
diff -r bda7527ccf05 -r cc2d676d5395 src/Doc/Tutorial/Misc/natsum.thy
--- a/src/Doc/Tutorial/Misc/natsum.thy	Wed Dec 26 16:07:28 2018 +0100
+++ b/src/Doc/Tutorial/Misc/natsum.thy	Wed Dec 26 16:25:20 2018 +0100
@@ -2,7 +2,7 @@
 theory natsum imports Main begin
 (*>*)
 text\<open>\noindent
-In particular, there are @{text"case"}-expressions, for example
+In particular, there are \<open>case\<close>-expressions, for example
 @{term[display]"case n of 0 => 0 | Suc m => m"}
 primitive recursion, for example
 \<close>
@@ -38,17 +38,17 @@
   \cdx{max}, \isadxboldpos{\isasymle}{$HOL2arithrel} and
   \isadxboldpos{<}{$HOL2arithrel} are overloaded: they are available
   not just for natural numbers but for other types as well.
-  For example, given the goal @{text"x + 0 = x"}, there is nothing to indicate
+  For example, given the goal \<open>x + 0 = x\<close>, there is nothing to indicate
   that you are talking about natural numbers. Hence Isabelle can only infer
-  that @{term x} is of some arbitrary type where @{text 0} and @{text"+"} are
+  that @{term x} is of some arbitrary type where \<open>0\<close> and \<open>+\<close> are
   declared. As a consequence, you will be unable to prove the
   goal. To alert you to such pitfalls, Isabelle flags numerals without a
   fixed type in its output: @{prop"x+0 = x"}. (In the absence of a numeral,
   it may take you some time to realize what has happened if \pgmenu{Show
   Types} is not set).  In this particular example, you need to include
-  an explicit type constraint, for example @{text"x+0 = (x::nat)"}. If there
+  an explicit type constraint, for example \<open>x+0 = (x::nat)\<close>. If there
   is enough contextual information this may not be necessary: @{prop"Suc x =
-  x"} automatically implies @{text"x::nat"} because @{term Suc} is not
+  x"} automatically implies \<open>x::nat\<close> because @{term Suc} is not
   overloaded.
 
   For details on overloading see \S\ref{sec:overloading}.
@@ -57,20 +57,20 @@
 \end{warn}
 \begin{warn}
   The symbols \isadxboldpos{>}{$HOL2arithrel} and
-  \isadxboldpos{\isasymge}{$HOL2arithrel} are merely syntax: @{text"x > y"}
-  stands for @{prop"y < x"} and similary for @{text"\<ge>"} and
-  @{text"\<le>"}.
+  \isadxboldpos{\isasymge}{$HOL2arithrel} are merely syntax: \<open>x > y\<close>
+  stands for @{prop"y < x"} and similary for \<open>\<ge>\<close> and
+  \<open>\<le>\<close>.
 \end{warn}
 \begin{warn}
-  Constant @{text"1::nat"} is defined to equal @{term"Suc 0"}. This definition
+  Constant \<open>1::nat\<close> is defined to equal @{term"Suc 0"}. This definition
   (see \S\ref{sec:ConstDefinitions}) is unfolded automatically by some
-  tactics (like @{text auto}, @{text simp} and @{text arith}) but not by
+  tactics (like \<open>auto\<close>, \<open>simp\<close> and \<open>arith\<close>) but not by
   others (especially the single step tactics in Chapter~\ref{chap:rules}).
   If you need the full set of numerals, see~\S\ref{sec:numerals}.
   \emph{Novices are advised to stick to @{term"0::nat"} and @{term Suc}.}
 \end{warn}
 
-Both @{text auto} and @{text simp}
+Both \<open>auto\<close> and \<open>simp\<close>
 (a method introduced below, \S\ref{sec:Simplification}) prove 
 simple arithmetic goals automatically:
 \<close>
@@ -81,7 +81,7 @@
 text\<open>\noindent
 For efficiency's sake, this built-in prover ignores quantified formulae,
 many logical connectives, and all arithmetic operations apart from addition.
-In consequence, @{text auto} and @{text simp} cannot prove this slightly more complex goal:
+In consequence, \<open>auto\<close> and \<open>simp\<close> cannot prove this slightly more complex goal:
 \<close>
 
 lemma "m \<noteq> (n::nat) \<Longrightarrow> m < n \<or> n < m"
@@ -89,10 +89,10 @@
 
 text\<open>\noindent The method \methdx{arith} is more general.  It attempts to
 prove the first subgoal provided it is a \textbf{linear arithmetic} formula.
-Such formulas may involve the usual logical connectives (@{text"\<not>"},
-@{text"\<and>"}, @{text"\<or>"}, @{text"\<longrightarrow>"}, @{text"="},
-@{text"\<forall>"}, @{text"\<exists>"}), the relations @{text"="},
-@{text"\<le>"} and @{text"<"}, and the operations @{text"+"}, @{text"-"},
+Such formulas may involve the usual logical connectives (\<open>\<not>\<close>,
+\<open>\<and>\<close>, \<open>\<or>\<close>, \<open>\<longrightarrow>\<close>, \<open>=\<close>,
+\<open>\<forall>\<close>, \<open>\<exists>\<close>), the relations \<open>=\<close>,
+\<open>\<le>\<close> and \<open><\<close>, and the operations \<open>+\<close>, \<open>-\<close>,
 @{term min} and @{term max}.  For example,\<close>
 
 lemma "min i (max j (k*k)) = max (min (k*k) i) (min i (j::nat))"
@@ -107,19 +107,19 @@
 (*<*)oops(*>*)
 
 text\<open>\noindent
-is not proved by @{text arith} because the proof relies 
+is not proved by \<open>arith\<close> because the proof relies 
 on properties of multiplication. Only multiplication by numerals (which is
 the same as iterated addition) is taken into account.
 
-\begin{warn} The running time of @{text arith} is exponential in the number
+\begin{warn} The running time of \<open>arith\<close> is exponential in the number
   of occurrences of \ttindexboldpos{-}{$HOL2arithfun}, \cdx{min} and
   \cdx{max} because they are first eliminated by case distinctions.
 
-If @{text k} is a numeral, \sdx{div}~@{text k}, \sdx{mod}~@{text k} and
-@{text k}~\sdx{dvd} are also supported, where the former two are eliminated
+If \<open>k\<close> is a numeral, \sdx{div}~\<open>k\<close>, \sdx{mod}~\<open>k\<close> and
+\<open>k\<close>~\sdx{dvd} are also supported, where the former two are eliminated
 by case distinctions, again blowing up the running time.
 
-If the formula involves quantifiers, @{text arith} may take
+If the formula involves quantifiers, \<open>arith\<close> may take
 super-exponential time and space.
 \end{warn}
 \<close>




