--- a/src/HOL/IMP/Transition.thy Wed Jan 12 17:14:27 2011 +0100
+++ b/src/HOL/IMP/Transition.thy Wed Jan 12 17:19:50 2011 +0100
@@ -272,7 +272,7 @@
lemma evalc_imp_evalc1:
assumes "\<langle>c,s\<rangle> \<longrightarrow>\<^sub>c s'"
shows "\<langle>c, s\<rangle> \<longrightarrow>\<^sub>1\<^sup>* \<langle>s'\<rangle>"
- using prems
+ using assms
proof induct
fix s show "\<langle>\<SKIP>,s\<rangle> \<longrightarrow>\<^sub>1\<^sup>* \<langle>s\<rangle>" by auto
next
@@ -550,7 +550,7 @@
shows "\<langle>c1;c2,s1\<rangle> \<longrightarrow>\<^sub>1\<^sup>* cs3"
proof -
-- {* The induction rule needs @{text P} to be a function of @{term "Some c1"} *}
- from prems
+ from assms
have "\<langle>(\<lambda>c. if c = None then c2 else the c; c2) (Some c1),s1\<rangle> \<longrightarrow>\<^sub>1\<^sup>* cs3"
apply (induct rule: converse_rtrancl_induct2)
apply simp