src/HOL/Library/Set_Algebras.thy
changeset 60500 903bb1495239
parent 58881 b9556a055632
child 60679 ade12ef2773c
     1.1 --- a/src/HOL/Library/Set_Algebras.thy	Wed Jun 17 10:57:11 2015 +0200
     1.2 +++ b/src/HOL/Library/Set_Algebras.thy	Wed Jun 17 11:03:05 2015 +0200
     1.3 @@ -2,17 +2,17 @@
     1.4      Author:     Jeremy Avigad and Kevin Donnelly; Florian Haftmann, TUM
     1.5  *)
     1.6  
     1.7 -section {* Algebraic operations on sets *}
     1.8 +section \<open>Algebraic operations on sets\<close>
     1.9  
    1.10  theory Set_Algebras
    1.11  imports Main
    1.12  begin
    1.13  
    1.14 -text {*
    1.15 +text \<open>
    1.16    This library lifts operations like addition and multiplication to
    1.17    sets.  It was designed to support asymptotic calculations. See the
    1.18    comments at the top of theory @{text BigO}.
    1.19 -*}
    1.20 +\<close>
    1.21  
    1.22  instantiation set :: (plus) plus
    1.23  begin
    1.24 @@ -364,7 +364,7 @@
    1.25      then show ?case by (auto intro!: f)
    1.26    next
    1.27      case (insert x F)
    1.28 -    from `finite F` `\<And>i. i \<in> insert x F \<Longrightarrow> P (S i)` have "P (setsum S F)"
    1.29 +    from \<open>finite F\<close> \<open>\<And>i. i \<in> insert x F \<Longrightarrow> P (S i)\<close> have "P (setsum S F)"
    1.30        by induct auto
    1.31      with insert show ?case
    1.32        by (simp, subst f) auto