That assumption is fundamentally flawed.
Furthermore, it can be seen by your continued defence of your implication above that: Either you don't understand the relationship between the Eurozone and the EU, or you know that the assumption (or implication) is fundamentally flawed and you are obfuscating matters to cover up the logical error.
Ha! Ha! Ha! "PERFORCE" - swallowing a dictionary won't retrieve your own illogical and humiliating arguments. Blimey, and we are expected to believe that only JRM comes from the 19th Century
Intrigued because I thought it was a word in normal usage, if not the most frequently encountered, I looked up ‘perforce’:
First: my copy of Chambers 20th Century Dictionary, published near the end of the century, lists perforce, but does not indicate it to be archaic or obsolete.
Miriam Webster online, presumably pretty much up to date, says that the definition by physical coercion is obsolete, but by saying that it makes clear that the alternative definition by force of circumstances is not obsolete.
And it is listed in the online Oxford Living Dictionaries, without any suggestion that it is archaic or obsolete.
Even if not the most commonly used word, or not in all circles, it is clear that it is accepted as being in current English usage. Methinks the laugh is on you.