src/HOL/IMP/Def_Ass.thy

 subsection "Definite Assignment Analysis"
 
 inductive D :: "vname set \<Rightarrow> com \<Rightarrow> vname set \<Rightarrow> bool" where
 Skip: "D A SKIP A" |
 Assign: "vars a \<subseteq> A \<Longrightarrow> D A (x ::= a) (insert x A)" |
-Semi: "\<lbrakk> D A\<^isub>1 c\<^isub>1 A\<^isub>2;  D A\<^isub>2 c\<^isub>2 A\<^isub>3 \<rbrakk> \<Longrightarrow> D A\<^isub>1 (c\<^isub>1; c\<^isub>2) A\<^isub>3" |
+Seq: "\<lbrakk> D A\<^isub>1 c\<^isub>1 A\<^isub>2;  D A\<^isub>2 c\<^isub>2 A\<^isub>3 \<rbrakk> \<Longrightarrow> D A\<^isub>1 (c\<^isub>1; c\<^isub>2) A\<^isub>3" |
 If: "\<lbrakk> vars b \<subseteq> A;  D A c\<^isub>1 A\<^isub>1;  D A c\<^isub>2 A\<^isub>2 \<rbrakk> \<Longrightarrow>
   D A (IF b THEN c\<^isub>1 ELSE c\<^isub>2) (A\<^isub>1 Int A\<^isub>2)" |
 While: "\<lbrakk> vars b \<subseteq> A;  D A c A' \<rbrakk> \<Longrightarrow> D A (WHILE b DO c) A"
 
 inductive_cases [elim!]: