author | wenzelm |
Thu, 05 Nov 2015 10:39:49 +0100 | |
changeset 61585 | a9599d3d7610 |
parent 60523 | be2d9f5ddc76 |
child 67091 | 1393c2340eec |
permissions | -rw-r--r-- |
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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 |