I made two assertions and I believe both are true. You seem to be stretching what I said to some form of "and ASML has done nothing else on top", which I didn't say. Maybe I should reduce "their core tech" to EUV, but that's clearly what I meant if you look up the history of the company.
No, I just didn't find any evidence that ASML licences "their core tech" from US. Let it be EUV but I still can't find any sources on it. Do you have some?