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/usr/sbin/grub-set-default is in grub2-common 1.99-21ubuntu3.19.

This file is owned by root:root, with mode 0o755.

The actual contents of the file can be viewed below.

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#! /bin/sh
#
# Set a default boot entry for GRUB.
# Copyright (C) 2004,2009  Free Software Foundation, Inc.
#
# GRUB is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# GRUB is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with GRUB.  If not, see <http://www.gnu.org/licenses/>.

# Initialize some variables.
transform="s,x,x,"

prefix=/usr
exec_prefix=${prefix}
bindir=${exec_prefix}/bin
PACKAGE_NAME=GRUB
PACKAGE_VERSION=1.99-21ubuntu3.19

self=`basename $0`

grub_editenv=${bindir}/`echo grub-editenv | sed ${transform}`
rootdir=
bootdir=
grubdir=`echo "/boot/grub" | sed 's,//*,/,g'`

# Usage: usage
# Print the usage.
usage () {
    cat <<EOF
Usage: $self [OPTION] entry
Set the default boot entry for GRUB.

  -h, --help              print this message and exit
  -v, --version           print the version information and exit
  --boot-directory=DIR    expect GRUB images under the directory DIR/grub
                          instead of the $grubdir directory

ENTRY is a number or a menu item title.

Report bugs to <bug-grub@gnu.org>.
EOF
}

argument () {
  opt=$1
  shift

  if test $# -eq 0; then
      echo "$0: option requires an argument -- '$opt'" 1>&2
      exit 1
  fi
  echo $1
}

# Check the arguments.
while test $# -gt 0
do
    option=$1
    shift

    case "$option" in
    -h | --help)
	usage
	exit 0 ;;
    -v | --version)
	echo "$self (${PACKAGE_NAME}) ${PACKAGE_VERSION}"
	exit 0 ;;

# Accept for compatibility
    --root-directory)
	rootdir=`argument $option "$@"`; shift ;;
    --root-directory=*)
	rootdir=`echo "$option" | sed 's/--root-directory=//'` ;;

    --boot-directory)
    bootdir=`argument $option "$@"`; shift;;
    --boot-directory=*)
    bootdir=`echo "$option" | sed 's/--boot-directory=//'` ;;

    -*)
	echo "Unrecognized option \`$option'" 1>&2
	usage
	exit 1
	;;
    *)
	if test "x$entry" != x; then
	    echo "More than one entry?" 1>&2
	    usage
	    exit 1
	fi
	entry="${option}" ;;
    esac
done

if test "x$entry" = x; then
    echo "entry not specified." 1>&2
    usage
    exit 1
fi

if [ -z "$bootdir" ]; then
    # Default bootdir if bootdir not initialized.
    bootdir=/boot

    if [ -n "$rootdir" ] ; then
        # Initialize bootdir if rootdir was initialized.
        bootdir=${rootdir}/boot
    fi
fi

grubdir=`echo "${bootdir}/grub" | sed 's,//*,/,g'`

$grub_editenv ${grubdir}/grubenv unset prev_saved_entry
$grub_editenv ${grubdir}/grubenv set saved_entry="$entry"

# Bye.
exit 0