What is the ruling regarding the intention of participants sharing an animal sacrifice?

Primary text

If the ruling that one animal suffices for seven is established, it is immaterial whether the participants are from one household or not, whether they are performing a mandatory sacrifice or a voluntary one, or if some intend the proximity to God (Qurbah) while others intend only to eat the meat. This is because each person fulfills their share through the sacrifice, and the intention of others does not harm their portion.