--- a/src/HOL/MetisExamples/TransClosure.thy Tue Oct 20 19:37:09 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,62 +0,0 @@
-(* Title: HOL/MetisTest/TransClosure.thy
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
-
-Testing the metis method
-*)
-
-theory TransClosure
-imports Main
-begin
-
-types addr = nat
-
-datatype val
- = Unit -- "dummy result value of void expressions"
- | Null -- "null reference"
- | Bool bool -- "Boolean value"
- | Intg int -- "integer value"
- | Addr addr -- "addresses of objects in the heap"
-
-consts R::"(addr \<times> addr) set"
-
-consts f:: "addr \<Rightarrow> val"
-
-declare [[ atp_problem_prefix = "TransClosure__test" ]]
-lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
- \<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
-by (metis Transitive_Closure.rtrancl_into_rtrancl converse_rtranclE trancl_reflcl)
-
-lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
- \<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
-proof (neg_clausify)
-assume 0: "f c = Intg x"
-assume 1: "(a, b) \<in> R\<^sup>*"
-assume 2: "(b, c) \<in> R\<^sup>*"
-assume 3: "f b \<noteq> Intg x"
-assume 4: "\<And>A. (b, A) \<notin> R \<or> (a, A) \<notin> R\<^sup>*"
-have 5: "b = c \<or> b \<in> Domain R"
- by (metis Not_Domain_rtrancl 2)
-have 6: "\<And>X1. (a, X1) \<in> R\<^sup>* \<or> (b, X1) \<notin> R"
- by (metis Transitive_Closure.rtrancl_into_rtrancl 1)
-have 7: "\<And>X1. (b, X1) \<notin> R"
- by (metis 6 4)
-have 8: "b \<notin> Domain R"
- by (metis 7 DomainE)
-have 9: "c = b"
- by (metis 5 8)
-have 10: "f b = Intg x"
- by (metis 0 9)
-show "False"
- by (metis 10 3)
-qed
-
-declare [[ atp_problem_prefix = "TransClosure__test_simpler" ]]
-lemma "\<lbrakk> f c = Intg x; \<forall> y. f b = Intg y \<longrightarrow> y \<noteq> x; (a,b) \<in> R\<^sup>*; (b,c) \<in> R\<^sup>* \<rbrakk>
- \<Longrightarrow> \<exists> c. (b,c) \<in> R \<and> (a,c) \<in> R\<^sup>*"
-apply (erule_tac x="b" in converse_rtranclE)
-apply (metis rel_pow_0_E rel_pow_0_I)
-apply (metis DomainE Domain_iff Transitive_Closure.rtrancl_into_rtrancl)
-done
-
-end