src/HOL/Recdef.thy
author berghofe
Wed Feb 07 17:30:53 2007 +0100 (2007-02-07)
changeset 22264 6a65e9b2ae05
parent 19770 be5c23ebe1eb
child 22399 80395c2c40cc
permissions -rw-r--r--
Theorems for converting between wf and wfP are now declared
as hints.
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(*  Title:      HOL/Recdef.thy
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    ID:         $Id$
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    Author:     Konrad Slind and Markus Wenzel, TU Muenchen
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*)
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header {* TFL: recursive function definitions *}
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theory Recdef
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imports Wellfounded_Relations
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uses
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  ("../TFL/casesplit.ML")
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  ("../TFL/utils.ML")
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  ("../TFL/usyntax.ML")
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  ("../TFL/dcterm.ML")
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  ("../TFL/thms.ML")
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  ("../TFL/rules.ML")
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  ("../TFL/thry.ML")
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  ("../TFL/tfl.ML")
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  ("../TFL/post.ML")
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  ("Tools/recdef_package.ML")
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begin
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lemma tfl_eq_True: "(x = True) --> x"
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  by blast
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lemma tfl_rev_eq_mp: "(x = y) --> y --> x";
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  by blast
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lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"
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  by blast
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lemma tfl_P_imp_P_iff_True: "P ==> P = True"
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  by blast
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lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"
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  by blast
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lemma tfl_disj_assoc: "(a \<or> b) \<or> c == a \<or> (b \<or> c)"
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  by simp
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lemma tfl_disjE: "P \<or> Q ==> P --> R ==> Q --> R ==> R"
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  by blast
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lemma tfl_exE: "\<exists>x. P x ==> \<forall>x. P x --> Q ==> Q"
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  by blast
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use "../TFL/casesplit.ML"
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use "../TFL/utils.ML"
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use "../TFL/usyntax.ML"
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use "../TFL/dcterm.ML"
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use "../TFL/thms.ML"
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use "../TFL/rules.ML"
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use "../TFL/thry.ML"
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use "../TFL/tfl.ML"
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use "../TFL/post.ML"
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use "Tools/recdef_package.ML"
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setup RecdefPackage.setup
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lemmas [recdef_simp] =
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  inv_image_def
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  measure_def
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  lex_prod_def
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  same_fst_def
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  less_Suc_eq [THEN iffD2]
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lemmas [recdef_cong] = 
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  if_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong
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lemma let_cong [recdef_cong]:
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    "M = N ==> (!!x. x = N ==> f x = g x) ==> Let M f = Let N g"
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  by (unfold Let_def) blast
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lemmas [recdef_wf] =
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  wf_trancl
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  wf_less_than
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  wf_lex_prod
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  wf_inv_image
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  wf_measure
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  wf_pred_nat
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  wf_same_fst
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  wf_empty
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  wf_implies_wfP
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  wfP_implies_wf
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(* The following should really go into Datatype or Finite_Set, but
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each one lacks the other theory as a parent . . . *)
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lemma insert_None_conv_UNIV: "insert None (range Some) = UNIV"
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by (rule set_ext, case_tac x, auto)
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instance option :: (finite) finite
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proof
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  have "finite (UNIV :: 'a set)" by (rule finite)
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  hence "finite (insert None (Some ` (UNIV :: 'a set)))" by simp
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  also have "insert None (Some ` (UNIV :: 'a set)) = UNIV"
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    by (rule insert_None_conv_UNIV)
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  finally show "finite (UNIV :: 'a option set)" .
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qed
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end