src/HOL/Library/Old_Recdef.thy
 author hoelzl Thu Sep 04 14:02:37 2014 +0200 (2014-09-04) changeset 58184 db1381d811ab parent 56248 67dc9549fa15 child 58825 2065f49da190 permissions -rw-r--r--
cleanup Wfrec; introduce dependent_wf/wellorder_choice
```     1 (*  Title:      HOL/Library/Old_Recdef.thy
```
```     2     Author:     Konrad Slind and Markus Wenzel, TU Muenchen
```
```     3 *)
```
```     4
```
```     5 header {* TFL: recursive function definitions *}
```
```     6
```
```     7 theory Old_Recdef
```
```     8 imports Main
```
```     9 keywords
```
```    10   "recdef" "defer_recdef" :: thy_decl and
```
```    11   "recdef_tc" :: thy_goal and
```
```    12   "permissive" "congs" "hints"
```
```    13 begin
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```    14
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```    15 subsection {* Lemmas for TFL *}
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```    16
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```    17 lemma tfl_wf_induct: "ALL R. wf R -->
```
```    18        (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))"
```
```    19 apply clarify
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```    20 apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast)
```
```    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)"
```
```    24   unfolding cut_def .
```
```    25
```
```    26 lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)"
```
```    27 apply clarify
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```    28 apply (rule cut_apply, assumption)
```
```    29 done
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```    30
```
```    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)"
```
```    33 apply clarify
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```    34 apply (erule wfrec)
```
```    35 done
```
```    36
```
```    37 lemma tfl_eq_True: "(x = True) --> x"
```
```    38   by blast
```
```    39
```
```    40 lemma tfl_rev_eq_mp: "(x = y) --> y --> x"
```
```    41   by blast
```
```    42
```
```    43 lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"
```
```    44   by blast
```
```    45
```
```    46 lemma tfl_P_imp_P_iff_True: "P ==> P = True"
```
```    47   by blast
```
```    48
```
```    49 lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"
```
```    50   by blast
```
```    51
```
```    52 lemma tfl_disj_assoc: "(a \<or> b) \<or> c == a \<or> (b \<or> c)"
```
```    53   by simp
```
```    54
```
```    55 lemma tfl_disjE: "P \<or> Q ==> P --> R ==> Q --> R ==> R"
```
```    56   by blast
```
```    57
```
```    58 lemma tfl_exE: "\<exists>x. P x ==> \<forall>x. P x --> Q ==> Q"
```
```    59   by blast
```
```    60
```
```    61 ML_file "~~/src/HOL/Tools/TFL/casesplit.ML"
```
```    62 ML_file "~~/src/HOL/Tools/TFL/utils.ML"
```
```    63 ML_file "~~/src/HOL/Tools/TFL/usyntax.ML"
```
```    64 ML_file "~~/src/HOL/Tools/TFL/dcterm.ML"
```
```    65 ML_file "~~/src/HOL/Tools/TFL/thms.ML"
```
```    66 ML_file "~~/src/HOL/Tools/TFL/rules.ML"
```
```    67 ML_file "~~/src/HOL/Tools/TFL/thry.ML"
```
```    68 ML_file "~~/src/HOL/Tools/TFL/tfl.ML"
```
```    69 ML_file "~~/src/HOL/Tools/TFL/post.ML"
```
```    70 ML_file "~~/src/HOL/Tools/recdef.ML"
```
```    71 setup Recdef.setup
```
```    72
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```    73 subsection {* Rule setup *}
```
```    74
```
```    75 lemmas [recdef_simp] =
```
```    76   inv_image_def
```
```    77   measure_def
```
```    78   lex_prod_def
```
```    79   same_fst_def
```
```    80   less_Suc_eq [THEN iffD2]
```
```    81
```
```    82 lemmas [recdef_cong] =
```
```    83   if_cong let_cong image_cong INF_cong SUP_cong bex_cong ball_cong imp_cong
```
```    84   map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong
```
```    85
```
```    86 lemmas [recdef_wf] =
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```    87   wf_trancl
```
```    88   wf_less_than
```
```    89   wf_lex_prod
```
```    90   wf_inv_image
```
```    91   wf_measure
```
```    92   wf_measures
```
```    93   wf_pred_nat
```
```    94   wf_same_fst
```
```    95   wf_empty
```
```    96
```
```    97 end
```