src/HOL/Library/Old_Recdef.thy
 author kuncar Fri Dec 09 18:07:04 2011 +0100 (2011-12-09) changeset 45802 b16f976db515 parent 44014 88bd7d74a2c1 child 46942 f5c2d66faa04 permissions -rw-r--r--
Quotient_Info stores only relation maps
1 (*  Title:      HOL/Library/Old_Recdef.thy
2     Author:     Konrad Slind and Markus Wenzel, TU Muenchen
3 *)
5 header {* TFL: recursive function definitions *}
7 theory Old_Recdef
8 imports Wfrec
9 uses
10   ("~~/src/HOL/Tools/TFL/casesplit.ML")
11   ("~~/src/HOL/Tools/TFL/utils.ML")
12   ("~~/src/HOL/Tools/TFL/usyntax.ML")
13   ("~~/src/HOL/Tools/TFL/dcterm.ML")
14   ("~~/src/HOL/Tools/TFL/thms.ML")
15   ("~~/src/HOL/Tools/TFL/rules.ML")
16   ("~~/src/HOL/Tools/TFL/thry.ML")
17   ("~~/src/HOL/Tools/TFL/tfl.ML")
18   ("~~/src/HOL/Tools/TFL/post.ML")
19   ("~~/src/HOL/Tools/recdef.ML")
20 begin
22 subsection {* Lemmas for TFL *}
24 lemma tfl_wf_induct: "ALL R. wf R -->
25        (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))"
26 apply clarify
27 apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast)
28 done
30 lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)"
31 apply clarify
32 apply (rule cut_apply, assumption)
33 done
35 lemma tfl_wfrec:
36      "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)"
37 apply clarify
38 apply (erule wfrec)
39 done
41 lemma tfl_eq_True: "(x = True) --> x"
42   by blast
44 lemma tfl_rev_eq_mp: "(x = y) --> y --> x";
45   by blast
47 lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"
48   by blast
50 lemma tfl_P_imp_P_iff_True: "P ==> P = True"
51   by blast
53 lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"
54   by blast
56 lemma tfl_disj_assoc: "(a \<or> b) \<or> c == a \<or> (b \<or> c)"
57   by simp
59 lemma tfl_disjE: "P \<or> Q ==> P --> R ==> Q --> R ==> R"
60   by blast
62 lemma tfl_exE: "\<exists>x. P x ==> \<forall>x. P x --> Q ==> Q"
63   by blast
65 use "~~/src/HOL/Tools/TFL/casesplit.ML"
66 use "~~/src/HOL/Tools/TFL/utils.ML"
67 use "~~/src/HOL/Tools/TFL/usyntax.ML"
68 use "~~/src/HOL/Tools/TFL/dcterm.ML"
69 use "~~/src/HOL/Tools/TFL/thms.ML"
70 use "~~/src/HOL/Tools/TFL/rules.ML"
71 use "~~/src/HOL/Tools/TFL/thry.ML"
72 use "~~/src/HOL/Tools/TFL/tfl.ML"
73 use "~~/src/HOL/Tools/TFL/post.ML"
74 use "~~/src/HOL/Tools/recdef.ML"
75 setup Recdef.setup
77 subsection {* Rule setup *}
79 lemmas [recdef_simp] =
80   inv_image_def
81   measure_def
82   lex_prod_def
83   same_fst_def
84   less_Suc_eq [THEN iffD2]
86 lemmas [recdef_cong] =
87   if_cong let_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong
88   map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong
90 lemmas [recdef_wf] =
91   wf_trancl
92   wf_less_than
93   wf_lex_prod
94   wf_inv_image
95   wf_measure
96   wf_measures
97   wf_pred_nat
98   wf_same_fst
99   wf_empty
101 end