header {* TFL: recursive function definitions *}

theory Old_Recdef

imports Wfrec

keywords

"recdef" "defer_recdef" :: thy_decl and

"recdef_tc" :: thy_goal and

"permissive" "congs" "hints"

begin

subsection {* Lemmas for TFL *}

lemma tfl_wf_induct: "ALL R. wf R -->

(ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))"

apply clarify

apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast)

done

lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)"

apply clarify

apply (rule cut_apply, assumption)

done

lemma tfl_wfrec:

"ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)"

apply clarify

apply (erule wfrec)

done

lemma tfl_eq_True: "(x = True) --> x"

by blast

lemma tfl_rev_eq_mp: "(x = y) --> y --> x"

by blast

lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"

by blast

lemma tfl_P_imp_P_iff_True: "P ==> P = True"

by blast

lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"

by blast

lemma tfl_disj_assoc: "(a ∨ b) ∨ c == a ∨ (b ∨ c)"

by simp

lemma tfl_disjE: "P ∨ Q ==> P --> R ==> Q --> R ==> R"

by blast

lemma tfl_exE: "∃x. P x ==> ∀x. P x --> Q ==> Q"

by blast

ML_file "~~/src/HOL/Tools/TFL/casesplit.ML"

ML_file "~~/src/HOL/Tools/TFL/utils.ML"

ML_file "~~/src/HOL/Tools/TFL/usyntax.ML"

ML_file "~~/src/HOL/Tools/TFL/dcterm.ML"

ML_file "~~/src/HOL/Tools/TFL/thms.ML"

ML_file "~~/src/HOL/Tools/TFL/rules.ML"

ML_file "~~/src/HOL/Tools/TFL/thry.ML"

ML_file "~~/src/HOL/Tools/TFL/tfl.ML"

ML_file "~~/src/HOL/Tools/TFL/post.ML"

ML_file "~~/src/HOL/Tools/recdef.ML"

setup Recdef.setup

subsection {* Rule setup *}

lemmas [recdef_simp] =

inv_image_def

measure_def

lex_prod_def

same_fst_def

less_Suc_eq [THEN iffD2]

lemmas [recdef_cong] =

if_cong let_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong

map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong

lemmas [recdef_wf] =

wf_trancl

wf_less_than

wf_lex_prod

wf_inv_image

wf_measure

wf_measures

wf_pred_nat

wf_same_fst

wf_empty

end