src/HOL/Algebra/Congruence.thy

 definition
   set_eq :: "_ \<Rightarrow> 'a set \<Rightarrow> 'a set \<Rightarrow> bool" (infixl "{.=}\<index>" 50)
   where "A {.=}\<^bsub>S\<^esub> B \<longleftrightarrow> ((\<forall>x \<in> A. x .\<in>\<^bsub>S\<^esub> B) \<and> (\<forall>x \<in> B. x .\<in>\<^bsub>S\<^esub> A))"
 
 definition
-  eq_class_of :: "_ \<Rightarrow> 'a \<Rightarrow> 'a set" ("class'_of\<index> _")
+  eq_class_of :: "_ \<Rightarrow> 'a \<Rightarrow> 'a set" ("class'_of\<index>")
   where "class_of\<^bsub>S\<^esub> x = {y \<in> carrier S. x .=\<^bsub>S\<^esub> y}"
 
 definition
-  eq_closure_of :: "_ \<Rightarrow> 'a set \<Rightarrow> 'a set" ("closure'_of\<index> _")
+  eq_closure_of :: "_ \<Rightarrow> 'a set \<Rightarrow> 'a set" ("closure'_of\<index>")
   where "closure_of\<^bsub>S\<^esub> A = {y \<in> carrier S. y .\<in>\<^bsub>S\<^esub> A}"
 
 definition
-  eq_is_closed :: "_ \<Rightarrow> 'a set \<Rightarrow> bool" ("is'_closed\<index> _")
+  eq_is_closed :: "_ \<Rightarrow> 'a set \<Rightarrow> bool" ("is'_closed\<index>")
   where "is_closed\<^bsub>S\<^esub> A \<longleftrightarrow> A \<subseteq> carrier S \<and> closure_of\<^bsub>S\<^esub> A = A"
 
 abbreviation
   not_eq :: "_ \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" (infixl ".\<noteq>\<index>" 50)
   where "x .\<noteq>\<^bsub>S\<^esub> y == ~(x .=\<^bsub>S\<^esub> y)"