src/ZF/List.ML

--- a/src/ZF/List.ML	Wed Dec 07 12:34:47 1994 +0100
+++ b/src/ZF/List.ML	Wed Dec 07 13:12:04 1994 +0100
@@ -28,7 +28,7 @@
 by (fast_tac (sum_cs addSIs (equalityI :: map rew intrs)
                      addEs [rew elim]) 1)
 end;
-val list_unfold = result();
+qed "list_unfold";
 
 (**  Lemmas to justify using "list" in other recursive type definitions **)
 
@@ -36,7 +36,7 @@
 by (rtac lfp_mono 1);
 by (REPEAT (rtac list.bnd_mono 1));
 by (REPEAT (ares_tac (univ_mono::basic_monos) 1));
-val list_mono = result();
+qed "list_mono";
 
 (*There is a similar proof by list induction.*)
 goalw List.thy ([e-mail]_defs) "list(univ(A)) <= univ(A)";
@@ -44,14 +44,14 @@
 by (rtac (A_subset_univ RS univ_mono) 2);
 by (fast_tac (ZF_cs addSIs [zero_in_univ, Inl_in_univ, Inr_in_univ,
 			    Pair_in_univ]) 1);
-val list_univ = result();
+qed "list_univ";
 
 (*These two theorems are unused -- useful??*)
 val list_subset_univ = standard ([list_mono, list_univ] MRS subset_trans);
 
 goal List.thy "!!l A B. [| l: list(A);  A <= univ(B) |] ==> l: univ(B)";
 by (REPEAT (ares_tac [list_subset_univ RS subsetD] 1));
-val list_into_univ = result();
+qed "list_into_univ";
 
 val major::prems = goal List.thy
     "[| l: list(A);    \
@@ -60,18 +60,18 @@
 \    |] ==> list_case(c,h,l) : C(l)";
 by (rtac (major RS list.induct) 1);
 by (ALLGOALS (asm_simp_tac (ZF_ss addsimps (list.case_eqns @ prems))));
-val list_case_type = result();
+qed "list_case_type";
 
 
 (** For recursion **)
 
 goalw List.thy list.con_defs "rank(a) < rank(Cons(a,l))";
 by (simp_tac rank_ss 1);
-val rank_Cons1 = result();
+qed "rank_Cons1";
 
 goalw List.thy list.con_defs "rank(l) < rank(Cons(a,l))";
 by (simp_tac rank_ss 1);
-val rank_Cons2 = result();
+qed "rank_Cons2";
 
 
 (*** List functions ***)
@@ -80,55 +80,55 @@
 
 goalw List.thy [hd_def] "hd(Cons(a,l)) = a";
 by (resolve_tac list.case_eqns 1);
-val hd_Cons = result();
+qed "hd_Cons";
 
 goalw List.thy [tl_def] "tl(Nil) = Nil";
 by (resolve_tac list.case_eqns 1);
-val tl_Nil = result();
+qed "tl_Nil";
 
 goalw List.thy [tl_def] "tl(Cons(a,l)) = l";
 by (resolve_tac list.case_eqns 1);
-val tl_Cons = result();
+qed "tl_Cons";
 
 goal List.thy "!!l. l: list(A) ==> tl(l) : list(A)";
 by (etac list.elim 1);
 by (ALLGOALS (asm_simp_tac (ZF_ss addsimps (list.intrs @ [tl_Nil,tl_Cons]))));
-val tl_type = result();
+qed "tl_type";
 
 (** drop **)
 
 goalw List.thy [drop_def] "drop(0, l) = l";
 by (rtac rec_0 1);
-val drop_0 = result();
+qed "drop_0";
 
 goalw List.thy [drop_def] "!!i. i:nat ==> drop(i, Nil) = Nil";
 by (etac nat_induct 1);
 by (ALLGOALS (asm_simp_tac (nat_ss addsimps [tl_Nil])));
-val drop_Nil = result();
+qed "drop_Nil";
 
 goalw List.thy [drop_def]
     "!!i. i:nat ==> drop(succ(i), Cons(a,l)) = drop(i,l)";
 by (etac nat_induct 1);
 by (ALLGOALS (asm_simp_tac (nat_ss addsimps [tl_Cons])));
-val drop_succ_Cons = result();
+qed "drop_succ_Cons";
 
 goalw List.thy [drop_def] 
     "!!i l. [| i:nat; l: list(A) |] ==> drop(i,l) : list(A)";
 by (etac nat_induct 1);
 by (ALLGOALS (asm_simp_tac (nat_ss addsimps [tl_type])));
-val drop_type = result();
+qed "drop_type";
 
 (** list_rec -- by Vset recursion **)
 
 goal List.thy "list_rec(Nil,c,h) = c";
 by (rtac (list_rec_def RS def_Vrec RS trans) 1);
 by (simp_tac (ZF_ss addsimps list.case_eqns) 1);
-val list_rec_Nil = result();
+qed "list_rec_Nil";
 
 goal List.thy "list_rec(Cons(a,l), c, h) = h(a, l, list_rec(l,c,h))";
 by (rtac (list_rec_def RS def_Vrec RS trans) 1);
 by (simp_tac (rank_ss addsimps (rank_Cons2::list.case_eqns)) 1);
-val list_rec_Cons = result();
+qed "list_rec_Cons";
 
 (*Type checking -- proved by induction, as usual*)
 val prems = goal List.thy
@@ -139,7 +139,7 @@
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac
 	      (ZF_ss addsimps (prems@[list_rec_Nil,list_rec_Cons]))));
-val list_rec_type = result();
+qed "list_rec_type";
 
 (** Versions for use with definitions **)
 
@@ -147,13 +147,13 @@
     "[| !!l. j(l)==list_rec(l, c, h) |] ==> j(Nil) = c";
 by (rewtac rew);
 by (rtac list_rec_Nil 1);
-val def_list_rec_Nil = result();
+qed "def_list_rec_Nil";
 
 val [rew] = goal List.thy
     "[| !!l. j(l)==list_rec(l, c, h) |] ==> j(Cons(a,l)) = h(a,l,j(l))";
 by (rewtac rew);
 by (rtac list_rec_Cons 1);
-val def_list_rec_Cons = result();
+qed "def_list_rec_Cons";
 
 fun list_recs def = map standard
     	([def] RL [def_list_rec_Nil, def_list_rec_Cons]);
@@ -165,12 +165,12 @@
 val prems = goalw List.thy [map_def] 
     "[| l: list(A);  !!x. x: A ==> h(x): B |] ==> map(h,l) : list(B)";
 by (REPEAT (ares_tac (prems @ list.intrs @ [list_rec_type]) 1));
-val map_type = result();
+qed "map_type";
 
 val [major] = goal List.thy "l: list(A) ==> map(h,l) : list({h(u). u:A})";
 by (rtac (major RS map_type) 1);
 by (etac RepFunI 1);
-val map_type2 = result();
+qed "map_type2";
 
 (** length **)
 
@@ -179,7 +179,7 @@
 goalw List.thy [length_def] 
     "!!l. l: list(A) ==> length(l) : nat";
 by (REPEAT (ares_tac [list_rec_type, nat_0I, nat_succI] 1));
-val length_type = result();
+qed "length_type";
 
 (** app **)
 
@@ -188,7 +188,7 @@
 goalw List.thy [app_def] 
     "!!xs ys. [| xs: list(A);  ys: list(A) |] ==> xs@ys : list(A)";
 by (REPEAT (ares_tac [list_rec_type, list.Cons_I] 1));
-val app_type = result();
+qed "app_type";
 
 (** rev **)
 
@@ -197,7 +197,7 @@
 goalw List.thy [rev_def] 
     "!!xs. xs: list(A) ==> rev(xs) : list(A)";
 by (REPEAT (ares_tac (list.intrs @ [list_rec_type, app_type]) 1));
-val rev_type = result();
+qed "rev_type";
 
 
 (** flat **)
@@ -207,7 +207,7 @@
 goalw List.thy [flat_def] 
     "!!ls. ls: list(list(A)) ==> flat(ls) : list(A)";
 by (REPEAT (ares_tac (list.intrs @ [list_rec_type, app_type]) 1));
-val flat_type = result();
+qed "flat_type";
 
 
 (** list_add **)
@@ -217,7 +217,7 @@
 goalw List.thy [list_add_def] 
     "!!xs. xs: list(nat) ==> list_add(xs) : nat";
 by (REPEAT (ares_tac [list_rec_type, nat_0I, add_type] 1));
-val list_add_type = result();
+qed "list_add_type";
 
 (** List simplification **)
 
@@ -241,25 +241,25 @@
     "l: list(A) ==> map(%u.u, l) = l";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val map_ident = result();
+qed "map_ident";
 
 val prems = goal List.thy
     "l: list(A) ==> map(h, map(j,l)) = map(%u.h(j(u)), l)";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val map_compose = result();
+qed "map_compose";
 
 val prems = goal List.thy
     "xs: list(A) ==> map(h, xs@ys) = map(h,xs) @ map(h,ys)";
 by (list_ind_tac "xs" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val map_app_distrib = result();
+qed "map_app_distrib";
 
 val prems = goal List.thy
     "ls: list(list(A)) ==> map(h, flat(ls)) = flat(map(map(h),ls))";
 by (list_ind_tac "ls" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [map_app_distrib])));
-val map_flat = result();
+qed "map_flat";
 
 val prems = goal List.thy
     "l: list(A) ==> \
@@ -267,7 +267,7 @@
 \    list_rec(l, c, %x xs r. d(h(x), map(h,xs), r))";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val list_rec_map = result();
+qed "list_rec_map";
 
 (** theorems about list(Collect(A,P)) -- used in ex/term.ML **)
 
@@ -278,7 +278,7 @@
     "l: list({x:A. h(x)=j(x)}) ==> map(h,l) = map(j,l)";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val map_list_Collect = result();
+qed "map_list_Collect";
 
 (*** theorems about length ***)
 
@@ -286,13 +286,13 @@
     "xs: list(A) ==> length(map(h,xs)) = length(xs)";
 by (list_ind_tac "xs" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val length_map = result();
+qed "length_map";
 
 val prems = goal List.thy
     "xs: list(A) ==> length(xs@ys) = length(xs) #+ length(ys)";
 by (list_ind_tac "xs" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val length_app = result();
+qed "length_app";
 
 (* [| m: nat; n: nat |] ==> m #+ succ(n) = succ(n) #+ m 
    Used for rewriting below*)
@@ -302,13 +302,13 @@
     "xs: list(A) ==> length(rev(xs)) = length(xs)";
 by (list_ind_tac "xs" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [length_app, add_commute_succ])));
-val length_rev = result();
+qed "length_rev";
 
 val prems = goal List.thy
     "ls: list(list(A)) ==> length(flat(ls)) = list_add(map(length,ls))";
 by (list_ind_tac "ls" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [length_app])));
-val length_flat = result();
+qed "length_flat";
 
 (** Length and drop **)
 
@@ -319,7 +319,7 @@
 by (etac list.induct 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [drop_0,drop_succ_Cons])));
 by (fast_tac ZF_cs 1);
-val drop_length_Cons_lemma = result();
+qed "drop_length_Cons_lemma";
 val drop_length_Cons = standard (drop_length_Cons_lemma RS spec);
 
 goal List.thy
@@ -338,7 +338,7 @@
 by (dtac bspec 1);
 by (fast_tac ZF_cs 2);
 by (fast_tac (ZF_cs addEs [succ_in_naturalD,length_type]) 1);
-val drop_length_lemma = result();
+qed "drop_length_lemma";
 val drop_length = standard (drop_length_lemma RS bspec);
 
 
@@ -347,25 +347,25 @@
 val [major] = goal List.thy "xs: list(A) ==> xs@Nil=xs";
 by (rtac (major RS list.induct) 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val app_right_Nil = result();
+qed "app_right_Nil";
 
 val prems = goal List.thy "xs: list(A) ==> (xs@ys)@zs = xs@(ys@zs)";
 by (list_ind_tac "xs" prems 1);
 by (ALLGOALS (asm_simp_tac list_ss));
-val app_assoc = result();
+qed "app_assoc";
 
 val prems = goal List.thy
     "ls: list(list(A)) ==> flat(ls@ms) = flat(ls)@flat(ms)";
 by (list_ind_tac "ls" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [app_assoc])));
-val flat_app_distrib = result();
+qed "flat_app_distrib";
 
 (*** theorems about rev ***)
 
 val prems = goal List.thy "l: list(A) ==> rev(map(h,l)) = map(h,rev(l))";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [map_app_distrib])));
-val rev_map_distrib = result();
+qed "rev_map_distrib";
 
 (*Simplifier needs the premises as assumptions because rewriting will not
   instantiate the variable ?A in the rules' typing conditions; note that
@@ -375,19 +375,19 @@
     "!!xs. [| xs: list(A);  ys: list(A) |] ==> rev(xs@ys) = rev(ys)@rev(xs)";
 by (etac list.induct 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [app_right_Nil,app_assoc])));
-val rev_app_distrib = result();
+qed "rev_app_distrib";
 
 val prems = goal List.thy "l: list(A) ==> rev(rev(l))=l";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [rev_app_distrib])));
-val rev_rev_ident = result();
+qed "rev_rev_ident";
 
 val prems = goal List.thy
     "ls: list(list(A)) ==> rev(flat(ls)) = flat(map(rev,rev(ls)))";
 by (list_ind_tac "ls" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps 
        [map_app_distrib, flat_app_distrib, rev_app_distrib, app_right_Nil])));
-val rev_flat = result();
+qed "rev_flat";
 
 
 (*** theorems about list_add ***)
@@ -401,21 +401,21 @@
     (asm_simp_tac (list_ss addsimps [add_0_right, add_assoc RS sym])));
 by (rtac (add_commute RS subst_context) 1);
 by (REPEAT (ares_tac [refl, list_add_type] 1));
-val list_add_app = result();
+qed "list_add_app";
 
 val prems = goal List.thy
     "l: list(nat) ==> list_add(rev(l)) = list_add(l)";
 by (list_ind_tac "l" prems 1);
 by (ALLGOALS
     (asm_simp_tac (list_ss addsimps [list_add_app, add_0_right])));
-val list_add_rev = result();
+qed "list_add_rev";
 
 val prems = goal List.thy
     "ls: list(list(nat)) ==> list_add(flat(ls)) = list_add(map(list_add,ls))";
 by (list_ind_tac "ls" prems 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps [list_add_app])));
 by (REPEAT (ares_tac [refl, list_add_type, map_type, add_commute] 1));
-val list_add_flat = result();
+qed "list_add_flat";
 
 (** New induction rule **)
 
@@ -427,5 +427,5 @@
 by (rtac (major RS rev_rev_ident RS subst) 1);
 by (rtac (major RS rev_type RS list.induct) 1);
 by (ALLGOALS (asm_simp_tac (list_ss addsimps prems)));
-val list_append_induct = result();
+qed "list_append_induct";