src/HOL/List.thy
 changeset 44890 22f665a2e91c parent 44635 3d046864ebe6 child 44916 840d8c3d9113
```--- a/src/HOL/List.thy	Sun Sep 11 22:56:05 2011 +0200
+++ b/src/HOL/List.thy	Mon Sep 12 07:55:43 2011 +0200
@@ -659,10 +659,10 @@
lemma append_eq_append_conv2: "(xs @ ys = zs @ ts) =
(EX us. xs = zs @ us & us @ ys = ts | xs @ us = zs & ys = us@ ts)"
apply (induct xs arbitrary: ys zs ts)
- apply fastsimp
+ apply fastforce
apply(case_tac zs)
apply simp
-apply fastsimp
+apply fastforce
done

lemma same_append_eq [iff, induct_simp]: "(xs @ ys = xs @ zs) = (ys = zs)"
@@ -997,9 +997,9 @@
case (Cons a xs)
show ?case
proof cases
-    assume "x = a" thus ?case using Cons by fastsimp
+    assume "x = a" thus ?case using Cons by fastforce
next
-    assume "x \<noteq> a" thus ?case using Cons by(fastsimp intro!: Cons_eq_appendI)
+    assume "x \<noteq> a" thus ?case using Cons by(fastforce intro!: Cons_eq_appendI)
qed
qed

@@ -1016,7 +1016,7 @@
proof cases
assume "x = a" thus ?case using snoc by (metis List.set.simps(1) emptyE)
next
-    assume "x \<noteq> a" thus ?case using snoc by fastsimp
+    assume "x \<noteq> a" thus ?case using snoc by fastforce
qed
qed

@@ -1078,7 +1078,7 @@
next
assume "\<not> P x"
hence "\<exists>x\<in>set xs. P x" using snoc(2) by simp
-    thus ?thesis using `\<not> P x` snoc(1) by fastsimp
+    thus ?thesis using `\<not> P x` snoc(1) by fastforce
qed
qed

@@ -1216,7 +1216,7 @@
qed
next
assume "\<not> P y"
-    with Cons obtain us vs where "?P (y#ys) (y#us) vs" by fastsimp
+    with Cons obtain us vs where "?P (y#ys) (y#us) vs" by fastforce
then have "?Q (y#us)" by simp
then show ?thesis ..
qed
@@ -2986,7 +2986,7 @@
"k < size ns \<Longrightarrow> ns ! k \<le> listsum (ns::nat list)"
apply(induct ns arbitrary: k)
apply simp
done

lemma listsum_update_nat:
@@ -4671,7 +4671,7 @@
\<longleftrightarrow> (xs, ys) \<in> listrel1 r \<and> x = y \<or> xs = ys \<and> (x,y) \<in> r" (is "?L \<longleftrightarrow> ?R")
proof
assume ?L thus ?R
-    by (fastsimp simp: listrel1_def snoc_eq_iff_butlast butlast_append)
+    by (fastforce simp: listrel1_def snoc_eq_iff_butlast butlast_append)
next
assume ?R then show ?L unfolding listrel1_def by force
qed
@@ -4734,7 +4734,7 @@
apply (induct set: acc)
apply clarify
apply (rule accI)
-apply (fastsimp dest!: in_set_conv_decomp[THEN iffD1] simp: listrel1_def)
+apply (fastforce dest!: in_set_conv_decomp[THEN iffD1] simp: listrel1_def)
done

lemma wf_listrel1_iff[simp]: "wf(listrel1 r) = wf r"```