src/HOL/ex/Recdefs.ML
 changeset 5124 1ce3cccfacdb child 5518 654ead0ba4f7
```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/Recdefs.ML	Fri Jul 03 17:35:39 1998 +0200
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+(*  Title:      HOL/ex/Recdefs.ML
+    ID:         \$Id\$
+    Author:     Konrad Lawrence C Paulson
+    Copyright   1997  University of Cambridge
+
+A few proofs to demonstrate the functions defined in Recdefs.thy
+Lemma statements from Konrad Slind's Web site
+*)
+
+
+Goal "(x mem qsort (ord,l)) = (x mem l)";
+by (res_inst_tac [("u","ord"),("v","l")] qsort.induct 1);
+by (ALLGOALS Asm_simp_tac);
+by (Blast_tac 1);
+qed "qsort_mem_stable";
+
+
+(** The silly g function: example of nested recursion **)
+
+
+Goal "g x < Suc x";
+by (res_inst_tac [("u","x")] g.induct 1);
+by Auto_tac;
+by (trans_tac 1);
+qed "g_terminates";
+
+Goal "g x = 0";
+by (res_inst_tac [("u","x")] g.induct 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [g_terminates])));
+qed "g_zero";
+
+(*** the contrived `mapf' ***)
+
+(* proving the termination condition: *)
+val [tc] = mapf.tcs;
+goalw_cterm [] (cterm_of (sign_of thy) (HOLogic.mk_Trueprop tc));
+by (rtac allI 1);
+by (case_tac "n=0" 1);
+by (ALLGOALS Asm_simp_tac);
+val lemma = result();
+
+(* removing the termination condition from the generated thms: *)
+val [mapf_0,mapf_Suc] = mapf.rules;
+val mapf_Suc = lemma RS mapf_Suc;
+
+val mapf_induct = lemma RS mapf.induct;```