src/HOL/IMP/Def_Init_Big.thy

 where
 None: "(c,None) \<Rightarrow> None" |
 Skip: "(SKIP,s) \<Rightarrow> s" |
 AssignNone: "aval a s = None \<Longrightarrow> (x ::= a, Some s) \<Rightarrow> None" |
 Assign: "aval a s = Some i \<Longrightarrow> (x ::= a, Some s) \<Rightarrow> Some(s(x := Some i))" |
-Seq:    "(c\<^isub>1,s\<^isub>1) \<Rightarrow> s\<^isub>2 \<Longrightarrow> (c\<^isub>2,s\<^isub>2) \<Rightarrow> s\<^isub>3 \<Longrightarrow> (c\<^isub>1;;c\<^isub>2,s\<^isub>1) \<Rightarrow> s\<^isub>3" |
+Seq:    "(c\<^sub>1,s\<^sub>1) \<Rightarrow> s\<^sub>2 \<Longrightarrow> (c\<^sub>2,s\<^sub>2) \<Rightarrow> s\<^sub>3 \<Longrightarrow> (c\<^sub>1;;c\<^sub>2,s\<^sub>1) \<Rightarrow> s\<^sub>3" |
 
-IfNone:  "bval b s = None \<Longrightarrow> (IF b THEN c\<^isub>1 ELSE c\<^isub>2,Some s) \<Rightarrow> None" |
-IfTrue:  "\<lbrakk> bval b s = Some True;  (c\<^isub>1,Some s) \<Rightarrow> s' \<rbrakk> \<Longrightarrow>
-  (IF b THEN c\<^isub>1 ELSE c\<^isub>2,Some s) \<Rightarrow> s'" |
-IfFalse: "\<lbrakk> bval b s = Some False;  (c\<^isub>2,Some s) \<Rightarrow> s' \<rbrakk> \<Longrightarrow>
-  (IF b THEN c\<^isub>1 ELSE c\<^isub>2,Some s) \<Rightarrow> s'" |
+IfNone:  "bval b s = None \<Longrightarrow> (IF b THEN c\<^sub>1 ELSE c\<^sub>2,Some s) \<Rightarrow> None" |
+IfTrue:  "\<lbrakk> bval b s = Some True;  (c\<^sub>1,Some s) \<Rightarrow> s' \<rbrakk> \<Longrightarrow>
+  (IF b THEN c\<^sub>1 ELSE c\<^sub>2,Some s) \<Rightarrow> s'" |
+IfFalse: "\<lbrakk> bval b s = Some False;  (c\<^sub>2,Some s) \<Rightarrow> s' \<rbrakk> \<Longrightarrow>
+  (IF b THEN c\<^sub>1 ELSE c\<^sub>2,Some s) \<Rightarrow> s'" |
 
 WhileNone: "bval b s = None \<Longrightarrow> (WHILE b DO c,Some s) \<Rightarrow> None" |
 WhileFalse: "bval b s = Some False \<Longrightarrow> (WHILE b DO c,Some s) \<Rightarrow> Some s" |
 WhileTrue:
   "\<lbrakk> bval b s = Some True;  (c,Some s) \<Rightarrow> s';  (WHILE b DO c,s') \<Rightarrow> s'' \<rbrakk> \<Longrightarrow>