src/HOL/Recdef.thy
author oheimb
Tue Feb 20 18:47:27 2001 +0100 (2001-02-20)
changeset 11165 3b69feb7d053
parent 10773 0deff0197496
child 11284 981ea92a86dd
permissions -rw-r--r--
added image_cong to default congs of recdef
     1 (*  Title:      HOL/Recdef.thy
     2     ID:         $Id$
     3     Author:     Konrad Slind and Markus Wenzel, TU Muenchen
     4 
     5 TFL: recursive function definitions.
     6 *)
     7 
     8 theory Recdef = Wellfounded_Relations + Datatype
     9 files
    10   ("../TFL/utils.ML")
    11   ("../TFL/usyntax.ML")
    12   ("../TFL/dcterm.ML")
    13   ("../TFL/thms.ML")
    14   ("../TFL/rules.ML")
    15   ("../TFL/thry.ML")
    16   ("../TFL/tfl.ML")
    17   ("../TFL/post.ML")
    18   ("Tools/recdef_package.ML"):
    19 
    20 lemma tfl_some: "\\<forall>P x. P x --> P (Eps P)"
    21   by (blast intro: someI)
    22 
    23 lemma tfl_eq_True: "(x = True) --> x"
    24   by blast
    25 
    26 lemma tfl_rev_eq_mp: "(x = y) --> y --> x";
    27   by blast
    28 
    29 lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"
    30   by blast
    31 
    32 lemma tfl_P_imp_P_iff_True: "P ==> P = True"
    33   by blast
    34 
    35 lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"
    36   by blast
    37 
    38 lemma tfl_disj_assoc: "(a \\<or> b) \\<or> c == a \\<or> (b \\<or> c)"
    39   by simp
    40 
    41 lemma tfl_disjE: "P \\<or> Q ==> P --> R ==> Q --> R ==> R"
    42   by blast
    43 
    44 lemma tfl_exE: "\\<exists>x. P x ==> \\<forall>x. P x --> Q ==> Q"
    45   by blast
    46 
    47 use "../TFL/utils.ML"
    48 use "../TFL/usyntax.ML"
    49 use "../TFL/dcterm.ML"
    50 use "../TFL/thms.ML"
    51 use "../TFL/rules.ML"
    52 use "../TFL/thry.ML"
    53 use "../TFL/tfl.ML"
    54 use "../TFL/post.ML"
    55 use "Tools/recdef_package.ML"
    56 setup RecdefPackage.setup
    57 
    58 lemmas [recdef_simp] =
    59   inv_image_def
    60   measure_def
    61   lex_prod_def
    62   less_Suc_eq [THEN iffD2]
    63 
    64 lemmas [recdef_cong] = if_cong image_cong
    65 
    66 lemma let_cong [recdef_cong]:
    67     "M = N ==> (!!x. x = N ==> f x = g x) ==> Let M f = Let N g"
    68   by (unfold Let_def) blast
    69 
    70 lemmas [recdef_wf] =
    71   wf_trancl
    72   wf_less_than
    73   wf_lex_prod
    74   wf_inv_image
    75   wf_measure
    76   wf_pred_nat
    77   wf_same_fst
    78   wf_empty
    79 
    80 end