Fortunately, those same legal principles in the US cannot be overridden by a treaty.
> This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any thing in the Constitution or Laws of any State to the Contrary notwithstanding.
And there is no explicit ordering of priority between them and the Constitution.
You don't have to get there axiomatically though; you can just look this up. Treaties are coequal with federal statutes, and are overridden by any conflicting statute passed after the treaty is ratified.