converted back from 0..< to <.

--- a/doc-src/IsarOverview/Isar/Induction.thy	Mon May 23 12:09:30 2005 +0200
+++ b/doc-src/IsarOverview/Isar/Induction.thy	Mon May 23 13:39:45 2005 +0200
@@ -77,7 +77,7 @@
 subsection{*Structural induction*}
 
 text{* We start with an inductive proof where both cases are proved automatically: *}
-lemma "2 * (\<Sum>i::nat = 0..<n+1. i) = n*(n+1)"
+lemma "2 * (\<Sum>i::nat < n+1. i) = n*(n+1)"
 by (induct n, simp_all)
 
 text{*\noindent The constraint @{text"::nat"} is needed because all of
@@ -97,7 +97,7 @@
 text{* \noindent We could refine this further to show more of the equational
 proof. Instead we explore the same avenue as for case distinctions:
 introducing context via the \isakeyword{case} command: *}
-lemma "2 * (\<Sum>i::nat = 0..<n+1. i) = n*(n+1)"
+lemma "2 * (\<Sum>i::nat < n+1. i) = n*(n+1)"
 proof (induct n)
   case 0 show ?case by simp
 next

--- a/doc-src/IsarOverview/Isar/document/Induction.tex	Mon May 23 12:09:30 2005 +0200
+++ b/doc-src/IsarOverview/Isar/document/Induction.tex	Mon May 23 13:39:45 2005 +0200
@@ -115,7 +115,7 @@
 We start with an inductive proof where both cases are proved automatically:%
 \end{isamarkuptext}%
 \isamarkuptrue%
-\isacommand{lemma}\ {\isachardoublequote}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat\ {\isacharequal}\ {\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}n{\isacharplus}{\isadigit{1}}{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}\isanewline
+\isacommand{lemma}\ {\isachardoublequote}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat\ {\isacharless}\ n{\isacharplus}{\isadigit{1}}{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}\isanewline
 \isamarkupfalse%
 \isamarkupfalse%
 %
@@ -146,7 +146,7 @@
 introducing context via the \isakeyword{case} command:%
 \end{isamarkuptext}%
 \isamarkuptrue%
-\isacommand{lemma}\ {\isachardoublequote}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat\ {\isacharequal}\ {\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}n{\isacharplus}{\isadigit{1}}{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}\isanewline
+\isacommand{lemma}\ {\isachardoublequote}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat\ {\isacharless}\ n{\isacharplus}{\isadigit{1}}{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}\isanewline
 \isamarkupfalse%
 \isamarkupfalse%
 \isamarkupfalse%