src/HOL/Algebra/FiniteProduct.thy
changeset 20318 0e0ea63fe768
parent 16638 3dc904d93767
child 22265 3c5c6bdf61de
--- a/src/HOL/Algebra/FiniteProduct.thy	Thu Aug 03 14:53:57 2006 +0200
+++ b/src/HOL/Algebra/FiniteProduct.thy	Thu Aug 03 14:57:26 2006 +0200
@@ -5,9 +5,13 @@
 This file is largely based on HOL/Finite_Set.thy.
 *)
 
-header {* Product Operator for Commutative Monoids *}
+theory FiniteProduct imports Group begin
+
 
-theory FiniteProduct imports Group begin
+section {* Product Operator for Commutative Monoids *}
+
+
+subsection {* Inductive Definition of a Relation for Products over Sets *}
 
 text {* Instantiation of locale @{text LC} of theory @{text Finite_Set} is not
   possible, because here we have explicit typing rules like 
@@ -58,7 +62,8 @@
   then show ?case ..
 qed
 
-subsection {* Left-commutative operations *}
+
+subsection {* Left-Commutative Operations *}
 
 locale LCD =
   fixes B :: "'b set"
@@ -226,7 +231,8 @@
 declare (in LCD)
   foldSetD_closed [rule del]
 
-subsection {* Commutative monoids *}
+
+subsection {* Commutative Monoids *}
 
 text {*
   We enter a more restrictive context, with @{text "f :: 'a => 'a => 'a"}
@@ -280,6 +286,7 @@
   by (simp add: foldD_Un_Int
     left_commute LCD.foldD_closed [OF LCD.intro [of D]] Un_subset_iff)
 
+
 subsection {* Products over Finite Sets *}
 
 constdefs (structure G)