author | wenzelm |
Fri, 26 Oct 2001 23:58:21 +0200 | |
changeset 11952 | b10f1e8862f4 |
parent 11825 | ef7d619e2c88 |
child 11990 | c1daefc08eff |
permissions | -rw-r--r-- |
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(* Title: HOL/Inductive.thy |
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ID: $Id$ |
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Author: Markus Wenzel, TU Muenchen |
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License: GPL (GNU GENERAL PUBLIC LICENSE) |
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*) |
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header {* Support for inductive sets and types *} |
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a5e0289dd56c
Inductive definitions are now introduced earlier in the theory hierarchy.
berghofe
parents:
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changeset
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theory Inductive = Gfp + Sum_Type + Relation |
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files |
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("Tools/inductive_package.ML") |
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("Tools/datatype_aux.ML") |
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("Tools/datatype_prop.ML") |
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("Tools/datatype_rep_proofs.ML") |
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("Tools/datatype_abs_proofs.ML") |
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("Tools/datatype_package.ML") |
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("Tools/primrec_package.ML"): |
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subsection {* Inductive sets *} |
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text {* Inversion of injective functions. *} |
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constdefs |
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myinv :: "('a => 'b) => ('b => 'a)" |
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"myinv (f :: 'a => 'b) == \<lambda>y. THE x. f x = y" |
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lemma myinv_f_f: "inj f ==> myinv f (f x) = x" |
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proof - |
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assume "inj f" |
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hence "(THE x'. f x' = f x) = (THE x'. x' = x)" |
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by (simp only: inj_eq) |
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also have "... = x" by (rule the_eq_trivial) |
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finally show ?thesis by (unfold myinv_def) |
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qed |
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lemma f_myinv_f: "inj f ==> y \<in> range f ==> f (myinv f y) = y" |
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proof (unfold myinv_def) |
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assume inj: "inj f" |
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assume "y \<in> range f" |
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then obtain x where "y = f x" .. |
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hence x: "f x = y" .. |
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thus "f (THE x. f x = y) = y" |
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proof (rule theI) |
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fix x' assume "f x' = y" |
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with x have "f x' = f x" by simp |
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with inj show "x' = x" by (rule injD) |
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qed |
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qed |
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hide const myinv |
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text {* Package setup. *} |
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use "Tools/inductive_package.ML" |
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setup InductivePackage.setup |
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theorems basic_monos [mono] = |
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subset_refl imp_refl disj_mono conj_mono ex_mono all_mono if_def2 |
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Collect_mono in_mono vimage_mono |
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imp_conv_disj not_not de_Morgan_disj de_Morgan_conj |
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not_all not_ex |
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Ball_def Bex_def |
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inductive_rulify2 |
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subsubsection {* Inductive datatypes and primitive recursion *} |
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text {* Package setup. *} |
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use "Tools/datatype_aux.ML" |
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use "Tools/datatype_prop.ML" |
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use "Tools/datatype_rep_proofs.ML" |
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use "Tools/datatype_abs_proofs.ML" |
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use "Tools/datatype_package.ML" |
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setup DatatypePackage.setup |
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use "Tools/primrec_package.ML" |
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setup PrimrecPackage.setup |
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end |