src/HOLCF/Bifinite.thy
changeset 33808 31169fdc5ae7
parent 33587 54f98d225163
child 35525 fa231b86cb1e
--- a/src/HOLCF/Bifinite.thy	Thu Nov 19 21:06:22 2009 -0800
+++ b/src/HOLCF/Bifinite.thy	Thu Nov 19 21:44:37 2009 -0800
@@ -114,6 +114,9 @@
 lemma cprod_map_Pair [simp]: "cprod_map\<cdot>f\<cdot>g\<cdot>(x, y) = (f\<cdot>x, g\<cdot>y)"
 unfolding cprod_map_def by simp
 
+lemma cprod_map_ID: "cprod_map\<cdot>ID\<cdot>ID = ID"
+unfolding expand_cfun_eq by auto
+
 lemma cprod_map_map:
   "cprod_map\<cdot>f1\<cdot>g1\<cdot>(cprod_map\<cdot>f2\<cdot>g2\<cdot>p) =
     cprod_map\<cdot>(\<Lambda> x. f1\<cdot>(f2\<cdot>x))\<cdot>(\<Lambda> x. g1\<cdot>(g2\<cdot>x))\<cdot>p"
@@ -207,6 +210,9 @@
 lemma cfun_map_beta [simp]: "cfun_map\<cdot>a\<cdot>b\<cdot>f\<cdot>x = b\<cdot>(f\<cdot>(a\<cdot>x))"
 unfolding cfun_map_def by simp
 
+lemma cfun_map_ID: "cfun_map\<cdot>ID\<cdot>ID = ID"
+unfolding expand_cfun_eq by simp
+
 lemma cfun_map_map:
   "cfun_map\<cdot>f1\<cdot>g1\<cdot>(cfun_map\<cdot>f2\<cdot>g2\<cdot>p) =
     cfun_map\<cdot>(\<Lambda> x. f2\<cdot>(f1\<cdot>x))\<cdot>(\<Lambda> x. g1\<cdot>(g2\<cdot>x))\<cdot>p"