Doesn't address my question. I would say that while Cornwall is not a constituent of the Treaty of Union, it is a constituent of one of the constituents of the Treaty of Union, and so as a subset of that constituent is indeed "a part of" (or similar designation) the UK. Just as both the city of New York and the State of New York are part of the United States, even though New York City is neither a founding member nor a state member at all.
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