# HG changeset patch
# User nipkow
# Date 1181798875 -7200
# Node ID 15f7a6745cce51889ca9103eb22a00238eea5b58
# Parent  d0e3f790bd73e82219004cc4d8fa5f573164ab3e
fixed filter syntax

diff -r d0e3f790bd73 -r 15f7a6745cce doc-src/TutorialI/Inductive/AB.thy
--- a/doc-src/TutorialI/Inductive/AB.thy	Thu Jun 14 00:48:42 2007 +0200
+++ b/doc-src/TutorialI/Inductive/AB.thy	Thu Jun 14 07:27:55 2007 +0200
@@ -68,13 +68,13 @@
 *}
 
 lemma correctness:
-  "(w \<in> S \<longrightarrow> size[x\<in>w. x=a] = size[x\<in>w. x=b])     \<and>
-   (w \<in> A \<longrightarrow> size[x\<in>w. x=a] = size[x\<in>w. x=b] + 1) \<and>
-   (w \<in> B \<longrightarrow> size[x\<in>w. x=b] = size[x\<in>w. x=a] + 1)"
+  "(w \<in> S \<longrightarrow> size[x\<leftarrow>w. x=a] = size[x\<leftarrow>w. x=b])     \<and>
+   (w \<in> A \<longrightarrow> size[x\<leftarrow>w. x=a] = size[x\<leftarrow>w. x=b] + 1) \<and>
+   (w \<in> B \<longrightarrow> size[x\<leftarrow>w. x=b] = size[x\<leftarrow>w. x=a] + 1)"
 
 txt{*\noindent
 These propositions are expressed with the help of the predefined @{term
-filter} function on lists, which has the convenient syntax @{text"[x\<in>xs. P
+filter} function on lists, which has the convenient syntax @{text"[x\<leftarrow>xs. P
 x]"}, the list of all elements @{term x} in @{term xs} such that @{prop"P x"}
 holds. Remember that on lists @{text size} and @{text length} are synonymous.
 
@@ -116,8 +116,8 @@
 *}
 
 lemma step1: "\<forall>i < size w.
-  \<bar>(int(size[x\<in>take (i+1) w. P x])-int(size[x\<in>take (i+1) w. \<not>P x]))
-   - (int(size[x\<in>take i w. P x])-int(size[x\<in>take i w. \<not>P x]))\<bar> \<le> 1"
+  \<bar>(int(size[x\<leftarrow>take (i+1) w. P x])-int(size[x\<leftarrow>take (i+1) w. \<not>P x]))
+   - (int(size[x\<leftarrow>take i w. P x])-int(size[x\<leftarrow>take i w. \<not>P x]))\<bar> \<le> 1"
 
 txt{*\noindent
 The lemma is a bit hard to read because of the coercion function
@@ -141,8 +141,8 @@
 *}
 
 lemma part1:
- "size[x\<in>w. P x] = size[x\<in>w. \<not>P x]+2 \<Longrightarrow>
-  \<exists>i\<le>size w. size[x\<in>take i w. P x] = size[x\<in>take i w. \<not>P x]+1"
+ "size[x\<leftarrow>w. P x] = size[x\<leftarrow>w. \<not>P x]+2 \<Longrightarrow>
+  \<exists>i\<le>size w. size[x\<leftarrow>take i w. P x] = size[x\<leftarrow>take i w. \<not>P x]+1"
 
 txt{*\noindent
 This is proved by @{text force} with the help of the intermediate value theorem,
@@ -161,10 +161,10 @@
 
 
 lemma part2:
-  "\<lbrakk>size[x\<in>take i w @ drop i w. P x] =
-    size[x\<in>take i w @ drop i w. \<not>P x]+2;
-    size[x\<in>take i w. P x] = size[x\<in>take i w. \<not>P x]+1\<rbrakk>
-   \<Longrightarrow> size[x\<in>drop i w. P x] = size[x\<in>drop i w. \<not>P x]+1"
+  "\<lbrakk>size[x\<leftarrow>take i w @ drop i w. P x] =
+    size[x\<leftarrow>take i w @ drop i w. \<not>P x]+2;
+    size[x\<leftarrow>take i w. P x] = size[x\<leftarrow>take i w. \<not>P x]+1\<rbrakk>
+   \<Longrightarrow> size[x\<leftarrow>drop i w. P x] = size[x\<leftarrow>drop i w. \<not>P x]+1"
 by(simp del: append_take_drop_id)
 
 text{*\noindent
@@ -191,9 +191,9 @@
 *}
 
 theorem completeness:
-  "(size[x\<in>w. x=a] = size[x\<in>w. x=b]     \<longrightarrow> w \<in> S) \<and>
-   (size[x\<in>w. x=a] = size[x\<in>w. x=b] + 1 \<longrightarrow> w \<in> A) \<and>
-   (size[x\<in>w. x=b] = size[x\<in>w. x=a] + 1 \<longrightarrow> w \<in> B)"
+  "(size[x\<leftarrow>w. x=a] = size[x\<leftarrow>w. x=b]     \<longrightarrow> w \<in> S) \<and>
+   (size[x\<leftarrow>w. x=a] = size[x\<leftarrow>w. x=b] + 1 \<longrightarrow> w \<in> A) \<and>
+   (size[x\<leftarrow>w. x=b] = size[x\<leftarrow>w. x=a] + 1 \<longrightarrow> w \<in> B)"
 
 txt{*\noindent
 The proof is by induction on @{term w}. Structural induction would fail here
@@ -237,9 +237,9 @@
  apply(clarify)
 txt{*\noindent
 This yields an index @{prop"i \<le> length v"} such that
-@{prop[display]"length [x\<in>take i v . x = a] = length [x\<in>take i v . x = b] + 1"}
+@{prop[display]"length [x\<leftarrow>take i v . x = a] = length [x\<leftarrow>take i v . x = b] + 1"}
 With the help of @{thm[source]part2} it follows that
-@{prop[display]"length [x\<in>drop i v . x = a] = length [x\<in>drop i v . x = b] + 1"}
+@{prop[display]"length [x\<leftarrow>drop i v . x = a] = length [x\<leftarrow>drop i v . x = b] + 1"}
 *}
 
  apply(drule part2[of "\<lambda>x. x=a", simplified])
diff -r d0e3f790bd73 -r 15f7a6745cce doc-src/TutorialI/Inductive/document/AB.tex
--- a/doc-src/TutorialI/Inductive/document/AB.tex	Thu Jun 14 00:48:42 2007 +0200
+++ b/doc-src/TutorialI/Inductive/document/AB.tex	Thu Jun 14 07:27:55 2007 +0200
@@ -103,9 +103,9 @@
 \isamarkuptrue%
 \isacommand{lemma}\isamarkupfalse%
 \ correctness{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}w\ {\isasymin}\ S\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}{\isacharparenright}\ \ \ \ \ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}w\ {\isasymin}\ A\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}w\ {\isasymin}\ B\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}%
+\ \ {\isachardoublequoteopen}{\isacharparenleft}w\ {\isasymin}\ S\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}{\isacharparenright}\ \ \ \ \ {\isasymand}\isanewline
+\ \ \ {\isacharparenleft}w\ {\isasymin}\ A\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isasymand}\isanewline
+\ \ \ {\isacharparenleft}w\ {\isasymin}\ B\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}%
 \isadelimproof
 %
 \endisadelimproof
@@ -114,7 +114,7 @@
 %
 \begin{isamarkuptxt}%
 \noindent
-These propositions are expressed with the help of the predefined \isa{filter} function on lists, which has the convenient syntax \isa{{\isacharbrackleft}x{\isasymin}xs{\isachardot}\ P\ x{\isacharbrackright}}, the list of all elements \isa{x} in \isa{xs} such that \isa{P\ x}
+These propositions are expressed with the help of the predefined \isa{filter} function on lists, which has the convenient syntax \isa{{\isacharbrackleft}x{\isasymleftarrow}xs{\isachardot}\ P\ x{\isacharbrackright}}, the list of all elements \isa{x} in \isa{xs} such that \isa{P\ x}
 holds. Remember that on lists \isa{size} and \isa{length} are synonymous.
 
 The proof itself is by rule induction and afterwards automatic:%
@@ -166,8 +166,8 @@
 \isamarkuptrue%
 \isacommand{lemma}\isamarkupfalse%
 \ step{\isadigit{1}}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymforall}i\ {\isacharless}\ size\ w{\isachardot}\isanewline
-\ \ {\isasymbar}{\isacharparenleft}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymin}take\ {\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}\ w{\isachardot}\ P\ x{\isacharbrackright}{\isacharparenright}{\isacharminus}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymin}take\ {\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ {\isacharminus}\ {\isacharparenleft}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymin}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}{\isacharparenright}{\isacharminus}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymin}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharparenright}{\isacharparenright}{\isasymbar}\ {\isasymle}\ {\isadigit{1}}{\isachardoublequoteclose}%
+\ \ {\isasymbar}{\isacharparenleft}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ {\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}\ w{\isachardot}\ P\ x{\isacharbrackright}{\isacharparenright}{\isacharminus}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ {\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharparenright}{\isacharparenright}\isanewline
+\ \ \ {\isacharminus}\ {\isacharparenleft}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}{\isacharparenright}{\isacharminus}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharparenright}{\isacharparenright}{\isasymbar}\ {\isasymle}\ {\isadigit{1}}{\isachardoublequoteclose}%
 \isadelimproof
 %
 \endisadelimproof
@@ -207,8 +207,8 @@
 \isamarkuptrue%
 \isacommand{lemma}\isamarkupfalse%
 \ part{\isadigit{1}}{\isacharcolon}\isanewline
-\ {\isachardoublequoteopen}size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{2}}\ {\isasymLongrightarrow}\isanewline
-\ \ {\isasymexists}i{\isasymle}size\ w{\isachardot}\ size{\isacharbrackleft}x{\isasymin}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isachardoublequoteclose}%
+\ {\isachardoublequoteopen}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{2}}\ {\isasymLongrightarrow}\isanewline
+\ \ {\isasymexists}i{\isasymle}size\ w{\isachardot}\ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isachardoublequoteclose}%
 \isadelimproof
 %
 \endisadelimproof
@@ -242,10 +242,10 @@
 \isamarkuptrue%
 \isacommand{lemma}\isamarkupfalse%
 \ part{\isadigit{2}}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymlbrakk}size{\isacharbrackleft}x{\isasymin}take\ i\ w\ {\isacharat}\ drop\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\isanewline
-\ \ \ \ size{\isacharbrackleft}x{\isasymin}take\ i\ w\ {\isacharat}\ drop\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{2}}{\isacharsemicolon}\isanewline
-\ \ \ \ size{\isacharbrackleft}x{\isasymin}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isasymrbrakk}\isanewline
-\ \ \ {\isasymLongrightarrow}\ size{\isacharbrackleft}x{\isasymin}drop\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}drop\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ \ {\isachardoublequoteopen}{\isasymlbrakk}size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w\ {\isacharat}\ drop\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\isanewline
+\ \ \ \ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w\ {\isacharat}\ drop\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{2}}{\isacharsemicolon}\isanewline
+\ \ \ \ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isasymrbrakk}\isanewline
+\ \ \ {\isasymLongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}drop\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}drop\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isachardoublequoteclose}\isanewline
 %
 \isadelimproof
 %
@@ -290,9 +290,9 @@
 \isamarkuptrue%
 \isacommand{theorem}\isamarkupfalse%
 \ completeness{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ \ \ \ \ {\isasymlongrightarrow}\ w\ {\isasymin}\ S{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymlongrightarrow}\ w\ {\isasymin}\ A{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymin}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymlongrightarrow}\ w\ {\isasymin}\ B{\isacharparenright}{\isachardoublequoteclose}%
+\ \ {\isachardoublequoteopen}{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ \ \ \ \ {\isasymlongrightarrow}\ w\ {\isasymin}\ S{\isacharparenright}\ {\isasymand}\isanewline
+\ \ \ {\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymlongrightarrow}\ w\ {\isasymin}\ A{\isacharparenright}\ {\isasymand}\isanewline
+\ \ \ {\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymlongrightarrow}\ w\ {\isasymin}\ B{\isacharparenright}{\isachardoublequoteclose}%
 \isadelimproof
 %
 \endisadelimproof
@@ -329,7 +329,8 @@
 Simplification disposes of the base case and leaves only a conjunction
 of two step cases to be proved:
 if \isa{w\ {\isacharequal}\ a\ {\isacharhash}\ v} and \begin{isabelle}%
-\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymin}v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymin}v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{2}}%
+\ \ \ \ \ length\ {\isacharparenleft}if\ x\ {\isacharequal}\ a\ then\ {\isacharbrackleft}x\ {\isasymin}\ v{\isacharbrackright}\ else\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
+\isaindent{\ \ \ \ \ }length\ {\isacharparenleft}if\ x\ {\isacharequal}\ b\ then\ {\isacharbrackleft}x\ {\isasymin}\ v{\isacharbrackright}\ else\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharplus}\ {\isadigit{2}}%
 \end{isabelle} then
 \isa{b\ {\isacharhash}\ v\ {\isasymin}\ A}, and similarly for \isa{w\ {\isacharequal}\ b\ {\isacharhash}\ v}.
 We only consider the first case in detail.
@@ -350,11 +351,11 @@
 \noindent
 This yields an index \isa{i\ {\isasymle}\ length\ v} such that
 \begin{isabelle}%
-\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymin}take\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymin}take\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}%
+\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymleftarrow}take\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymleftarrow}take\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}%
 \end{isabelle}
 With the help of \isa{part{\isadigit{2}}} it follows that
 \begin{isabelle}%
-\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymin}drop\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymin}drop\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}%
+\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymleftarrow}drop\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymleftarrow}drop\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}%
 \end{isabelle}%
 \end{isamarkuptxt}%
 \isamarkuptrue%