--- a/src/HOLCF/Sprod.thy Thu Nov 19 21:06:22 2009 -0800
+++ b/src/HOLCF/Sprod.thy Thu Nov 19 21:44:37 2009 -0800
@@ -245,6 +245,9 @@
"x \<noteq> \<bottom> \<Longrightarrow> y \<noteq> \<bottom> \<Longrightarrow> sprod_map\<cdot>f\<cdot>g\<cdot>(:x, y:) = (:f\<cdot>x, g\<cdot>y:)"
by (simp add: sprod_map_def)
+lemma sprod_map_ID: "sprod_map\<cdot>ID\<cdot>ID = ID"
+unfolding sprod_map_def by (simp add: expand_cfun_eq eta_cfun)
+
lemma sprod_map_map:
"\<lbrakk>f1\<cdot>\<bottom> = \<bottom>; g1\<cdot>\<bottom> = \<bottom>\<rbrakk> \<Longrightarrow>
sprod_map\<cdot>f1\<cdot>g1\<cdot>(sprod_map\<cdot>f2\<cdot>g2\<cdot>p) =