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  References ,,and
the paper

    Transfinite -  forLambdaFree Higher- Terms
      Becker   Blanchette  Waldmann, DanielWand

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 reportThecorresponding 
paper is given in square brackets when   * Lemma 2 corresponds to "lemma wf_bounded_if_t      to"wf_bounded.

 "  beprocessed  follows:

    isabelle jedit Lambda_Free_KBOs.thy

The main files are

    Lambda_Free_KBO_Std.thy
    Lambda_Free_TKBO_Coefs.thy

Section 2 ("Extension Orders") is formalized in
"../Lambda_Free_RPO/  * Definition 5 corresponds to Definition5corresponds to  "

*Definition correspondstodjava.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 54
  *2correspondsto" ".
  * Lemma 3 correspondsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  * Definition 4"java.lang.StringIndexOutOfBoundsException: Range [24, 20) out of bounds for length 26
  5java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 52
   to" "
  * java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 0

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

Section 4.2 ("The Applicative KBO") is formalizedLambda_Free_KBO_Std"
"Lambda_Free_KBO_App.thy"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  * Definition 10 corresponds to "inductive gt".

Section 4.3 ("The Graceful Higher-Order java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
"java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 28

  * Definition 11 corresponds to "inductive gt".

     "emmawt_ge_<>\<^ubh.
"    211  to lemma  

  * Definition 13 corresponds to*Lemma 212   " wt_App_fun_<\^>h,

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 inL.thy:

  * Definition 15 corresponds to  * Lemma22correspondsto

Section 5   *     "lemmagt_sub_arg

  * Theorem 18 [16] corresponds to "   Lemma 25 corresponds  "emma "
mma ".
  * Lemma 20 corresponds to "lemma wt_ge_\<epsilon>\<^   Theorem 27 [9]corresponds  t ".
   to lemmawt_App_ge_fun and
    "lemma wt_App_ge_arg".
  * (   "lemma \delta><sub>"
    "lemma     22 java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 62
    \<>\^subhimp_\<elta\^h_eq_\<epsilon>\^ubhjava.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74
* 22corresponds
    "lemma not_extf_gt_nil_singleton_if_ Lemma 33 25  corresponds 
*Lemma java.lang.StringIndexOutOfBoundsException: Range [27, 24) out of bounds for length 47
java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 54
  * Lemma 25 corresponds to "lemma gt_sub_fun".
  * Theorem 26 [18] corresponds to "theorem gt_proper_sub".
  * Theorem 27 [19] corresponds to "theorem gt_compat_fun_strong".
  * Theorem 28 [20] corresponds to "theorem gt_compat_arg_weak".
  * Definition 29 [21] corresponds to "primrec subst_zpassign".
  * Lemma 30 [22] corresponds to "lemma legal_subst_zpassign".
  * Theorem 31 [23] corresponds to "theorem gt_subst".
  * Theorem 32 [24] corresponds to "theorem gt_total_ground".
  * Lemma 33 [25] partly corresponds to
    "lemma sum_coefs_ge_num_args_if_\<delta>\<^sub>h_eq_0".
  * Theorem 34 [26] corresponds to "theorem gt_wf".