--- a/ex/InSort.ML Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,46 +0,0 @@
-(* Title: HOL/ex/insort.ML
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 1994 TU Muenchen
-
-Correctness proof of insertion sort.
-*)
-
-val insort_ss = sorting_ss addsimps
- [InSort.ins_Nil,InSort.ins_Cons,InSort.insort_Nil,InSort.insort_Cons];
-
-goalw InSort.thy [Sorting.total_def]
- "!!f. [| total(f); ~f(x,y) |] ==> f(y,x)";
-by(fast_tac HOL_cs 1);
-qed "totalD";
-
-goalw InSort.thy [Sorting.transf_def]
- "!!f. [| transf(f); f(b,a) |] ==> !x. f(a,x) --> f(b,x)";
-by(fast_tac HOL_cs 1);
-qed "transfD";
-
-goal InSort.thy "list_all(p,ins(f,x,xs)) = (list_all(p,xs) & p(x))";
-by(list.induct_tac "xs" 1);
-by(asm_simp_tac insort_ss 1);
-by(asm_simp_tac (insort_ss setloop (split_tac [expand_if])) 1);
-by(fast_tac HOL_cs 1);
-val insort_ss = insort_ss addsimps [result()];
-
-goal InSort.thy "(!x. p(x) --> q(x)) --> list_all(p,xs) --> list_all(q,xs)";
-by(list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac (insort_ss setloop (split_tac [expand_if]))));
-qed "list_all_imp";
-
-val prems = goal InSort.thy
- "[| total(f); transf(f) |] ==> sorted(f,ins(f,x,xs)) = sorted(f,xs)";
-by(list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac (insort_ss setloop (split_tac [expand_if]))));
-by(cut_facts_tac prems 1);
-by(cut_inst_tac [("p","f(a)"),("q","f(x)")] list_all_imp 1);
-by(fast_tac (HOL_cs addDs [totalD,transfD]) 1);
-val insort_ss = insort_ss addsimps [result()];
-
-goal InSort.thy "!!f. [| total(f); transf(f) |] ==> sorted(f,insort(f,xs))";
-by(list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac insort_ss));
-result();