author  krauss 
Mon, 05 Jun 2006 14:26:07 +0200  
changeset 19770  be5c23ebe1eb 
parent 19564  d3e2f532459a 
child 19934  8190655ea2d4 
permissions  rwrr 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

1 
theory FunDef 
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

2 
imports Accessible_Part Datatype Recdef 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

3 
uses 
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

4 
("Tools/function_package/sum_tools.ML") 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

5 
("Tools/function_package/fundef_common.ML") 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

6 
("Tools/function_package/fundef_lib.ML") 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

7 
("Tools/function_package/context_tree.ML") 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

8 
("Tools/function_package/fundef_prep.ML") 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

9 
("Tools/function_package/fundef_proof.ML") 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

10 
("Tools/function_package/termination.ML") 
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

11 
("Tools/function_package/mutual.ML") 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

12 
("Tools/function_package/fundef_package.ML") 
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

13 
("Tools/function_package/fundef_datatype.ML") 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

14 
("Tools/function_package/auto_term.ML") 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

15 
begin 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

16 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

17 
lemma fundef_ex1_existence: 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

18 
assumes f_def: "\<And>x. f x \<equiv> THE y. (x,y)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

19 
assumes ex1: "\<exists>!y. (x,y)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

20 
shows "(x, f x)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

21 
by (simp only:f_def, rule theI', rule ex1) 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

22 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

23 
lemma fundef_ex1_uniqueness: 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

24 
assumes f_def: "\<And>x. f x \<equiv> THE y. (x,y)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

25 
assumes ex1: "\<exists>!y. (x,y)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

26 
assumes elm: "(x, h x)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

27 
shows "h x = f x" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

28 
by (simp only:f_def, rule the1_equality[symmetric], rule ex1, rule elm) 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

29 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

30 
lemma fundef_ex1_iff: 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

31 
assumes f_def: "\<And>x. f x \<equiv> THE y. (x,y)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

32 
assumes ex1: "\<exists>!y. (x,y)\<in>G" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

33 
shows "((x, y)\<in>G) = (f x = y)" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

34 
apply (auto simp:ex1 f_def the1_equality) 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

35 
by (rule theI', rule ex1) 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

36 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

37 
lemma True_implies: "(True \<Longrightarrow> PROP P) \<equiv> PROP P" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

38 
by simp 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

39 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

40 

19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

41 
subsection {* Projections *} 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

42 
consts 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

43 
lpg::"(('a + 'b) * 'a) set" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

44 
rpg::"(('a + 'b) * 'b) set" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

45 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

46 
inductive lpg 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

47 
intros 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

48 
"(Inl x, x) : lpg" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

49 
inductive rpg 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

50 
intros 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

51 
"(Inr y, y) : rpg" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

52 
definition 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

53 
"lproj x = (THE y. (x,y) : lpg)" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

54 
"rproj x = (THE y. (x,y) : rpg)" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

55 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

56 
lemma lproj_inl: 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

57 
"lproj (Inl x) = x" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

58 
by (auto simp:lproj_def intro: the_equality lpg.intros elim: lpg.cases) 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

59 
lemma rproj_inr: 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

60 
"rproj (Inr x) = x" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

61 
by (auto simp:rproj_def intro: the_equality rpg.intros elim: rpg.cases) 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

62 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

63 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

64 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

65 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

66 
use "Tools/function_package/sum_tools.ML" 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

67 
use "Tools/function_package/fundef_common.ML" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

68 
use "Tools/function_package/fundef_lib.ML" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

69 
use "Tools/function_package/context_tree.ML" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

70 
use "Tools/function_package/fundef_prep.ML" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

71 
use "Tools/function_package/fundef_proof.ML" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

72 
use "Tools/function_package/termination.ML" 
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

73 
use "Tools/function_package/mutual.ML" 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

74 
use "Tools/function_package/fundef_package.ML" 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

75 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

76 
setup FundefPackage.setup 
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

77 

19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

78 
use "Tools/function_package/fundef_datatype.ML" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

79 
setup FundefDatatype.setup 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

80 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

81 
use "Tools/function_package/auto_term.ML" 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

82 
setup FundefAutoTerm.setup 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

83 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

84 

be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

85 
lemmas [fundef_cong] = 
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
19564
diff
changeset

86 
let_cong if_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong 
19564
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

87 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

88 

d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
parents:
diff
changeset

89 
end 