Detect if coreutils is installed on mac

Without using brew, how can I detect if coreutils is installed on the mac where my bash script is running.

here is my script:

#!/usr/bin/env bash

check_bash_version () {
  echo "checking which bash version is installed...."
  sleep 3
  echo "Bash versioncheck completed"
  sleep 1
  if [[ "${BASH_VERSINFO[0]}" -lt 4 ]]; then
    echo "You need to be using Bash version =< 4. Please upgrade"
    exit 1
  fi
}

check_coreutils () {
  echo "checking if coreutils is installed...."
  sleep 3
  # what goes here
}

main() {
  # Main function.

  # check if MacOS
  if [[ "$(uname)" == "Darwin" ]]; then
    check_bash_version
    check_coreutils
  fi
}