src/HOL/Library/Old_Recdef.thy
author wenzelm
Wed, 08 Mar 2017 10:50:59 +0100
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tuned proofs;
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(*  Title:      HOL/Library/Old_Recdef.thy
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    Author:     Konrad Slind and Markus Wenzel, TU Muenchen
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*)
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section \<open>TFL: recursive function definitions\<close>
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theory Old_Recdef
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imports Main
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keywords
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  "recdef" :: thy_decl and
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  "permissive" "congs" "hints"
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begin
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subsection \<open>Lemmas for TFL\<close>
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lemma tfl_wf_induct: "ALL R. wf R -->
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       (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))"
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apply clarify
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apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast)
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done
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lemma tfl_cut_def: "cut f r x \<equiv> (\<lambda>y. if (y,x) \<in> r then f y else undefined)"
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  unfolding cut_def .
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lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)"
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apply clarify
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apply (rule cut_apply, assumption)
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done
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lemma tfl_wfrec:
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     "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)"
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apply clarify
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apply (erule wfrec)
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done
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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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ML_file "old_recdef.ML"
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subsection \<open>Rule setup\<close>
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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 let_cong image_cong INF_cong SUP_cong bex_cong ball_cong imp_cong
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  map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong
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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_measures
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  wf_pred_nat
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  wf_same_fst
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  wf_empty
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end