diff -r 04cc6b4b3439 -r 50eab0183aea doc-src/TutorialI/Inductive/document/AB.tex --- a/doc-src/TutorialI/Inductive/document/AB.tex Thu Jun 16 11:38:52 2005 +0200 +++ b/doc-src/TutorialI/Inductive/document/AB.tex Thu Jun 16 18:25:54 2005 +0200 @@ -110,7 +110,8 @@ 1 on our way from 0 to 2. Formally, we appeal to the following discrete intermediate value theorem \isa{nat{\isadigit{0}}{\isacharunderscore}intermed{\isacharunderscore}int{\isacharunderscore}val} \begin{isabelle}% -\ \ \ \ \ {\isasymlbrakk}{\isasymforall}i{\isacharless}n{\isachardot}\ {\isasymbar}f\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharminus}\ f\ i{\isasymbar}\ {\isasymle}\ {\isadigit{1}}{\isacharsemicolon}\ f\ {\isadigit{0}}\ {\isasymle}\ k{\isacharsemicolon}\ k\ {\isasymle}\ f\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymexists}i{\isasymle}n{\isachardot}\ f\ i\ {\isacharequal}\ k% +\ \ \ \ \ {\isasymlbrakk}{\isasymforall}i{\isacharless}n{\isachardot}\ {\isasymbar}f\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharminus}\ f\ i{\isasymbar}\ {\isasymle}\ {\isadigit{1}}{\isacharsemicolon}\ f\ {\isadigit{0}}\ {\isasymle}\ k{\isacharsemicolon}\ k\ {\isasymle}\ f\ n{\isasymrbrakk}\isanewline +\isaindent{\ \ \ \ \ }{\isasymLongrightarrow}\ {\isasymexists}i{\isasymle}n{\isachardot}\ f\ i\ {\isacharequal}\ k% \end{isabelle} where \isa{f} is of type \isa{nat\ {\isasymRightarrow}\ int}, \isa{int} are the integers, \isa{{\isasymbar}{\isachardot}{\isasymbar}} is the absolute value function\footnote{See