src/HOL/Library/Old_Recdef.thy
 author wenzelm Fri Jun 19 19:13:15 2015 +0200 (2015-06-19) changeset 60520 09fc5eaa21ce parent 60500 903bb1495239 child 60523 be2d9f5ddc76 permissions -rw-r--r--
moved sources;
```     1 (*  Title:      HOL/Library/Old_Recdef.thy
```
```     2     Author:     Konrad Slind and Markus Wenzel, TU Muenchen
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```     3 *)
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```     4
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```     5 section \<open>TFL: recursive function definitions\<close>
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```     6
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```     7 theory Old_Recdef
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```     8 imports Main
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```     9 keywords
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```    10   "recdef" "defer_recdef" :: thy_decl and
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```    11   "recdef_tc" :: thy_goal and
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```    12   "permissive" "congs" "hints"
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```    13 begin
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```    14
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```    15 subsection \<open>Lemmas for TFL\<close>
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```    16
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```    17 lemma tfl_wf_induct: "ALL R. wf R -->
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```    18        (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))"
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```    19 apply clarify
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```    20 apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast)
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```    21 done
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```    22
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```    23 lemma tfl_cut_def: "cut f r x \<equiv> (\<lambda>y. if (y,x) \<in> r then f y else undefined)"
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```    24   unfolding cut_def .
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```    25
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```    26 lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)"
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```    27 apply clarify
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```    28 apply (rule cut_apply, assumption)
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```    29 done
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```    30
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```    31 lemma tfl_wfrec:
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```    32      "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)"
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```    33 apply clarify
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```    34 apply (erule wfrec)
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```    35 done
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```    36
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```    37 lemma tfl_eq_True: "(x = True) --> x"
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```    38   by blast
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```    39
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```    40 lemma tfl_rev_eq_mp: "(x = y) --> y --> x"
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```    41   by blast
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```    42
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```    43 lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"
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```    44   by blast
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```    45
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```    46 lemma tfl_P_imp_P_iff_True: "P ==> P = True"
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```    47   by blast
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```    48
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```    49 lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"
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```    50   by blast
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```    51
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```    52 lemma tfl_disj_assoc: "(a \<or> b) \<or> c == a \<or> (b \<or> c)"
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```    53   by simp
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```    54
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```    55 lemma tfl_disjE: "P \<or> Q ==> P --> R ==> Q --> R ==> R"
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```    56   by blast
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```    57
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```    58 lemma tfl_exE: "\<exists>x. P x ==> \<forall>x. P x --> Q ==> Q"
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```    59   by blast
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```    60
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```    61 ML_file "old_recdef.ML"
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```    62
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```    63
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```    64 subsection \<open>Rule setup\<close>
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```    65
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```    66 lemmas [recdef_simp] =
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```    67   inv_image_def
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```    68   measure_def
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```    69   lex_prod_def
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```    70   same_fst_def
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```    71   less_Suc_eq [THEN iffD2]
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```    72
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```    73 lemmas [recdef_cong] =
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```    74   if_cong let_cong image_cong INF_cong SUP_cong bex_cong ball_cong imp_cong
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```    75   map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong
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```    76
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```    77 lemmas [recdef_wf] =
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```    78   wf_trancl
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```    79   wf_less_than
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```    80   wf_lex_prod
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```    81   wf_inv_image
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```    82   wf_measure
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```    83   wf_measures
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```    84   wf_pred_nat
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```    85   wf_same_fst
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```    86   wf_empty
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```    87
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```    88 end
```