doc-src/TutorialI/Recdef/document/Induction.tex
changeset 11023 6e6c8d1ec89e
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    47 are invented by Isabelle and have nothing to do with the names in the
    47 are invented by Isabelle and have nothing to do with the names in the
    48 definition of \isa{sep}.
    48 definition of \isa{sep}.
    49 
    49 
    50 In general, the format of invoking recursion induction is
    50 In general, the format of invoking recursion induction is
    51 \begin{quote}
    51 \begin{quote}
    52 \isacommand{apply}\isa{{\isacharparenleft}induct{\isacharunderscore}tac\ }$x@1 \dots x@n$ \isa{rule{\isacharcolon}} $f$\isa{{\isachardot}induct{\isacharparenright}}
    52 \isacommand{apply}\isa{{\isacharparenleft}induct{\isacharunderscore}tac}$x@1 \dots x@n$ \isa{rule{\isacharcolon}} $f$\isa{{\isachardot}induct{\isacharparenright}}
    53 \end{quote}\index{*induct_tac}%
    53 \end{quote}\index{*induct_tac}%
    54 where $x@1~\dots~x@n$ is a list of free variables in the subgoal and $f$ the
    54 where $x@1~\dots~x@n$ is a list of free variables in the subgoal and $f$ the
    55 name of a function that takes an $n$-tuple. Usually the subgoal will
    55 name of a function that takes an $n$-tuple. Usually the subgoal will
    56 contain the term $f(x@1,\dots,x@n)$ but this need not be the case. The
    56 contain the term $f(x@1,\dots,x@n)$ but this need not be the case. The
    57 induction rules do not mention $f$ at all. For example \isa{sep{\isachardot}induct}
    57 induction rules do not mention $f$ at all. For example \isa{sep{\isachardot}induct}