author paulson Mon, 20 Mar 2000 12:54:31 +0100 changeset 8527 ce6ae118b6b2 parent 8526 0be2c98f15a7 child 8528 6c48043ccd0e
tidied
 src/HOL/Induct/Perm.ML file | annotate | diff | comparison | revisions
```--- a/src/HOL/Induct/Perm.ML	Mon Mar 20 11:15:28 2000 +0100
+++ b/src/HOL/Induct/Perm.ML	Mon Mar 20 12:54:31 2000 +0100
@@ -6,14 +6,15 @@
Permutations: example of an inductive definition
*)

-(*It would be nice to prove
-    xs <~~> ys = (!x. count xs x = count ys x)
-See mset on HOL/ex/Sorting.thy
+(*It would be nice to prove (for "multiset", defined on HOL/ex/Sorting.thy)
+    xs <~~> ys = (ALL x. multiset xs x = multiset ys x)
*)

+
Goal "l <~~> l";
by (induct_tac "l" 1);
-by (REPEAT (ares_tac perm.intrs 1));
+by Auto_tac;
qed "perm_refl";

@@ -23,23 +24,28 @@
Goal "xs <~~> ys ==> xs=[] --> ys=[]";
by (etac perm.induct 1);
by (ALLGOALS Asm_simp_tac);
-qed "perm_Nil_lemma";
+bind_thm ("xperm_empty_imp",    (* [] <~~> ys ==> ys=[] *)
+	  [refl, result()] MRS rev_mp);

-(*A more general version is actually easier to understand!*)
+(*This more general theorem is easier to understand!*)
Goal "xs <~~> ys ==> length(xs) = length(ys)";
by (etac perm.induct 1);
by (ALLGOALS Asm_simp_tac);
qed "perm_length";

+Goal "[] <~~> xs ==> xs=[]";
+by (dtac perm_length 1);
+by Auto_tac;
+qed "perm_empty_imp";
+
Goal "xs <~~> ys ==> ys <~~> xs";
by (etac perm.induct 1);
-by (REPEAT (ares_tac perm.intrs 1));
+by Auto_tac;
qed "perm_sym";

Goal "xs <~~> ys ==> x mem xs --> x mem ys";
by (etac perm.induct 1);
-by (Fast_tac 4);
-by (ALLGOALS Asm_simp_tac);
+by Auto_tac;
val perm_mem_lemma = result();

bind_thm ("perm_mem", perm_mem_lemma RS mp);
@@ -49,17 +55,15 @@
(*We can insert the head anywhere in the list*)
Goal "a # xs @ ys <~~> xs @ a # ys";
by (induct_tac "xs" 1);
-by (ALLGOALS Simp_tac);
-by (etac ([perm.swap, perm.Cons] MRS perm.trans) 1);
+by Auto_tac;
qed "perm_append_Cons";

Goal "xs@ys <~~> ys@xs";
by (induct_tac "xs" 1);
by (ALLGOALS Simp_tac);
-by (etac ([perm.Cons, perm_append_Cons] MRS perm.trans) 1);
+by (blast_tac (claset() addIs [perm_append_Cons]) 1);
qed "perm_append_swap";

-
Goal "a # xs <~~> xs @ [a]";
by (rtac perm.trans 1);
by (rtac perm_append_swap 2);
@@ -69,32 +73,20 @@
Goal "rev xs <~~> xs";
by (induct_tac "xs" 1);
by (ALLGOALS Simp_tac);
-by (rtac (perm_append_single RS perm_sym RS perm.trans) 1);
-by (etac perm.Cons 1);
+by (blast_tac (claset() addIs [perm_sym, perm_append_single]) 1);
qed "perm_rev";

Goal "xs <~~> ys ==> l@xs <~~> l@ys";
by (induct_tac "l" 1);
-by (Simp_tac 1);
-by (asm_simp_tac (simpset() addsimps [perm.Cons]) 1);
+by Auto_tac;
qed "perm_append1";

Goal "xs <~~> ys ==> xs@l <~~> ys@l";
-by (rtac (perm_append_swap RS perm.trans) 1);
-by (etac (perm_append1 RS perm.trans) 1);
-by (rtac perm_append_swap 1);
+by (blast_tac (claset() addSIs [perm_append_swap, perm_append1]) 1);
qed "perm_append2";

(** Further results mostly by Thomas Marthedal Rasmussen **)

-val perm_rules = [perm.trans, perm.swap, perm.Cons];
-
-Goal "[] <~~> xs ==> xs = []";
-by (rtac mp 1);
-by (res_inst_tac [("ys","xs"),("xs","[]")] perm_Nil_lemma 1);
-by Auto_tac;
-qed "perm_empty_imp";
-
Goal "([] <~~> xs) = (xs = [])";
by (blast_tac (claset() addIs [perm_empty_imp]) 1);
qed "perm_empty";
@@ -117,15 +109,13 @@

Goal "([y] <~~> ys) = (ys = [y])";
-by Auto_tac;
-by (dtac perm_sym 1);
-by Auto_tac;
+by (blast_tac (claset() addDs [perm_sym]) 1);
qed "perm_sing_eq2";

Goal "x:set ys --> ys <~~> x#(remove x ys)";
by (induct_tac "ys" 1);
-by (auto_tac (claset() addIs perm_rules, simpset()));
+by Auto_tac;
qed_spec_mp "perm_remove";

Goal "remove x (remove y l) = remove y (remove x l)";
@@ -136,7 +126,6 @@
(*Congruence rule*)
Goal "xs <~~> ys ==> remove z xs <~~> remove z ys";
by (etac perm.induct 1);
-by (auto_tac (claset() addIs perm_rules, simpset()));
by Auto_tac;
qed "perm_remove_perm";

@@ -151,14 +140,14 @@
qed "cons_perm_imp_perm";

Goal "(z#xs <~~> z#ys) = (xs <~~> ys)";
-by (blast_tac (claset() addIs [cons_perm_imp_perm, perm.Cons]) 1);
+by (blast_tac (claset() addIs [cons_perm_imp_perm]) 1);
qed "cons_perm_eq";

Goal "ALL xs ys. zs@xs <~~> zs@ys --> xs <~~> ys";
by (res_inst_tac [("xs","zs")] rev_induct 1);
by (ALLGOALS Full_simp_tac);
-by (blast_tac (claset() addSDs [spec]) 1);
+by (Blast_tac 1);
qed_spec_mp "append_perm_imp_perm";

Goal "(zs@xs <~~> zs@ys) = (xs <~~> ys)";
@@ -170,7 +159,7 @@