diff -r f04b33ce250f -r a4dc62a46ee4 List.ML
--- a/List.ML	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,157 +0,0 @@
-(*  Title: 	HOL/List
-    ID:         $Id$
-    Author: 	Tobias Nipkow
-    Copyright   1994 TU Muenchen
-
-List lemmas
-*)
-
-open List;
-
-val [Nil_not_Cons,Cons_not_Nil] = list.distinct;
-
-bind_thm("Cons_neq_Nil", Cons_not_Nil RS notE);
-bind_thm("Nil_neq_Cons", sym RS Cons_neq_Nil);
-
-bind_thm("Cons_inject", (hd list.inject) RS iffD1 RS conjE);
-
-val list_ss = HOL_ss addsimps list.simps;
-
-goal List.thy "!x. xs ~= x#xs";
-by (list.induct_tac "xs" 1);
-by (ALLGOALS (asm_simp_tac list_ss));
-qed "not_Cons_self";
-
-goal List.thy "(xs ~= []) = (? y ys. xs = y#ys)";
-by (list.induct_tac "xs" 1);
-by(simp_tac list_ss 1);
-by(asm_simp_tac list_ss 1);
-by(REPEAT(resolve_tac [exI,refl,conjI] 1));
-qed "neq_Nil_conv";
-
-val list_ss = arith_ss addsimps list.simps @
-  [null_Nil, null_Cons, hd_Cons, tl_Cons, ttl_Nil, ttl_Cons,
-   mem_Nil, mem_Cons,
-   append_Nil, append_Cons,
-   map_Nil, map_Cons,
-   flat_Nil, flat_Cons,
-   list_all_Nil, list_all_Cons,
-   filter_Nil, filter_Cons,
-   foldl_Nil, foldl_Cons,
-   length_Nil, length_Cons];
-
-
-(** @ - append **)
-
-goal List.thy "(xs@ys)@zs = xs@(ys@zs)";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed "append_assoc";
-
-goal List.thy "xs @ [] = xs";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed "append_Nil2";
-
-goal List.thy "(xs@ys = []) = (xs=[] & ys=[])";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed "append_is_Nil";
-
-goal List.thy "(xs @ ys = xs @ zs) = (ys=zs)";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed "same_append_eq";
-
-
-(** mem **)
-
-goal List.thy "x mem (xs@ys) = (x mem xs | x mem ys)";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac (list_ss setloop (split_tac [expand_if]))));
-qed "mem_append";
-
-goal List.thy "x mem [x:xs.P(x)] = (x mem xs & P(x))";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac (list_ss setloop (split_tac [expand_if]))));
-qed "mem_filter";
-
-(** list_all **)
-
-goal List.thy "(Alls x:xs.True) = True";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed "list_all_True";
-
-goal List.thy "list_all(p,xs@ys) = (list_all(p,xs) & list_all(p,ys))";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed "list_all_conj";
-
-goal List.thy "(Alls x:xs.P(x)) = (!x. x mem xs --> P(x))";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac (list_ss setloop (split_tac [expand_if]))));
-by(fast_tac HOL_cs 1);
-qed "list_all_mem_conv";
-
-
-(** list_case **)
-
-goal List.thy
- "P(list_case(a,f,xs)) = ((xs=[] --> P(a)) & \
-\                         (!y ys. xs=y#ys --> P(f(y,ys))))";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-by(fast_tac HOL_cs 1);
-qed "expand_list_case";
-
-goal List.thy  "(xs=[] --> P([])) & (!y ys. xs=y#ys --> P(y#ys)) --> P(xs)";
-by(list.induct_tac "xs" 1);
-by(fast_tac HOL_cs 1);
-by(fast_tac HOL_cs 1);
-bind_thm("list_eq_cases",
-  impI RSN (2,allI RSN (2,allI RSN (2,impI RS (conjI RS (result() RS mp))))));
-
-(** flat **)
-
-goal List.thy  "flat(xs@ys) = flat(xs)@flat(ys)";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac (list_ss addsimps [append_assoc])));
-qed"flat_append";
-
-(** length **)
-
-goal List.thy "length(xs@ys) = length(xs)+length(ys)";
-by (list.induct_tac "xs" 1);
-by(ALLGOALS(asm_simp_tac list_ss));
-qed"length_append";
-
-(** nth **)
-
-val [nth_0,nth_Suc] = nat_recs nth_def; 
-store_thm("nth_0",nth_0);
-store_thm("nth_Suc",nth_Suc);
-
-(** Additional mapping lemmas **)
-
-goal List.thy "map(%x.x, xs) = xs";
-by (list.induct_tac "xs" 1);
-by (ALLGOALS (asm_simp_tac list_ss));
-qed "map_ident";
-
-goal List.thy "map(f, xs@ys) = map(f,xs) @ map(f,ys)";
-by (list.induct_tac "xs" 1);
-by (ALLGOALS (asm_simp_tac list_ss));
-qed "map_append";
-
-goalw List.thy [o_def] "map(f o g, xs) = map(f, map(g, xs))";
-by (list.induct_tac "xs" 1);
-by (ALLGOALS (asm_simp_tac list_ss));
-qed "map_compose";
-
-val list_ss = list_ss addsimps
-  [not_Cons_self, append_assoc, append_Nil2, append_is_Nil, same_append_eq,
-   mem_append, mem_filter,
-   map_ident, map_append, map_compose,
-   flat_append, length_append, list_all_True, list_all_conj, nth_0, nth_Suc];
-