Русско-англо-русский юридический словарь

Sources of international law include treaties, international customs, general principles of law as recognized around the world, the decisions of national and lower courts, and scholarly writings. (Wikipedia)

A cross-appeal is a request filed by an appellee requesting that a higher court review a decision made by a lower court. The difference between an appeal and a cross-appeal is essentially arbitrary and dependent only on who filed the request for a higher court's review first. The first party to file is called the petitioner or appellant, and its request for review is an appeal. If an opposing party (called the respondent or appellee) also wishes to request review of a lower court's decision, that request is called a cross-appeal. (law.cornell.edu)

The appeal court will allow an appeal where the decision of the lower court was either:

• Wrong (in that it erred in law or in fact or in the exercise of its discretion).
• Unjust because of a serious procedural or other irregularity in the proceedings in the lower court.

lower court n. 1) any court of lesser rank, such as municipal or justice court below a superior or county court, a superior or county court below an appeals court, or a federal District Court of Appeals below the U. S. Supreme Court. 2) a reference in an appeal to the trial court which originally heard the case. Typical language in an appeals decision: "In the lower court, the judge ruled Defendant had no basis for...." (TheFreeDictionary)