--- a/src/HOLCF/Bifinite.thy Mon Nov 09 15:29:58 2009 -0800
+++ b/src/HOLCF/Bifinite.thy Mon Nov 09 15:51:32 2009 -0800
@@ -114,6 +114,11 @@
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_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"
+by (induct p) simp
+
lemma ep_pair_cprod_map:
assumes "ep_pair e1 p1" and "ep_pair e2 p2"
shows "ep_pair (cprod_map\<cdot>e1\<cdot>e2) (cprod_map\<cdot>p1\<cdot>p2)"
@@ -202,6 +207,11 @@
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_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"
+by (rule ext_cfun) simp
+
lemma ep_pair_cfun_map:
assumes "ep_pair e1 p1" and "ep_pair e2 p2"
shows "ep_pair (cfun_map\<cdot>p1\<cdot>e2) (cfun_map\<cdot>e1\<cdot>p2)"
--- a/src/HOLCF/Sprod.thy Mon Nov 09 15:29:58 2009 -0800
+++ b/src/HOLCF/Sprod.thy Mon Nov 09 15:51:32 2009 -0800
@@ -245,6 +245,16 @@
"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_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) =
+ sprod_map\<cdot>(\<Lambda> x. f1\<cdot>(f2\<cdot>x))\<cdot>(\<Lambda> x. g1\<cdot>(g2\<cdot>x))\<cdot>p"
+apply (induct p, simp)
+apply (case_tac "f2\<cdot>x = \<bottom>", simp)
+apply (case_tac "g2\<cdot>y = \<bottom>", simp)
+apply simp
+done
+
lemma ep_pair_sprod_map:
assumes "ep_pair e1 p1" and "ep_pair e2 p2"
shows "ep_pair (sprod_map\<cdot>e1\<cdot>e2) (sprod_map\<cdot>p1\<cdot>p2)"
--- a/src/HOLCF/Ssum.thy Mon Nov 09 15:29:58 2009 -0800
+++ b/src/HOLCF/Ssum.thy Mon Nov 09 15:51:32 2009 -0800
@@ -226,6 +226,15 @@
lemma ssum_map_sinr [simp]: "x \<noteq> \<bottom> \<Longrightarrow> ssum_map\<cdot>f\<cdot>g\<cdot>(sinr\<cdot>x) = sinr\<cdot>(g\<cdot>x)"
unfolding ssum_map_def by simp
+lemma ssum_map_map:
+ "\<lbrakk>f1\<cdot>\<bottom> = \<bottom>; g1\<cdot>\<bottom> = \<bottom>\<rbrakk> \<Longrightarrow>
+ ssum_map\<cdot>f1\<cdot>g1\<cdot>(ssum_map\<cdot>f2\<cdot>g2\<cdot>p) =
+ ssum_map\<cdot>(\<Lambda> x. f1\<cdot>(f2\<cdot>x))\<cdot>(\<Lambda> x. g1\<cdot>(g2\<cdot>x))\<cdot>p"
+apply (induct p, simp)
+apply (case_tac "f2\<cdot>x = \<bottom>", simp, simp)
+apply (case_tac "g2\<cdot>y = \<bottom>", simp, simp)
+done
+
lemma ep_pair_ssum_map:
assumes "ep_pair e1 p1" and "ep_pair e2 p2"
shows "ep_pair (ssum_map\<cdot>e1\<cdot>e2) (ssum_map\<cdot>p1\<cdot>p2)"
--- a/src/HOLCF/Up.thy Mon Nov 09 15:29:58 2009 -0800
+++ b/src/HOLCF/Up.thy Mon Nov 09 15:51:32 2009 -0800
@@ -303,6 +303,9 @@
lemma u_map_up [simp]: "u_map\<cdot>f\<cdot>(up\<cdot>x) = up\<cdot>(f\<cdot>x)"
unfolding u_map_def by simp
+lemma u_map_map: "u_map\<cdot>f\<cdot>(u_map\<cdot>g\<cdot>p) = u_map\<cdot>(\<Lambda> x. f\<cdot>(g\<cdot>x))\<cdot>p"
+by (induct p) simp_all
+
lemma ep_pair_u_map: "ep_pair e p \<Longrightarrow> ep_pair (u_map\<cdot>e) (u_map\<cdot>p)"
apply default
apply (case_tac x, simp, simp add: ep_pair.e_inverse)