src/HOL/ex/Sorting.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/Sorting.ML	Wed Mar 22 12:42:34 1995 +0100
@@ -0,0 +1,26 @@
+(*  Title: 	HOL/ex/sorting.ML
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+Some general lemmas
+*)
+
+val sorting_ss = list_ss addsimps
+      [Sorting.mset_Nil,Sorting.mset_Cons,
+       Sorting.sorted_Nil,Sorting.sorted_Cons,
+       Sorting.sorted1_Nil,Sorting.sorted1_One,Sorting.sorted1_Cons];
+
+goal Sorting.thy "!x.mset (xs@ys) x = mset xs x + mset ys x";
+by(list.induct_tac "xs" 1);
+by(ALLGOALS(asm_simp_tac (sorting_ss setloop (split_tac [expand_if]))));
+qed "mset_app_distr";
+
+goal Sorting.thy "!x. mset [x:xs. ~p(x)] x + mset [x:xs.p(x)] x = \
+\                     mset xs x";
+by(list.induct_tac "xs" 1);
+by(ALLGOALS(asm_simp_tac (sorting_ss setloop (split_tac [expand_if]))));
+qed "mset_compl_add";
+
+val sorting_ss = sorting_ss addsimps
+      [mset_app_distr, mset_compl_add];