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/bin/live-system is in live-tools 1:20151214.

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The actual contents of the file can be viewed below.

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#!/bin/sh

# live-tools(7) - System Support Scripts
# Copyright (C) 2006-2015 Daniel Baumann <mail@daniel-baumann.ch>
#
# This program comes with ABSOLUTELY NO WARRANTY; for details see COPYING.
# This is free software, and you are welcome to redistribute it
# under certain conditions; see COPYING for details.

# Redirect stdout to stderr
exec 1>&2

case "${1}" in
	-h|--help|-u|--usage)
		echo "live-system - determine if running system is a live system"
		echo
		echo "Usage: ${0} [-v|--verbose]"

		exit 2
		;;

	-v|--verbose)
		_VERBOSE="true"
		;;
esac

[ "${_VERBOSE}" ] && echo -n "Checking for live system..."

if [ ! -e /proc/cmdline ]
then
	[ "${_VERBOSE}" ] && echo
	echo "E: /proc/cmdline - No such file."

	exit 2
fi

if grep -qs "boot=live" /proc/cmdline
then
	[ "${_VERBOSE}" ] && echo -n " yes, this is a live system"

	if [ -d /lib/live/mount/medium/install ]
	then
		if ls /lib/live/mount/medium/install/pool/main/l/live-installer/live-installer_*.udeb > /dev/null 2>&1
		then
			[ "${_VERBOSE}" ] && echo " with debian-installer (live) support."
		else
			[ "${_VERBOSE}" ] && echo " with debian-installer (normal) support."
		fi
	else
		[ "${_VERBOSE}" ] && echo "without debian-installer support."
	fi

	exit 0
else
	[ "${_VERBOSE}" ] && echo " no, this is not a live system."

	exit 1
fi