But that solution assumes that we know the old formatting of \theenumi.
The following solution is better as I doesn't assume that:

\let\oldtheenumi\theenumi
\newcounter{cntr}
\setcounter{cntr}{1}
\renewcommand{\theenumi}{\setcounter{enumi}{\value{cntr}}\oldtheenumi\addtocounter{cntr}{1}}

(sections and enumerations)

\let\theenumi\oldtheenumi

On Sun, 17 Aug 2003, Henrik Edlund wrote:

HE> For the record, how I solved it with two ERTs:
HE>
HE> \let\oldtheenumi\theenumi
HE> \newcounter{cntr}
HE> \setcounter{cntr}{1}
HE> \renewcommand{\theenumi}{\arabic{cntr}\addtocounter{cntr}{1}}
HE>
HE> (A couple of enumerations in different sections in LyX)
HE>
HE> \let\theenumi\oldtheenumi

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