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
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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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TFL: recursive function definitions.
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*)
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theory Recdef = Wellfounded_Relations + Datatype
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files
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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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lemma tfl_some: "\\<forall>P x. P x --> P (Eps P)"
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  by (blast intro: someI)
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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/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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  less_Suc_eq [THEN iffD2]
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lemmas [recdef_cong] = if_cong image_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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end