
diff -r dd74d0a56df9 -r 12490253d025 doc-src/TutorialI/Inductive/Acc.thy
--- a/doc-src/TutorialI/Inductive/Acc.thy	Thu Nov 02 15:44:13 2000 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,78 +0,0 @@
-(*  Title:      HOL/ex/Acc.thy
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1994  University of Cambridge
-
-Inductive definition of acc(r)
-
-See Ch. Paulin-Mohring, Inductive Definitions in the System Coq.
-Research Report 92-49, LIP, ENS Lyon.  Dec 1992.
-*)
-
-header {* The accessible part of a relation *}
-
-theory Acc = Main:
-
-consts
-  acc  :: "('a \<times> 'a) set => 'a set"  -- {* accessible part *}
-
-inductive "acc r"
-  intros
-    accI [rule_format]:
-      "\<forall>y. (y, x) \<in> r --> y \<in> acc r ==> x \<in> acc r"
-
-syntax
-  termi :: "('a \<times> 'a) set => 'a set"
-translations
-  "termi r" == "acc (r^-1)"
-
-
-theorem acc_induct:
-  "[| a \<in> acc r;
-      !!x. [| x \<in> acc r;  \<forall>y. (y, x) \<in> r --> P y |] ==> P x
-  |] ==> P a"
-proof -
-  assume major: "a \<in> acc r"
-  assume hyp: "!!x. [| x \<in> acc r;  \<forall>y. (y, x) \<in> r --> P y |] ==> P x"
-  show ?thesis
-    apply (rule major [THEN acc.induct])
-    apply (rule hyp)
-     apply (rule accI)
-     apply fast
-    apply fast
-    done
-qed
-
-theorem acc_downward: "[| b \<in> acc r; (a, b) \<in> r |] ==> a \<in> acc r"
-  apply (erule acc.elims)
-  apply fast
-  done
-
-lemma acc_downwards_aux: "(b, a) \<in> r^* ==> a \<in> acc r --> b \<in> acc r"
-  apply (erule rtrancl_induct)
-   apply blast
-  apply (blast dest: acc_downward)
-  done
-
-theorem acc_downwards: "[| a \<in> acc r; (b, a) \<in> r^* |] ==> b \<in> acc r"
-  apply (blast dest: acc_downwards_aux)
-  done
-
-theorem acc_wfI: "\<forall>x. x \<in> acc r ==> wf r"
-  apply (rule wfUNIVI)
-  apply (induct_tac P x rule: acc_induct)
-   apply blast
-  apply blast
-  done
-
-theorem acc_wfD: "wf r ==> x \<in> acc r"
-  apply (erule wf_induct)
-  apply (rule accI)
-  apply blast
-  done
-
-theorem wf_acc_iff: "wf r = (\<forall>x. x \<in> acc r)"
-  apply (blast intro: acc_wfI dest: acc_wfD)
-  done
-
-end




