src/HOLCF/Ssum.thy
 changeset 17837 2922be3544f8 parent 17817 405fb812e738 child 18078 20e5a6440790
```--- a/src/HOLCF/Ssum.thy	Tue Oct 11 23:47:29 2005 +0200
+++ b/src/HOLCF/Ssum.thy	Wed Oct 12 01:43:37 2005 +0200
@@ -48,6 +48,12 @@
lemma Rep_Ssum_sinr: "Rep_Ssum (sinr\<cdot>b) = <\<bottom>, b>"
by (unfold sinr_def, simp add: cont_Abs_Ssum Abs_Ssum_inverse Ssum_def)

+lemma compact_sinl [simp]: "compact x \<Longrightarrow> compact (sinl\<cdot>x)"
+by (rule compact_Ssum, simp add: Rep_Ssum_sinl)
+
+lemma compact_sinr [simp]: "compact x \<Longrightarrow> compact (sinr\<cdot>x)"
+by (rule compact_Ssum, simp add: Rep_Ssum_sinr)
+
lemma sinl_strict [simp]: "sinl\<cdot>\<bottom> = \<bottom>"
by (simp add: sinl_Abs_Ssum Abs_Ssum_strict cpair_strict)

@@ -67,14 +73,10 @@
by (rule sinr_eq [THEN iffD1])

lemma sinl_defined_iff [simp]: "(sinl\<cdot>x = \<bottom>) = (x = \<bottom>)"
-apply (rule sinl_strict [THEN subst])
-apply (rule sinl_eq)
-done
+by (cut_tac sinl_eq [of "x" "\<bottom>"], simp)

lemma sinr_defined_iff [simp]: "(sinr\<cdot>x = \<bottom>) = (x = \<bottom>)"
-apply (rule sinr_strict [THEN subst])
-apply (rule sinr_eq)
-done
+by (cut_tac sinr_eq [of "x" "\<bottom>"], simp)

lemma sinl_defined [intro!]: "x \<noteq> \<bottom> \<Longrightarrow> sinl\<cdot>x \<noteq> \<bottom>"
by simp```