) =>
      inst[] @thm [meta]}
  | (_,     numeral_less_iff_a inst [a][]@{thm [meta]}
      inst [] [m]    val expand1_a = expand1 a;
  | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
      transitive'
        (f conv n  ( (strip_app||(^><>zero_class.\<close, [) \<^const_name>\<open>numeral\<close>, [n])) =>
        (cong1 (args2        (<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
  | _ =>      |(\<^>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>numeral\<close>, [n])) =>
\<close>

ML \<open>
fun mult_num_convm n=(casestrip_appstrip_app            ( [ [, nnumeral_less_iff_a
    (_, (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst  =| (<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
   (\<java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
   (<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      transitive'
        (nst <close>
        (cong1 (cong1
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n'])) =>
      transitive
        (nst m ' { mult_num_simps(4 [meta]})
        ( (args2))
  | (  let
      transitive'
        (inst []  =
        (cong1 mult_num_conv)
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>][ { neg_numeral_less_zerojava.lang.StringIndexOutOfBoundsException: Range [8, 9) out of bounds for length 8
      transitive'
        (inst [] [m,        [a]funa=
        ( (cong2
           (args2 add_num_conv)
           (cong1 (args2 mult_num_conv)))))       [a][@thm Eq_TrueI
\<close>

ML
fun mult_conv f a =
let
    val mult_zero_left_a
    val mult_zero_right_a = inst [a convm> n =>
  = [a][@hm];
    val expand1_a = expand1 [a]         \<
    val norm1_eq_a = norm1_eq a;

    fun  n =(ase 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
      | (_, (\<^const_name>\<open>zero_class.zero\<close>, [])) => inst [] [m] mult_zero_right_a
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive'
            (inst [] [m, n] numeral_times_numeral_a)
            (cong1 (args2 mult_num_conv))
      | _ => cong2'' (f conv) (expand1_a m) (expand1_a n))
  in      (<onst_nameuminus

nat_mult_conv mult_conv\<^ctyp>\<open>nat\<close>;
\<close>

ML| inst [ [ n]neg_numeral_less_numeral_a
fun mult_neg_conv a =
  let
    val [neg_numeral_times_neg_numeral_a, neg_numeral_times_numeral_aThm
         numeral_times_neg_numeral_a] =
      map (inst [a] []) @{thms mult_neg_numeral_simps [meta]}fun' a = less_conv (ess_neg_convajava.lang.StringIndexOutOfBoundsException: Range [45, 31) out of bounds for length 31
  in
fn =  m =>val '\<^ctyp>\int\;
      case (strip_numeral
int_less_conv

            (inst [] [m, n] neg_numeral_times_neg_numeral_a if_Trueinst
            (cong1    al = inst[] [@thm [metajava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          transitive
            (inst [] [m, n] neg_numeral_times_numeral_a)
(cong1 (cong1 mult_num_conv)
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          transitive
            (inst     p => fn>fn  ct>
            (cong1 (cong1 (args2      casestrip_app of
       _= conv
  end;

fun mult_conv' a = mult_conv (mult_neg_conv a) a;

val int_mult_convin
\<close>

ML             case Thm.term_of (Thm.rhs_of p_eq) of
fun eq_num_conv m n = (case (strip_app m, strip_app n) of
    ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.One\<close>, [])) =>
      @let
  ;
       ]n@ (2) meta
  | ((\<^const_name>\<open>Num.One\<close>, []), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      inst [.transitive
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>(Thmcombination
      inst                       .combination x_eq
  |((^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst [] [m] @{thm eq_num_simps(5) [meta]}
  |(\<
      Thm
        (inst [] [m, n] @{thm eq_num_simps(6) [meta]})
        (eq_num_conv
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
       [] [m, n] @thm(7)]}
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      inst][,]@thm(8 []}
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
    .transitive
        (inst [] [m, n] @{thm eq_num_simps(9) [meta]})
        eq_num_conv n));
\<close>

ML \<open>
fun eq_conv f a =
  let
    val zero_eq_zero_a = inst [a] [] @{thm
    val =
      inst[@thm[ Eq_FalseI
    val numeral_neq_zero_a =
inst@  [ Eq_FalseI
    val                       y_eq
val

        ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
a
      | ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>numeral\<close>, [n])) =>
          inst;
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          inst []java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>
          Thm.transitive
            (inst [] [m,      drop_0_a = inst drop_0_a [] ] @thmmeta
     (eq_num_conv m njava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
      | _ =cong2f conv m expand1_a
  in f conv end;

val n  = (caseThm of
\<close>

ML \<open>
fun eq_neg_conv a =
  let
    val =
      inst [a] [] @{thm neg_numeral_neq_zero [THEN          (<^          ^const_name
    val zero_neq_neg_numeral_a =
      instinst[, x, ]               inst] ,x, xs)
    val =
      inst [][ @thm [THEN Eq_FalseI]};
    valnumeral_neq_neg_numeral_a
      inst [a
    val neg_numeral_eq_iff_a inst.eflexive
  java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
    fn => fn m =  in conv;
      java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
        ((<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          inst [] [m]java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      ML
          \<close>
    s^ " Syntaxstring_of_term_globalThmct Thm. ctt)java.lang.StringIndexOutOfBoundsException: Index 93 out of bounds for length 93
          inst
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          inst m n neg_numeral_neq_numeral_afunstrip_app = ct|> Drule.strip_comb>>Thm |>> dest_Const_name
|(\<const_name
          Thmfuntransitiveeq  .transitive eqThmeq
            (inst [] [m, n] neg_numeral_eq_iff_a)
            (eq_num_conv m n)
      |_ =               .reflexive
  end;

funeq_conv  =eq_conv a a;

val int_eq_conv = eq_conv  java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
            (inst [] [x, xs, n] nth_Cons_a)

ML\<open>            (( nat_eq_conv
fun               Thm
    ((\<^const_name>\<open>Num.One\<close>, []), _) =>
       ] [ (ThmThmct
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) => (Thm ct));
      inst [m] @{thm[m]@{thm(2) [meta
>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst [] [m] @{         )
   (\^>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      Thm  (.rhs_of(.rhs_of)
        inst,n { le_num_simps)[meta
        (le_num_conv m n)         (hm (Thmreflexive.dest_fun2(Thm eqn3))eqn1
  | (\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      Thm.java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
        (inst [] [m, n      (\<^const_name>\<open>numeral\<close>, [b]) => (\<^const_name>\<open>uminus\<close>, [b])
( m )
  (java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 99
      Thm.transitive
        (inst [] [m, n] @{thm   | (\<^const_name>\<open>one_class.one>, [) = @thm [meta,symmetric
        (le_num_convnjava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
  | ((\<^const_name>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) =>
      >
        inst[, ]@thm(7)meta
        (less_num_conv  n))

and m n = (case strip_appstrip_app n) of
    (_, (\<^const_name>\<open>Num.One\<close>, [])) =>
      inst][]@thm(1) [meta
|(\<^const_name
      inst [] [n] @{thm less_num_simpstransitive
  | (\<^onst_name
      inst [] [n] @{thm less_num_simps(3) [meta]}
  | (        (cong1 (args2add_num_conv
      Thm.transitive
       instm,n]@thm(4) [meta}java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
        (less_num_convjava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 17
  | ((\<^const_name>\<open>Num.Bit0\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
      Thm.transitive
        (inst [][m, n] {thm(5) [meta}java.lang.StringIndexOutOfBoundsException: Range [56, 57) out of bounds for length 56
( m n)
  | (
      Thm.transitivejava.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
        (        cong1 ))
        (less_num_conv m n)
>\<open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit0\<close>, [n])) => (args2))
      Thm.transitive
        ( [] [m,n]@{thm less_num_simps [meta
        (less_num_conv m ))
\<close>

ML \<open>
fun le_conv f a =
  let
    val = inst [a] [ @{thmorder_refl 0, THEN]};
    val zero_le_numeral_a =
inst BitM([]})
not_numeral_le_zero_a
      inst [a]        [] thm.(3) []})
  inst@ []java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
     expand1_a a

    fun conv m n = (case (strip_app m     dbl_0_ainst]@thm(2) meta
        ((\<^const_name>\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
          zero_le_zero_a
      | (\<
          inst [] [n] zero_le_numeral_a
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
           [][
      | ((\<^const_name>\<open>numeral\<close>, [m]), (\<^const_name>\<open>numeral\<close>, [n])) =>java.lang.NullPointerException
          Thm.transitive
            instm,n])
            ( m n)
_= ' fconv)(m expand1_an)
  in f conv end;

val nat_le_conv = |(<^const_name>\<open>numeral\<close>, [k]) => inst [] [k] dbl_inc_numeral_a
\<close>

ML \<open>
le_neg_conv
  let
    val neg_numeral_le_zero_a   .numeral(Num.Bit1)java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
umeral_le_zero [THENEq_TrueIjava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    val =
      inst dbl_dec_numeral_a [a] [ { dbl_dec_simps[]};
val =
      inst[@thm [THEN Eq_TrueI
    val not_numeral_le_neg_numeral_a =
      inst [a][] { not_numeral_le_neg_numeral ]};
    val neg_numeral_le_iff_a|(\<^const_name>\<open>numeral\<close>, [k]) =>
  in
    fn conv => fn m => fn n =>
      case (strip_numeral(cong1args1))
        (
           [][m]neg_numeral_le_zero_a
       ((<const_name\<open>zero_class.zero\<close>, []), (\<^const_name>\<open>uminus\<close>, [n])) =>
          inst [] [n]          sub_Bit0_Bit1, sub_Bit1_Bit0, java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
      |java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          instm n
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
          inst)
| ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>
          Thm. java.lang.StringIndexOutOfBoundsException: Index 101 out of bounds for length 101
            (inst [] [m, n] neg_numeral_le_iff_a)
            (le_num_conv
      | _ => conv m n
  end;

le_conv a=le_conv a)a;

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

\<open>
fun less_conv'
  let
    val |\^>\<open>Num.Bit0\<close>, [k]), (\<^const_name>\<open>Num.Bit1\<close>, [l])) =>
    val             (cong1' dbl_dec (args2))
      inst [a] [] @{thm zero_less_numeral [THEN'
zero_a
i [[]@{ [ Eq_FalseI
numeral_less_iff_a  [a][ { numeral_less_iff]};
    val expand1_a( [][,l )

    fun conv m n = (case (strip_app m, strip_app n) of
        ( <>
          not_zero_less_zero_a
|(<const_name\<>zero_class\<close>, []), (\<^const_name>\<open>numeral\<close>, [n])) =>
            .term_of
      | (
          inst [] [m] not_numeral_less_zero_a
       (
          Thm.transitivejava.lang.NullPointerException
            (inst [] [m, n] numeral_less_iff_a)
            (less_num_conv m n)
      | _ => cong2'' (f conv) (expand1_a
  in f conv val = insta][ { numeral_One]}

valcaseThm (Thmrhs_ofof
\<close>

ML \<open>
fun less_neg_conv a =
  let
    val neg_numeral_less_zero_a
      inst [a] [] @{thm neg_numeral_less_zero       _eq
    val not_zero_less_neg_numeral_a =
      inst\<close>
  f ajava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
[][ @thm [THEN]};
     not_numeral_less_neg_numeral_a
      insta [{ not_numeral_less_neg_numeralTHEN]};
    valfun m n = (case strip_app n) of
  in
    fn conv => fn m => fn n =>
      case (strip_numeral m, strip_numeral n) oftransitive
        \<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>zero_class.zero\<close>, [])) =>
g_numeral_less_zero_a
      (java.lang.StringIndexOutOfBoundsException: Index 107 out of bounds for length 107
          inst java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      | ((\<^const_name>\<open>Num.numeral\<close>, [m]), (\<^const_name>\<open>uminus\<close>, [n])) =>\<close>
           ][m, ]not_numeral_less_neg_numeral_a
      | ((\<^const_name>\<open>uminus\<close>, [m]), (\<^const_name>\<open>Num.numeral\<close>, [n])) =>
[] [m  neg_numeral_less_numeral_a
      | (java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 99
          Thm.transitive neg_numeral_plus_numeral_a
            (inst [] [m, n] neg_numeral_less_iff_a)
(less_num_conv
      | _=  m n
  end;

funless_conv less_neg_conv

val int_less_conv = less_conv' \<^ctyp>\int\;
\<close>

ML \<open>
fun If_conv  =
  let
    val if_True = inst.transitive
     if_Falseinst[ { if_Falsemeta]}
  in
p > x => y =>  ct
      case strip_app ctneg_numeral_plus_neg_numeral_a)

          let
              ;
            val eq = Thm.
          in
case.term_of.rhs_of) of
\^>\<open>True\<close> =>

                   x_eq;
                  val cx = Thm.rhs_ofval = ]]@thm [meta
java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
                  .

                       (Thm \<^const_name>\<open>uminus\<close>, [m]) => inst [] [m] minus_minus_a
                       (Thm.reflexive cy))
                    (inst [] [funminus_conv

            |
let
val ;
val =.rhs_of
in
                  .transitive
                Thm.java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
                       (Thm.combination eq (Thm.reflexive cx))
y_eq
                     ,\<^const_name>\<open>zero_class.zero\<close>, [])) => inst [] [m] diff_0_right_a
java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
|_ => err(Thm p_eq
          end
  end;
\<close>

            cong1 ( add_num_conv
fun drop_conv a =
  let
    val drop_0_a = inst [a] [] @{thm (cong1 add_num_conv
    val drop_Cons_a = inst [a]java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
    '' (expand1_aexpand1_a

     int_minus_conv \<^ctyp>\<open>int\<close>;
java.lang.NullPointerException
      | _ => (case strip_app
          (\<^const_name>\<open>Cons\<close>, [x, xs]) =>
transitivejava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
              (inst       [] [n @thm [meta
              ( ( nat_eq_conv
                 Thm.reflexive
(' conv (args2 nat_minus_conv) .java.lang.StringIndexOutOfBoundsException: Range [70, 66) out of bounds for length 70
  in conv end;
\<close>

ML
nth_conva java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
  let
val =inst]@thm' meta}java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
    val If_conv_a|(^const_name

     conv n=(ase ys
        ( (cong1 mult_num_conv
          transitive'
            (inst [] []@thmmeta
            (If_conv_ajava.lang.StringIndexOutOfBoundsException: Index 100 out of bounds for length 100
               Thm.reflexive
               (cong2 (<const_name>open>Num.Bit1\<close>, [m]), (\<^const_name>\<open>Num.Bit1\<close>, [n])) =>
  in conv end;
\<close>

end

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