--- a/src/HOLCF/Cfun.thy Wed Feb 17 08:05:16 2010 -0800
+++ b/src/HOLCF/Cfun.thy Wed Feb 17 08:19:46 2010 -0800
@@ -521,7 +521,7 @@
text {* results about strictify *}
lemma cont_strictify1: "cont (\<lambda>f. if x = \<bottom> then \<bottom> else f\<cdot>x)"
-by (simp add: cont_if)
+by simp
lemma monofun_strictify2: "monofun (\<lambda>x. if x = \<bottom> then \<bottom> else f\<cdot>x)"
apply (rule monofunI)
--- a/src/HOLCF/Deflation.thy Wed Feb 17 08:05:16 2010 -0800
+++ b/src/HOLCF/Deflation.thy Wed Feb 17 08:19:46 2010 -0800
@@ -316,16 +316,14 @@
subsection {* Uniqueness of ep-pairs *}
lemma ep_pair_unique_e_lemma:
- assumes "ep_pair e1 p" and "ep_pair e2 p"
+ assumes 1: "ep_pair e1 p" and 2: "ep_pair e2 p"
shows "e1 \<sqsubseteq> e2"
proof (rule below_cfun_ext)
- interpret e1: ep_pair e1 p by fact
- interpret e2: ep_pair e2 p by fact
fix x
have "e1\<cdot>(p\<cdot>(e2\<cdot>x)) \<sqsubseteq> e2\<cdot>x"
- by (rule e1.e_p_below)
+ by (rule ep_pair.e_p_below [OF 1])
thus "e1\<cdot>x \<sqsubseteq> e2\<cdot>x"
- by (simp only: e2.e_inverse)
+ by (simp only: ep_pair.e_inverse [OF 2])
qed
lemma ep_pair_unique_e:
@@ -333,18 +331,16 @@
by (fast intro: below_antisym elim: ep_pair_unique_e_lemma)
lemma ep_pair_unique_p_lemma:
- assumes "ep_pair e p1" and "ep_pair e p2"
+ assumes 1: "ep_pair e p1" and 2: "ep_pair e p2"
shows "p1 \<sqsubseteq> p2"
proof (rule below_cfun_ext)
- interpret p1: ep_pair e p1 by fact
- interpret p2: ep_pair e p2 by fact
fix x
have "e\<cdot>(p1\<cdot>x) \<sqsubseteq> x"
- by (rule p1.e_p_below)
+ by (rule ep_pair.e_p_below [OF 1])
hence "p2\<cdot>(e\<cdot>(p1\<cdot>x)) \<sqsubseteq> p2\<cdot>x"
by (rule monofun_cfun_arg)
thus "p1\<cdot>x \<sqsubseteq> p2\<cdot>x"
- by (simp only: p2.e_inverse)
+ by (simp only: ep_pair.e_inverse [OF 2])
qed
lemma ep_pair_unique_p: